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Support for contact during the optimization
You can avoid contact in optimized regions of your model by defining geometric restrictions, such as casting or minimum member size restrictions. In some cases, you cannot specify the exact boundary conditions early in the design phase. In addition, nonlinear boundary conditions, such as contact definitions, can change if the Optimization module changes the topology of the model.
The optimization process is more efficient if you create an Abaqus model with the appropriate contact definitions and allow Abaqus to calculate the contact. The contact conditions are included in the optimization through the forces at the nodes and the stresses in the elements, and both topology and shape optimization permit contact conditions in the Abaqus model.
You can define a contact surface directly on the edge of the design space in topology optimization. However, if the design edge belongs to a contact surface in shape optimization, you must invert the shape optimization algorithm by entering a negative growth scale factor. You may encounter convergence difficulties in your Abaqus model if you have a complex contact problem or if the optimization results in large changes in the model.
Restrictions on an Abaqus model used for topology optimization
Topology optimization determines the optimal material distribution in the design space, given the prescribed conditions applied to the model along with the objective function and constraints. Your optimization must apply appropriate constraints and restrictions; otherwise, the Optimization module can extensively alter the topology of the component. The resolution of the structure that has been optimized with topology optimization is very dependent on the discretization. A fine mesh produces a structure with a higher resolution than a coarse mesh; however, it will also substantially increase the processing time required. You must determine the appropriate compromise between structural resolution and processing time.
During topology optimization the Optimization module modifies the material definition of the elements in the design area. As a result, you must provide the initial density of the materials in the design area, even if it is not required by the Abaqus analysis.
Restrictions on an Abaqus model used for shape optimization
Abaqus performs a shape optimization by modifying the boundaries or surfaces of a component. The optimization uses the stress condition to calculate new coordinates for nodes on the surface of the component and then adjusts the underlying mesh accordingly. The mesh quality must be sufficient to ensure that the analysis results are mostly unchanged by the movement of the surface nodes. High stress gradients must not be present within an element.
When the Optimization module is performing a shape optimization on a shell structure, it optimizes the form of the shell structure and not its thickness. The nodal position along shell edges can be modified; however, Abaqus does not modify the shell definition.
Restrictions on an Abaqus model used for sizing optimization
Abaqus performs a sizing optimization by modifying the thickness of shell elements in the design region. The element thickness must be uniform, and only single-layered shells are supported. Prescribed
displacements are allowed in a static stress/displacement analysis; however, they are not supported in a frequency analysis.
Restrictions on an Abaqus model used for bead optimization
Abaqus performs a bead optimization by moving nodes of shell elements in the direction of the shell normal in the design region. The element thickness must be uniform, and only single-layered shells are supported. Prescribed displacements are allowed in a static stress/displacement analysis; however, they are not supported in a frequency analysis.
Supported materials in the design area
The material models supported by structural optimization in the elements in the design area depend on the type of optimization—condition-based topology optimization, general topology optimization, or shape optimization.
Materials supported by condition-based topology optimization
Condition-based topology optimization in Abaqus supports linear elastic, plastic, and hyperelastic material models.
Support for linear elastic material models
The following linear elastic material models are supported by condition-based topology optimization:
• Linear elastic materials with isotropic behavior.
• Linear elastic materials with fully anisotropic behavior.
• Linear elastic materials with orthotropic behavior. All of the behavior models are supported, except for orthotropic shear behavior for warping elements and coupled and uncoupled traction behavior for cohesive elements.
Support for plastic material models
Metal plasticity material properties—the plastic part of the material model for elastic-plastic materials that use the Mises or Hill yield surface—are supported by condition-based topology optimization. Isotropic hardening is supported; however, cyclic loading is not supported—each material point can be unloaded only once and should not become elastoplastic again.
Support for hyperelastic material models
All of the hyperelastic material models are supported by condition-based topology optimization, except for the Marlow material model and the hyperelastic material models with test data.
Support for temperature and field variable dependency
Condition-based topology optimization supports materials that have temperature and field variable dependency.
Materials supported by general topology optimization
General topology optimization in Abaqus supports linear elastic, plastic, and hyperelastic material models.
Support for linear elastic material models
The following linear elastic material models are supported by general topology optimization:
• Linear elastic materials with isotropic behavior.
• Linear elastic materials with fully anisotropic behavior.
• Linear elastic materials with orthotropic behavior. All of the behavior models are supported, except for orthotropic shear behavior for warping elements and coupled and uncoupled traction behavior for cohesive elements.
Support for plastic material models
Metal plasticity material properties—the plastic part of the material model for elastic-plastic materials that use the Mises or Hill yield surface—are supported by general topology optimization. Isotropic hardening is supported; however, cyclic loading is not supported—each material point can be unloaded only once and should not become elastoplastic again.
Support for hyperelastic material models
All of the hyperelastic material models are supported by general topology optimization, except for the Marlow material model and the hyperelastic material models with test data.
Support for temperature and field variable dependency
Materials that have temperature and field variable dependency are supported by general topology optimization.
Material support in shape optimization
All of the Abaqus material models are supported by shape optimization.
Material support in sizing optimization
Nonlinear materials in the design area are not supported by sizing optimization. All of the Abaqus material models, including nonlinear materials, are supported outside the design area.
Material support in bead optimization
Nonlinear materials in the design area are not supported by bead optimization. All of the Abaqus material models, including nonlinear materials, are supported outside the design area.
Support for coordinate systems
In most cases, you will use the same coordinate system to define your model and the optimization