Meshing 010
Content
Background on Meshing
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Background on Meshing Finite Element Analysis (FEA) provides a reliable numerical technique for analyzing engineering designs. The process starts with the creation of a geometric model. Then, the program subdivides the model into small pieces of simple shapes (elements) connected at common points (nodes). Finite element analysis programs look at the model as a network of discrete interconnected elements. The Finite Element Method (FEM) predicts the behavior of the model by combining the information obtained from all elements making up the model. Meshing is a very crucial step in design analysis. The automatic mesher in the software generates a mesh based on a global element size, tolerance, and local mesh control specifications. Mesh control lets you specify different sizes of elements for components, faces, edges, and vertices. The software estimates a global element size for the model taking into consideration its volume, surface area, and other geometric details. The size of the generated mesh (number of nodes and elements) depends on the geometry and dimensions of the model, element size, mesh tolerance, mesh control, and contact specifications. In the early stages of design analysis where approximate results may suffice, you can specify a larger element size for a faster solution. For a more accurate solution, a smaller element size may be required. Meshing generates 3D tetrahedral solid elements, 2D triangular shell elements, and 1D beam elements. A mesh consists of one type of elements unless the mixed mesh type is specified. Solid elements are naturally suitable for bulky models. Shell elements are naturally suitable for modeling thin parts (sheet metals), and beams and trusses are suitable for modeling structural members. This section discusses the following topics: z
Solid, Shell, and Beam Meshing
z
Meshing Parameters
z
Meshing Options
z
Controlling the Mesh
z
Contact Options for Structural and Thermal Studies
z
Mesh Quality Checks
z
Probing the Mesh Plot
z
Meshing Failure Diagnostics
z
Meshing Tips
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Solid Mesh
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Solid Mesh In meshing a part or an assembly with solid elements, the software generates one of the following types of elements based on the active mesh options for the study: z
Draft quality mesh. The automatic mesher generates linear tetrahedral solid elements.
z
High quality mesh. The automatic mesher generates parabolic tetrahedral solid elements.
Linear elements are also called first-order, or lower-order elements. Parabolic elements are also called second-order, or higher-order elements. A linear tetrahedral element is defined by four corner nodes connected by six straight edges. A parabolic tetrahedral element is defined by four corner nodes, six mid-side nodes, and six edges. The following figures show schematic drawings of linear and parabolic tetrahedral solid elements.
Linear solid element
Parabolic solid element
In general, for the same mesh density (number of elements), parabolic elements yield better results than linear elements because: 1) they represent curved boundaries more accurately, and 2) they produce better mathematical approximations. However, parabolic elements require greater computational resources than linear elements. For structural problems, each node in a solid element has three degrees of freedom that represent the translations in three orthogonal directions. The software uses the X, Y, and Z directions of the global Cartesian coordinate system in formulating the problem. For thermal problems, each node has one degree of freedom which is the temperature.
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Shell Mesh
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Shell Mesh When using shell elements, the software generates one of the following types of elements depending on the active meshing options for the study.: z
Draft quality mesh. The automatic mesher generates linear triangular shell elements.
z
High quality mesh. The automatic mesher generates parabolic triangular shell elements.
A linear triangular shell element is defined by three corner nodes connected by three straight edges. A parabolic triangular element is defined by three corner nodes, three mid-side nodes, and three parabolic edges. For studies using sheet metals, the thickness of the shells is automatically extracted from the geometry of the model. To set the desired option for a study, right-click the Mesh icon, select Create Mesh, and expand Advanced. Shell elements are 2D elements capable of resisting membrane and bending loads.
Linear triangular element
Parabolic triangular element
For structural studies, each node in shell elements has six degrees of freedom; three translations and three rotations. The translational degrees of freedom are motions in the global X, Y, and Z directions. The rotational degrees of freedom are rotations about the global X, Y, and Z axes. For thermal problems, each node has one degree of freedom which is the temperature.
Sheet metal model
Shell mesh created at mid-surface
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Shell Mesh
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NOTE: For drop test studies only, sheet metal parts mesh with solid elements. The software generates a shell mesh automatically for the following geometries: z
Sheet metals with uniform thicknesses. Sheet metals mesh with shell elements, except for drop test studies. The software assigns the thickness of shell based on sheet metal thickness. You can edit the default shell definition before running the study, except thickness.
z
Surface bodies. Surface bodies mesh with shell elements. The software assigns a thin shell formulation to each surface body. You can edit the default shell definition before running the study.
NOTES: z
The program automatically creates a mixed mesh when solid and surface or sheet metal geometries are included in the same model.
z
A reasonably fine draft quality mesh gives results that are generally similar to results obtained from a high quality mesh with the same number of elements. The difference between the two results increases if the model includes curved geometry.
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Beams
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Beams Beam elements can resist bending, shear, and torsional loads. The typical frame shown below is modeled with beams elements to transfer the load to the supports. Modeling such frames with truss elements fails since there is no mechanism to transfer the applied horizontal load to the supports.
Beam elements require defining the exact cross section so that the program can calculate the moments of inertia, neutral axes and the distances from the extreme fibers to the neutral axes. The stresses vary on the cross-section and along the beam. Consider a small segment along a beam element subjected to simplified 2D forces ( axial force P, shearing force V, and bending moment M):
In a general case 3 forces and 3 moments act on the segment. Uniform axial stress = P/A (similar to truss elements) Uniform shearing stress = V/A The bending moment M causes a bending stress that varies linearly with the vertical distance y from the neutral axis. Bending stress (y) = My/I where I is the moment of inertia about the neutral axis. The bending stress is the largest at the extreme fibers. In this example, the largest compression occurs at the top fiber
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Beams
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and the largest tension occurs at the extreme bottom fibers.
Joints A joint is identified at free ends of structural members and at the intersection of two or more structural members. The Edit Joint PropertyManager provides a tool to help you define joints properly. The program creates a node at the center of the cross section of each joint member. Due to trimming and the use of different cross sections for different members, the nodes of members associated with a joint may not coincide. The program creates special elements near the joint to simulate a rigid connection based on geometric and material properties.
Material Properties The modulus of elasticity and Poisson's Ratio are always required. Density is required only if gravitational loads are considered.
Restraints You can apply restraints to joints only. There are 6 degrees of freedom at each joint. You can apply zero or non-zero prescribed translations and rotations.
Bonding In a study with beams, solids and shell surfaces, you can bond beams and beam joints to solid and shell faces. Bonding between touching structural members with a surface or sheet metal face is automatically created.
Loads You can apply: z
Concentrated forces and moments at joints and reference points.
z
Distributed loads along the whole length of a beam.
z
Gravitational loads. The program calculates gravitational forces based on the specified accelerations and densities.
Meshing Beam and truss members are displayed as solid cylinders regardless of their actual cross-section shape. A structural member is automatically identified as a beam and meshed by a number of uniform elements so you can view the variation of deformation and stresses along the length of the member.
Results Results for each element are presented in its local directions. There is no averaging of stresses for truss and beam elements. You can view uniform axial stresses, torsional, bending stresses in two orthogonal directions (dir 1 and dir 2), and the worst stresses on extreme fibers generated by combining axial and bending stresses. A beam section is subjected to an axial force P and two moments M1 and M2 as shown below:
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Beams
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The software provides the following options for viewing stresses: z
Axial: Uniform axial stress = P/A
z
Bending in local direction 1: Bending stresses due to M2. This is referred to as Bending Ms/Ss in the plot name, title, and legend.
z
Bending in local direction 2: Bending stress due to M1. This is referred to as Bending Mt/St in the plot name, title, and legend.
Click here to learn about beam directions. z
Worst case: The software automatically calculates the highest stresses at a critical point on the crosssection by combining axial and bending stresses due to M1 and M2. This is the recommended stress to view.
In general, the software calculates 4 stress values at the extreme fibers of each end. When viewing worst case stresses, the software shows one value for each beam segment. This value is the largest in magnitude out of the 8 values calculated for the beam segment. These values are accurate for beam with cross-sections that are symmetric in two directions. These values are conservative for other cases.
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Mesh - Default Options (New Study)
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Default Options - Mesh You set meshing options for studies using solid, shell, and mixed mesh. Beam studies do not use this PropertyManager. The mesh that the software generates depends on the following factors: z
Active meshing options for the study (specified in the Mesh PropertyManager)
z
Mesh control specifications
z
Contact conditions defined in the Connections folder
NOTES z
When you create a new study (Study PropertyManager), it inherits the default meshing options set in the Mesh page of the Default Options tab. You can modify the meshing options for each study in the Mesh PropertyManager. If you create a duplicate of a study, the new study inherits the meshing options of the source study.
z
Meshing options are essential factors in determining the quality of the results. Results based on different option settings should converge to each other, if an adequately small element size is used.
To modify the mesh options for a study, right-click the Mesh icon in the Simulation study tree, select Create Mesh, and expand Mesh Parameters and Advanced.
Mesh Quality Sets the mesh quality: z
Draft. Each solid element will have 4 corner nodes only. Each shell element will have 3 corner nodes.
z
High. Each solid element will have 10 nodes: 4 corner nodes and one node at the middle of each edge (a total of six mid-side nodes). Each shell element will have 6 nodes: 3 corner nodes and 3 mid-side nodes.
It is highly recommended to use the High quality option for final results and for models with curved geometry. Draft quality meshing can be used for quick evaluation.
z
Jacobian points. Sets the number of integration points to be used in checking the distortion level of tetrahedral elements. You can select 4, 16, 29 points or At Nodes. See the Mesh Quality Checks section for more details.
The software performs Jacobian check by default for high quality mesh. It is recommended to use the At Nodes option when using the p-method to solve static problems.
Mesher type Sets the preferred meshing technique to be used. z
Standard mesh. Activates the Voronoi-Delaunay meshing scheme for subsequent meshing operations. This mesher is faster than the curvature- based mesher and should be used in most cases.
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Mesh - Default Options (New Study)
z
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Curvature based mesh. Activates the Curvature-based meshing scheme for subsequent meshing operations. The mesher creates more elements in higher-curvature areas automatically (without need for mesh control). For assemblies, the mesher requires setting the global bond option to incompatible. If component contact features are created, they should also specify incompatible bonding.
Curvature-based mesh is always compatible for touching or partially touching edges of sheet metal bodies and surface bodies.
{
Min number of elements in a circle. Sets the minimum number of elements the mesher creates at curvatures.
See how the element size is determined z
Show advanced options for contact set definitions (No penetration and shrink fit only). When selected, the contact options are displayed in the Contact Set PropertyManager under Advanced. If this option is not selected, the software applies by default a node to surface contact type to all contact set definitions.
Mesher Options (for Standard Mesher) Sets mesh options for the standard mesher. z
Automatic transition. When checked, the program automatically applies mesh controls to small features, holes, fillets, and other fine details of your model. Uncheck Automatic transition before meshing large models with many small features and details to avoid generating a very large number of elements unnecessarily. Example1 | Example2
z
Automatic trials for solid. Instructs the program to automatically retry to mesh the model using a different global element size. You control the maximum number of trials allowed and the factors by which the global element and tolerance are scaled for each trial. {
Number of trials. Sets the maximum number of mesh trials.
{
Global element size factor for each trial. Factor by which the new global element size is multiplied to calculate the new global element size.
{
Tolerance factor for each loop. Factor by which the new tolerance is multiplied to calculate the new tolerance.
z
Remesh failed parts with incompatible mesh. If selected, the software tries to use incompatible meshing for bonded bodies that fail compatible meshing. Used for solid mesh only.
z
Automatic shell surface re-alignment for non-composite shells. When selected, the software automatically realigns the shell surfaces (non-composites) so that all bottom/top faces have uniform orientation. If this option is not selected, you may need to flip the misaligned shell surfaces manually. Select the desired faces, right-click the Mesh icon in the Simulation study tree and select Flip Shell Elements.
Mesher Options (for Curvature Based Mesher) Sets mesh options for the alternate mesher. z
Min number of elements in a circle. Sets the minimum number of elements on a full circle. The maximum angle for any element is 360 divided by the specified number. The limits are 4 and 36.
To set default meshing options for new studies:
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Mesh - Default Options (New Study)
1.
Click Simulation, Options, Default Options, Mesh.
2.
Specify the desired settings.
3.
Click OK.
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To modify meshing options for a study: 1.
In the Simulation study tree, right-click the Mesh icons and select Create Mesh.
2.
Specify the desired settings under Mesh Parameters and Advanced
3.
Under Options select Save setting without meshing, or Run (solve) the analysis.
4.
Click
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Mesh Control Parameters
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Mesh Control Parameters Mesh control refers to specifying different element sizes at different regions in the model. A smaller element size in a region improves the accuracy of results in that region. You can specify mesh control at vertices, points, edges, faces, and components. Mesh control is not available for beams. To access the Mesh Control PropertyManager, right-click the Mesh icon and select Apply Mesh Control.
Mesh Control Parameters The mesh control parameters are: z
Element size (e) for the specified entities
z
Element growth ratio (r)
Assuming that the element size used for meshing an entity is (e), the average element size in layers radiating from the 2 3 n entity will be: e, e*r, e*r , e*r , ...., e*r . If the calculated average element size of a layer exceeds (E), where (E) is the Global Size , the program uses (E) instead. The mesh radiates from vertices to edges, from edges to faces, from faces to components, and from a component to connected components. To apply mesh control to mixed types of entities: 1.
In the Simulation study tree, right-click the Mesh icon and select Apply Mesh Control.
The Mesh Control PropertyManager appears. 2.
In the graphics area, select the entities for which you want to apply mesh controls.
3.
Under Control Parameters, do the following:
4.
a.
Select a unit and type a value in the Element Size box
b.
Type a value in the Ratio box
Click
.
.
.
To apply mesh control to multiple components: 1.
In the Simulation study tree, right-click the Mesh icon and select Apply Mesh Control.
The Mesh Control PropertyManager appears.
2.
Click the FeatureManager design tree tab 3.
.
In the FeatureManager flyout, select the components to which you want to apply mesh control.
The selected components appear in the Selected Entities list box. 4.
Under Selected Entities, select Use per part size.
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Mesh Control Parameters
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The software assigns an optimum element size for mesh control to individual components based on their volume. Move the Mesh Density slider towards Coarse to increase the element size by a factor of 2, or towards Fine to decrease the element size by a factor of 0.5.
5.
Click
.
Related Topics Component Mesh Control Examples of Mesh Control
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Meshing Options
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Meshing Options Meshing Options are essential factors in determining the quality of the mesh and hence the results. Results based on different preference settings should converge to each other if an adequately small element size is used. Meshing options are not used for beams. You can set the Mesh quality to Draft or High. A draft quality mesh does not have mid-side nodes. Draft quality can be used for quick evaluation and in solid models where bending effects are small. High quality mesh is recommended in most cases, especially for models with curved geometry. The Standard mesher uses the Voronoi-Delaunay meshing scheme for subsequent meshing operations. This mesher is faster than the Curvature based mesher and should be used in most cases. Try the Curvature based mesher only when the standard mesher keeps failing. The Curvature based mesher supports mesh control on components, faces and edges. The Jacobian points when Mesh quality is set to High sets the number of points to be used in checking the distortion level of high order tetrahedral elements.
For high order shells, the Jacobian check uses 6 points located at the nodes. Automatic transition automatically applies mesh controls to small features, details, holes, and fillets. Uncheck Automatic transition before meshing large models with many small features and details to avoid generating a very large number of elements unnecessarily. Automatic trials for solids instructs the mesher to automatically retry to mesh the model using a smaller global element size. You control the maximum number of trials allowed and the ratio by which the global element size and tolerance are reduced each time. Remesh failed parts with incompatible mesh. Using this option can help mesh bonded solids that fail compatible meshing. If Automatic looping is on and bonding solids using compatible mesh is requested, the software tries incompatible meshing automatically for solids that fail to mesh with the compatible option. Setting the color for plotting the bottom faces of shell elements helps you align shell elements properly. Setting the meshing Options
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Mesh Quality Checks
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Mesh Quality Checks The quality of mesh plays a key role in the accuracy of the results. The software uses two important checks to measure the quality of elements in a mesh. z
Aspect Ratio Check. For a solid mesh, numerical accuracy is best achieved by a mesh with uniform perfect tetrahedral elements whose edges are equal in length. For a general geometry, it is not possible to create a mesh of perfect tetrahedral elements. Due to small edges, curved geometry, thin features, and sharp corners, some of the generated elements can have some of their edges much longer than others. When the edges of an element become much different in length, the accuracy of the results deteriorates.
The aspect ratio of a perfect tetrahedral element is used as the basis for calculating aspect ratios of other elements. The aspect ratio of an element is defined as the ratio between the longest edge and the shortest normal dropped from a vertex to the opposite face normalized with respect to a perfect tetrahedral. By definition, the aspect ratio of a perfect tetrahedral element is 1.0. The aspect ratio check assumes straight edges connecting the four corner nodes. The aspect ratio check is automatically used by the program to check the quality of the mesh.
z
Jacobian Points. Parabolic elements can map curved geometry much more accurately than linear elements of the same size. The mid-side nodes of the boundary edges of an element are placed on the actual geometry of the model. In extremely sharp or curved boundaries, placing the mid-side nodes on the actual geometry can result in generating distorted elements with edges crossing over each other. The Jacobian of an extremely distorted element becomes negative. An element with a negative Jacobian causes the analysis program to stop.
The Jacobian check is based on a number of points located within each element. The software gives you a choice to base the Jacobian check on 4, 16, 29 Gaussian points or At Nodes.
It is recommended to set Jacobian check to At Nodes when using the p-method to solve static problems. The Jacobian ratio of a parabolic tetrahedral element, with all mid-side nodes located exactly at the middle of the straight edges, is 1.0. The Jacobian ratio increases as the curvatures of the edges increase. The Jacobian ratio at a point inside the element provides a measure of the degree of distortion of the element at that location. The software calculates the Jacobian ratio at the selected number of Gaussian points for each tetrahedral element. Based on stochastic studies it is generally seen that a Jacobian Ratio of forty or less is acceptable. The software adjusts the locations of the mid-side nodes of distorted elements automatically to make sure that all elements pass the Jacobian check.
For high order shells, the Jacobian check uses 6 points located at the nodes.
To set the Jacobian check options for a study: 1.
In the Simulation study tree, right-click the Mesh icon and select Create.
2.
Expand Advanced.
3.
Specify the number of points for Jacobian points.
4.
Under Options, select Save settings without meshing to save the options without meshing or click to save the options and mesh the model.
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Meshing Tips
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Meshing Tips z
When you mesh a study, the software meshes all unsuppressed solids, shells, and beams: {
Use Solid mesh for bulky objects.
{
Use Shell elements for thin objects like sheet metals.
{
Use Beam or Truss elements for extruded or revolved objects with constant cross-sections.
{
For assemblies, check component interference. To detect interference in an assembly, click Tools, Interference Detection. Interference is allowed only when using shrink fit. The Treat coincidence as interference and Include multibody part interferences options allow you to detect touching areas. Theses are the only areas affected by the global and component contact settings.
You can also find touching faces by right-clicking the Connections folder and selecting Find contact sets.
z
Compatible meshing is more accurate than incompatible meshing in the interface region. Requesting compatible meshing can cause mesh failure in some cases. Requesting incompatible meshing can result in successful results. You can request compatible meshing and select Remesh failed parts with incompatible mesh so that the software uses incompatible meshing only for bodies that fail to mesh.
z
If meshing fails, use the Failure Diagnostics tool to locate the cause of mesh failure. Try the proposed options to solve the problem. You can also try different element size, define mesh control, or activate Enable automatic looping for solids.
z
The SolidWorks Simplify utility lets you suppress features that meet a specified simplification factor. In the Simulation study tree, right-click Mesh and select Simplify Model for Meshing Simplify utility.
. This displays the
Simplification of geometry can alter stress results significantly.
z
It is good practice to check mesh options before meshing. For example, the Automatic transition can result in generating an unnecessarily large number of elements for models with many small features. The high quality and Standard mesher are recommended for most cases. The Automatic looping can help solve meshing problems automatically, but you can adjust its settings for a particular model. The Alternate mesher automatically uses smaller element sizes in regions with high curvature.
z
To improve results in important areas, use mesh control to set a smaller element size. When meshing an assembly with a wide range of component sizes, default meshing results in a relatively coarse mesh for small components. Component mesh control offers an easy way to give more importance to the selected small components. Use this option to identify important small components.
For static studies, you can use the h-adaptive method to refine the mesh automatically.
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Meshing Tips
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Meshing Tips z
When you mesh a study, the software meshes all unsuppressed solids, shells, and beams: {
Use Solid mesh for bulky objects.
{
Use Shell elements for thin objects like sheet metals.
{
Use Beam or Truss elements for extruded or revolved objects with constant cross-sections.
{
For assemblies, check component interference. To detect interference in an assembly, click Tools, Interference Detection. Interference is allowed only when using shrink fit. The Treat coincidence as interference and Include multibody part interferences options allow you to detect touching areas. Theses are the only areas affected by the global and component contact settings.
You can also find touching faces by right-clicking the Connections folder and selecting Find contact sets.
z
Compatible meshing is more accurate than incompatible meshing in the interface region. Requesting compatible meshing can cause mesh failure in some cases. Requesting incompatible meshing can result in successful results. You can request compatible meshing and select Remesh failed parts with incompatible mesh so that the software uses incompatible meshing only for bodies that fail to mesh.
z
If meshing fails, use the Failure Diagnostics tool to locate the cause of mesh failure. Try the proposed options to solve the problem. You can also try different element size, define mesh control, or activate Enable automatic looping for solids.
z
The SolidWorks Simplify utility lets you suppress features that meet a specified simplification factor. In the Simulation study tree, right-click Mesh and select Simplify Model for Meshing Simplify utility.
. This displays the
Simplification of geometry can alter stress results significantly.
z
It is good practice to check mesh options before meshing. For example, the Automatic transition can result in generating an unnecessarily large number of elements for models with many small features. The high quality and Standard mesher are recommended for most cases. The Automatic looping can help solve meshing problems automatically, but you can adjust its settings for a particular model. The Alternate mesher automatically uses smaller element sizes in regions with high curvature.
z
To improve results in important areas, use mesh control to set a smaller element size. When meshing an assembly with a wide range of component sizes, default meshing results in a relatively coarse mesh for small components. Component mesh control offers an easy way to give more importance to the selected small components. Use this option to identify important small components.
For static studies, you can use the h-adaptive method to refine the mesh automatically.
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Probing Results
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Probing Results In many cases, you may want to know the numerical value of the plotted field at a particular location. Use the probe tool to display the numerical value of the plotted field at the closest node or element's center to the point of clicking. You can graph the results or save them to a file. To probe a result plot at selected locations: 1.
Activate the desired plot.
2.
Click Probe
(Simulation Result Tools toolbar) or Simulation, Result Tools, Probe or right-click the
plot in the Simulation study tree and select Probe
.
3.
In the PropertyManager, under Options, select At Location.
4.
Select locations on the model and view the results in the graphics area and under Results in the PropertyManager.
5.
Click
.
To probe a result plot at sensor locations: 1.
Activate the desired plot.
2.
Click Probe
(Simulation Result Tools toolbar) or Simulation, Result Tools, Probe or right-click the
plot in the Simulation study tree and select Probe
.
3.
In the PropertyManager, under Options, select From Sensors. You must first define sensors before this option becomes active.
4.
Under Results, select a sensor name from Sensor List.
5.
View the results in the graphics area and under Results in the PropertyManager.
6.
Click
.
When probing results from sensor locations defined at coordinates, the location of the nearest node is used instead of the exact location of the sensor.
To probe a result plot on selected entities: 1.
Activate the desired plot.
2.
Click Probe
(Simulation Result Tools toolbar) or Simulation, Result Tools, Probe or right-click the
plot in the Simulation study tree and select Probe
.
3.
In the PropertyManager, under Options, select On selected sntities.
4.
Under Results, select entities for Faces, Edges, Vertices
and click Update.
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Probing Results
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5.
View the results in the graphics area and under Results in the PropertyManager.
6.
Click
.
Related Topics Probing Mesh Plots Probing Section Plots Graphing Probed Results
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Probing Section Plots
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Probing Section Plots You can probe section plots on the faces cut by a section plane. The software uses linear interpolation to calculate the value. To probe a section plot: 1.
Create a section plot of the desired result on the undeformed shape of the model.
2.
Click Probe
3.
In the PropertyManager, select a probing method under Options.
4.
Select locations on the faces cut by the section plane and view the results in the graphics area and under Results in the PropertyManager.
5.
Click
(Simulation Result Tools toolbar) or Simulation, Result Tools, Probe.
.
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Background on Meshing Finite Element Analysis (FEA) provides a reliable numerical technique for analyzing engineering designs. The process starts with the creation of a geometric model. Then, the program subdivides the model into small pieces of simple shapes (elements) connected at common points (nodes). Finite element analysis programs look at the model as a network of discrete interconnected elements. The Finite Element Method (FEM) predicts the behavior of the model by combining the information obtained from all elements making up the model. Meshing is a very crucial step in design analysis. The automatic mesher in the software generates a mesh based on a global element size, tolerance, and local mesh control specifications. Mesh control lets you specify different sizes of elements for components, faces, edges, and vertices. The software estimates a global element size for the model taking into consideration its volume, surface area, and other geometric details. The size of the generated mesh (number of nodes and elements) depends on the geometry and dimensions of the model, element size, mesh tolerance, mesh control, and contact specifications. In the early stages of design analysis where approximate results may suffice, you can specify a larger element size for a faster solution. For a more accurate solution, a smaller element size may be required. Meshing generates 3D tetrahedral solid elements, 2D triangular shell elements, and 1D beam elements. A mesh consists of one type of elements unless the mixed mesh type is specified. Solid elements are naturally suitable for bulky models. Shell elements are naturally suitable for modeling thin parts (sheet metals), and beams and trusses are suitable for modeling structural members. This section discusses the following topics: z
Solid, Shell, and Beam Meshing
z
Meshing Parameters
z
Meshing Options
z
Controlling the Mesh
z
Contact Options for Structural and Thermal Studies
z
Mesh Quality Checks
z
Probing the Mesh Plot
z
Meshing Failure Diagnostics
z
Meshing Tips
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Solid Mesh
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Solid Mesh In meshing a part or an assembly with solid elements, the software generates one of the following types of elements based on the active mesh options for the study: z
Draft quality mesh. The automatic mesher generates linear tetrahedral solid elements.
z
High quality mesh. The automatic mesher generates parabolic tetrahedral solid elements.
Linear elements are also called first-order, or lower-order elements. Parabolic elements are also called second-order, or higher-order elements. A linear tetrahedral element is defined by four corner nodes connected by six straight edges. A parabolic tetrahedral element is defined by four corner nodes, six mid-side nodes, and six edges. The following figures show schematic drawings of linear and parabolic tetrahedral solid elements.
Linear solid element
Parabolic solid element
In general, for the same mesh density (number of elements), parabolic elements yield better results than linear elements because: 1) they represent curved boundaries more accurately, and 2) they produce better mathematical approximations. However, parabolic elements require greater computational resources than linear elements. For structural problems, each node in a solid element has three degrees of freedom that represent the translations in three orthogonal directions. The software uses the X, Y, and Z directions of the global Cartesian coordinate system in formulating the problem. For thermal problems, each node has one degree of freedom which is the temperature.
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Shell Mesh
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Shell Mesh When using shell elements, the software generates one of the following types of elements depending on the active meshing options for the study.: z
Draft quality mesh. The automatic mesher generates linear triangular shell elements.
z
High quality mesh. The automatic mesher generates parabolic triangular shell elements.
A linear triangular shell element is defined by three corner nodes connected by three straight edges. A parabolic triangular element is defined by three corner nodes, three mid-side nodes, and three parabolic edges. For studies using sheet metals, the thickness of the shells is automatically extracted from the geometry of the model. To set the desired option for a study, right-click the Mesh icon, select Create Mesh, and expand Advanced. Shell elements are 2D elements capable of resisting membrane and bending loads.
Linear triangular element
Parabolic triangular element
For structural studies, each node in shell elements has six degrees of freedom; three translations and three rotations. The translational degrees of freedom are motions in the global X, Y, and Z directions. The rotational degrees of freedom are rotations about the global X, Y, and Z axes. For thermal problems, each node has one degree of freedom which is the temperature.
Sheet metal model
Shell mesh created at mid-surface
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Shell Mesh
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NOTE: For drop test studies only, sheet metal parts mesh with solid elements. The software generates a shell mesh automatically for the following geometries: z
Sheet metals with uniform thicknesses. Sheet metals mesh with shell elements, except for drop test studies. The software assigns the thickness of shell based on sheet metal thickness. You can edit the default shell definition before running the study, except thickness.
z
Surface bodies. Surface bodies mesh with shell elements. The software assigns a thin shell formulation to each surface body. You can edit the default shell definition before running the study.
NOTES: z
The program automatically creates a mixed mesh when solid and surface or sheet metal geometries are included in the same model.
z
A reasonably fine draft quality mesh gives results that are generally similar to results obtained from a high quality mesh with the same number of elements. The difference between the two results increases if the model includes curved geometry.
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Beams
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Beams Beam elements can resist bending, shear, and torsional loads. The typical frame shown below is modeled with beams elements to transfer the load to the supports. Modeling such frames with truss elements fails since there is no mechanism to transfer the applied horizontal load to the supports.
Beam elements require defining the exact cross section so that the program can calculate the moments of inertia, neutral axes and the distances from the extreme fibers to the neutral axes. The stresses vary on the cross-section and along the beam. Consider a small segment along a beam element subjected to simplified 2D forces ( axial force P, shearing force V, and bending moment M):
In a general case 3 forces and 3 moments act on the segment. Uniform axial stress = P/A (similar to truss elements) Uniform shearing stress = V/A The bending moment M causes a bending stress that varies linearly with the vertical distance y from the neutral axis. Bending stress (y) = My/I where I is the moment of inertia about the neutral axis. The bending stress is the largest at the extreme fibers. In this example, the largest compression occurs at the top fiber
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Beams
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and the largest tension occurs at the extreme bottom fibers.
Joints A joint is identified at free ends of structural members and at the intersection of two or more structural members. The Edit Joint PropertyManager provides a tool to help you define joints properly. The program creates a node at the center of the cross section of each joint member. Due to trimming and the use of different cross sections for different members, the nodes of members associated with a joint may not coincide. The program creates special elements near the joint to simulate a rigid connection based on geometric and material properties.
Material Properties The modulus of elasticity and Poisson's Ratio are always required. Density is required only if gravitational loads are considered.
Restraints You can apply restraints to joints only. There are 6 degrees of freedom at each joint. You can apply zero or non-zero prescribed translations and rotations.
Bonding In a study with beams, solids and shell surfaces, you can bond beams and beam joints to solid and shell faces. Bonding between touching structural members with a surface or sheet metal face is automatically created.
Loads You can apply: z
Concentrated forces and moments at joints and reference points.
z
Distributed loads along the whole length of a beam.
z
Gravitational loads. The program calculates gravitational forces based on the specified accelerations and densities.
Meshing Beam and truss members are displayed as solid cylinders regardless of their actual cross-section shape. A structural member is automatically identified as a beam and meshed by a number of uniform elements so you can view the variation of deformation and stresses along the length of the member.
Results Results for each element are presented in its local directions. There is no averaging of stresses for truss and beam elements. You can view uniform axial stresses, torsional, bending stresses in two orthogonal directions (dir 1 and dir 2), and the worst stresses on extreme fibers generated by combining axial and bending stresses. A beam section is subjected to an axial force P and two moments M1 and M2 as shown below:
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Beams
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The software provides the following options for viewing stresses: z
Axial: Uniform axial stress = P/A
z
Bending in local direction 1: Bending stresses due to M2. This is referred to as Bending Ms/Ss in the plot name, title, and legend.
z
Bending in local direction 2: Bending stress due to M1. This is referred to as Bending Mt/St in the plot name, title, and legend.
Click here to learn about beam directions. z
Worst case: The software automatically calculates the highest stresses at a critical point on the crosssection by combining axial and bending stresses due to M1 and M2. This is the recommended stress to view.
In general, the software calculates 4 stress values at the extreme fibers of each end. When viewing worst case stresses, the software shows one value for each beam segment. This value is the largest in magnitude out of the 8 values calculated for the beam segment. These values are accurate for beam with cross-sections that are symmetric in two directions. These values are conservative for other cases.
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Mesh - Default Options (New Study)
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Default Options - Mesh You set meshing options for studies using solid, shell, and mixed mesh. Beam studies do not use this PropertyManager. The mesh that the software generates depends on the following factors: z
Active meshing options for the study (specified in the Mesh PropertyManager)
z
Mesh control specifications
z
Contact conditions defined in the Connections folder
NOTES z
When you create a new study (Study PropertyManager), it inherits the default meshing options set in the Mesh page of the Default Options tab. You can modify the meshing options for each study in the Mesh PropertyManager. If you create a duplicate of a study, the new study inherits the meshing options of the source study.
z
Meshing options are essential factors in determining the quality of the results. Results based on different option settings should converge to each other, if an adequately small element size is used.
To modify the mesh options for a study, right-click the Mesh icon in the Simulation study tree, select Create Mesh, and expand Mesh Parameters and Advanced.
Mesh Quality Sets the mesh quality: z
Draft. Each solid element will have 4 corner nodes only. Each shell element will have 3 corner nodes.
z
High. Each solid element will have 10 nodes: 4 corner nodes and one node at the middle of each edge (a total of six mid-side nodes). Each shell element will have 6 nodes: 3 corner nodes and 3 mid-side nodes.
It is highly recommended to use the High quality option for final results and for models with curved geometry. Draft quality meshing can be used for quick evaluation.
z
Jacobian points. Sets the number of integration points to be used in checking the distortion level of tetrahedral elements. You can select 4, 16, 29 points or At Nodes. See the Mesh Quality Checks section for more details.
The software performs Jacobian check by default for high quality mesh. It is recommended to use the At Nodes option when using the p-method to solve static problems.
Mesher type Sets the preferred meshing technique to be used. z
Standard mesh. Activates the Voronoi-Delaunay meshing scheme for subsequent meshing operations. This mesher is faster than the curvature- based mesher and should be used in most cases.
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Mesh - Default Options (New Study)
z
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Curvature based mesh. Activates the Curvature-based meshing scheme for subsequent meshing operations. The mesher creates more elements in higher-curvature areas automatically (without need for mesh control). For assemblies, the mesher requires setting the global bond option to incompatible. If component contact features are created, they should also specify incompatible bonding.
Curvature-based mesh is always compatible for touching or partially touching edges of sheet metal bodies and surface bodies.
{
Min number of elements in a circle. Sets the minimum number of elements the mesher creates at curvatures.
See how the element size is determined z
Show advanced options for contact set definitions (No penetration and shrink fit only). When selected, the contact options are displayed in the Contact Set PropertyManager under Advanced. If this option is not selected, the software applies by default a node to surface contact type to all contact set definitions.
Mesher Options (for Standard Mesher) Sets mesh options for the standard mesher. z
Automatic transition. When checked, the program automatically applies mesh controls to small features, holes, fillets, and other fine details of your model. Uncheck Automatic transition before meshing large models with many small features and details to avoid generating a very large number of elements unnecessarily. Example1 | Example2
z
Automatic trials for solid. Instructs the program to automatically retry to mesh the model using a different global element size. You control the maximum number of trials allowed and the factors by which the global element and tolerance are scaled for each trial. {
Number of trials. Sets the maximum number of mesh trials.
{
Global element size factor for each trial. Factor by which the new global element size is multiplied to calculate the new global element size.
{
Tolerance factor for each loop. Factor by which the new tolerance is multiplied to calculate the new tolerance.
z
Remesh failed parts with incompatible mesh. If selected, the software tries to use incompatible meshing for bonded bodies that fail compatible meshing. Used for solid mesh only.
z
Automatic shell surface re-alignment for non-composite shells. When selected, the software automatically realigns the shell surfaces (non-composites) so that all bottom/top faces have uniform orientation. If this option is not selected, you may need to flip the misaligned shell surfaces manually. Select the desired faces, right-click the Mesh icon in the Simulation study tree and select Flip Shell Elements.
Mesher Options (for Curvature Based Mesher) Sets mesh options for the alternate mesher. z
Min number of elements in a circle. Sets the minimum number of elements on a full circle. The maximum angle for any element is 360 divided by the specified number. The limits are 4 and 36.
To set default meshing options for new studies:
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Mesh - Default Options (New Study)
1.
Click Simulation, Options, Default Options, Mesh.
2.
Specify the desired settings.
3.
Click OK.
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To modify meshing options for a study: 1.
In the Simulation study tree, right-click the Mesh icons and select Create Mesh.
2.
Specify the desired settings under Mesh Parameters and Advanced
3.
Under Options select Save setting without meshing, or Run (solve) the analysis.
4.
Click
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Mesh Control Parameters
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Mesh Control Parameters Mesh control refers to specifying different element sizes at different regions in the model. A smaller element size in a region improves the accuracy of results in that region. You can specify mesh control at vertices, points, edges, faces, and components. Mesh control is not available for beams. To access the Mesh Control PropertyManager, right-click the Mesh icon and select Apply Mesh Control.
Mesh Control Parameters The mesh control parameters are: z
Element size (e) for the specified entities
z
Element growth ratio (r)
Assuming that the element size used for meshing an entity is (e), the average element size in layers radiating from the 2 3 n entity will be: e, e*r, e*r , e*r , ...., e*r . If the calculated average element size of a layer exceeds (E), where (E) is the Global Size , the program uses (E) instead. The mesh radiates from vertices to edges, from edges to faces, from faces to components, and from a component to connected components. To apply mesh control to mixed types of entities: 1.
In the Simulation study tree, right-click the Mesh icon and select Apply Mesh Control.
The Mesh Control PropertyManager appears. 2.
In the graphics area, select the entities for which you want to apply mesh controls.
3.
Under Control Parameters, do the following:
4.
a.
Select a unit and type a value in the Element Size box
b.
Type a value in the Ratio box
Click
.
.
.
To apply mesh control to multiple components: 1.
In the Simulation study tree, right-click the Mesh icon and select Apply Mesh Control.
The Mesh Control PropertyManager appears.
2.
Click the FeatureManager design tree tab 3.
.
In the FeatureManager flyout, select the components to which you want to apply mesh control.
The selected components appear in the Selected Entities list box. 4.
Under Selected Entities, select Use per part size.
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Mesh Control Parameters
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The software assigns an optimum element size for mesh control to individual components based on their volume. Move the Mesh Density slider towards Coarse to increase the element size by a factor of 2, or towards Fine to decrease the element size by a factor of 0.5.
5.
Click
.
Related Topics Component Mesh Control Examples of Mesh Control
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Meshing Options
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Meshing Options Meshing Options are essential factors in determining the quality of the mesh and hence the results. Results based on different preference settings should converge to each other if an adequately small element size is used. Meshing options are not used for beams. You can set the Mesh quality to Draft or High. A draft quality mesh does not have mid-side nodes. Draft quality can be used for quick evaluation and in solid models where bending effects are small. High quality mesh is recommended in most cases, especially for models with curved geometry. The Standard mesher uses the Voronoi-Delaunay meshing scheme for subsequent meshing operations. This mesher is faster than the Curvature based mesher and should be used in most cases. Try the Curvature based mesher only when the standard mesher keeps failing. The Curvature based mesher supports mesh control on components, faces and edges. The Jacobian points when Mesh quality is set to High sets the number of points to be used in checking the distortion level of high order tetrahedral elements.
For high order shells, the Jacobian check uses 6 points located at the nodes. Automatic transition automatically applies mesh controls to small features, details, holes, and fillets. Uncheck Automatic transition before meshing large models with many small features and details to avoid generating a very large number of elements unnecessarily. Automatic trials for solids instructs the mesher to automatically retry to mesh the model using a smaller global element size. You control the maximum number of trials allowed and the ratio by which the global element size and tolerance are reduced each time. Remesh failed parts with incompatible mesh. Using this option can help mesh bonded solids that fail compatible meshing. If Automatic looping is on and bonding solids using compatible mesh is requested, the software tries incompatible meshing automatically for solids that fail to mesh with the compatible option. Setting the color for plotting the bottom faces of shell elements helps you align shell elements properly. Setting the meshing Options
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Mesh Quality Checks
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Mesh Quality Checks The quality of mesh plays a key role in the accuracy of the results. The software uses two important checks to measure the quality of elements in a mesh. z
Aspect Ratio Check. For a solid mesh, numerical accuracy is best achieved by a mesh with uniform perfect tetrahedral elements whose edges are equal in length. For a general geometry, it is not possible to create a mesh of perfect tetrahedral elements. Due to small edges, curved geometry, thin features, and sharp corners, some of the generated elements can have some of their edges much longer than others. When the edges of an element become much different in length, the accuracy of the results deteriorates.
The aspect ratio of a perfect tetrahedral element is used as the basis for calculating aspect ratios of other elements. The aspect ratio of an element is defined as the ratio between the longest edge and the shortest normal dropped from a vertex to the opposite face normalized with respect to a perfect tetrahedral. By definition, the aspect ratio of a perfect tetrahedral element is 1.0. The aspect ratio check assumes straight edges connecting the four corner nodes. The aspect ratio check is automatically used by the program to check the quality of the mesh.
z
Jacobian Points. Parabolic elements can map curved geometry much more accurately than linear elements of the same size. The mid-side nodes of the boundary edges of an element are placed on the actual geometry of the model. In extremely sharp or curved boundaries, placing the mid-side nodes on the actual geometry can result in generating distorted elements with edges crossing over each other. The Jacobian of an extremely distorted element becomes negative. An element with a negative Jacobian causes the analysis program to stop.
The Jacobian check is based on a number of points located within each element. The software gives you a choice to base the Jacobian check on 4, 16, 29 Gaussian points or At Nodes.
It is recommended to set Jacobian check to At Nodes when using the p-method to solve static problems. The Jacobian ratio of a parabolic tetrahedral element, with all mid-side nodes located exactly at the middle of the straight edges, is 1.0. The Jacobian ratio increases as the curvatures of the edges increase. The Jacobian ratio at a point inside the element provides a measure of the degree of distortion of the element at that location. The software calculates the Jacobian ratio at the selected number of Gaussian points for each tetrahedral element. Based on stochastic studies it is generally seen that a Jacobian Ratio of forty or less is acceptable. The software adjusts the locations of the mid-side nodes of distorted elements automatically to make sure that all elements pass the Jacobian check.
For high order shells, the Jacobian check uses 6 points located at the nodes.
To set the Jacobian check options for a study: 1.
In the Simulation study tree, right-click the Mesh icon and select Create.
2.
Expand Advanced.
3.
Specify the number of points for Jacobian points.
4.
Under Options, select Save settings without meshing to save the options without meshing or click to save the options and mesh the model.
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Meshing Tips
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Meshing Tips z
When you mesh a study, the software meshes all unsuppressed solids, shells, and beams: {
Use Solid mesh for bulky objects.
{
Use Shell elements for thin objects like sheet metals.
{
Use Beam or Truss elements for extruded or revolved objects with constant cross-sections.
{
For assemblies, check component interference. To detect interference in an assembly, click Tools, Interference Detection. Interference is allowed only when using shrink fit. The Treat coincidence as interference and Include multibody part interferences options allow you to detect touching areas. Theses are the only areas affected by the global and component contact settings.
You can also find touching faces by right-clicking the Connections folder and selecting Find contact sets.
z
Compatible meshing is more accurate than incompatible meshing in the interface region. Requesting compatible meshing can cause mesh failure in some cases. Requesting incompatible meshing can result in successful results. You can request compatible meshing and select Remesh failed parts with incompatible mesh so that the software uses incompatible meshing only for bodies that fail to mesh.
z
If meshing fails, use the Failure Diagnostics tool to locate the cause of mesh failure. Try the proposed options to solve the problem. You can also try different element size, define mesh control, or activate Enable automatic looping for solids.
z
The SolidWorks Simplify utility lets you suppress features that meet a specified simplification factor. In the Simulation study tree, right-click Mesh and select Simplify Model for Meshing Simplify utility.
. This displays the
Simplification of geometry can alter stress results significantly.
z
It is good practice to check mesh options before meshing. For example, the Automatic transition can result in generating an unnecessarily large number of elements for models with many small features. The high quality and Standard mesher are recommended for most cases. The Automatic looping can help solve meshing problems automatically, but you can adjust its settings for a particular model. The Alternate mesher automatically uses smaller element sizes in regions with high curvature.
z
To improve results in important areas, use mesh control to set a smaller element size. When meshing an assembly with a wide range of component sizes, default meshing results in a relatively coarse mesh for small components. Component mesh control offers an easy way to give more importance to the selected small components. Use this option to identify important small components.
For static studies, you can use the h-adaptive method to refine the mesh automatically.
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Meshing Tips
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Meshing Tips z
When you mesh a study, the software meshes all unsuppressed solids, shells, and beams: {
Use Solid mesh for bulky objects.
{
Use Shell elements for thin objects like sheet metals.
{
Use Beam or Truss elements for extruded or revolved objects with constant cross-sections.
{
For assemblies, check component interference. To detect interference in an assembly, click Tools, Interference Detection. Interference is allowed only when using shrink fit. The Treat coincidence as interference and Include multibody part interferences options allow you to detect touching areas. Theses are the only areas affected by the global and component contact settings.
You can also find touching faces by right-clicking the Connections folder and selecting Find contact sets.
z
Compatible meshing is more accurate than incompatible meshing in the interface region. Requesting compatible meshing can cause mesh failure in some cases. Requesting incompatible meshing can result in successful results. You can request compatible meshing and select Remesh failed parts with incompatible mesh so that the software uses incompatible meshing only for bodies that fail to mesh.
z
If meshing fails, use the Failure Diagnostics tool to locate the cause of mesh failure. Try the proposed options to solve the problem. You can also try different element size, define mesh control, or activate Enable automatic looping for solids.
z
The SolidWorks Simplify utility lets you suppress features that meet a specified simplification factor. In the Simulation study tree, right-click Mesh and select Simplify Model for Meshing Simplify utility.
. This displays the
Simplification of geometry can alter stress results significantly.
z
It is good practice to check mesh options before meshing. For example, the Automatic transition can result in generating an unnecessarily large number of elements for models with many small features. The high quality and Standard mesher are recommended for most cases. The Automatic looping can help solve meshing problems automatically, but you can adjust its settings for a particular model. The Alternate mesher automatically uses smaller element sizes in regions with high curvature.
z
To improve results in important areas, use mesh control to set a smaller element size. When meshing an assembly with a wide range of component sizes, default meshing results in a relatively coarse mesh for small components. Component mesh control offers an easy way to give more importance to the selected small components. Use this option to identify important small components.
For static studies, you can use the h-adaptive method to refine the mesh automatically.
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Probing Results
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Probing Results In many cases, you may want to know the numerical value of the plotted field at a particular location. Use the probe tool to display the numerical value of the plotted field at the closest node or element's center to the point of clicking. You can graph the results or save them to a file. To probe a result plot at selected locations: 1.
Activate the desired plot.
2.
Click Probe
(Simulation Result Tools toolbar) or Simulation, Result Tools, Probe or right-click the
plot in the Simulation study tree and select Probe
.
3.
In the PropertyManager, under Options, select At Location.
4.
Select locations on the model and view the results in the graphics area and under Results in the PropertyManager.
5.
Click
.
To probe a result plot at sensor locations: 1.
Activate the desired plot.
2.
Click Probe
(Simulation Result Tools toolbar) or Simulation, Result Tools, Probe or right-click the
plot in the Simulation study tree and select Probe
.
3.
In the PropertyManager, under Options, select From Sensors. You must first define sensors before this option becomes active.
4.
Under Results, select a sensor name from Sensor List.
5.
View the results in the graphics area and under Results in the PropertyManager.
6.
Click
.
When probing results from sensor locations defined at coordinates, the location of the nearest node is used instead of the exact location of the sensor.
To probe a result plot on selected entities: 1.
Activate the desired plot.
2.
Click Probe
(Simulation Result Tools toolbar) or Simulation, Result Tools, Probe or right-click the
plot in the Simulation study tree and select Probe
.
3.
In the PropertyManager, under Options, select On selected sntities.
4.
Under Results, select entities for Faces, Edges, Vertices
and click Update.
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Probing Results
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5.
View the results in the graphics area and under Results in the PropertyManager.
6.
Click
.
Related Topics Probing Mesh Plots Probing Section Plots Graphing Probed Results
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Probing Section Plots
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Probing Section Plots You can probe section plots on the faces cut by a section plane. The software uses linear interpolation to calculate the value. To probe a section plot: 1.
Create a section plot of the desired result on the undeformed shape of the model.
2.
Click Probe
3.
In the PropertyManager, select a probing method under Options.
4.
Select locations on the faces cut by the section plane and view the results in the graphics area and under Results in the PropertyManager.
5.
Click
(Simulation Result Tools toolbar) or Simulation, Result Tools, Probe.
.
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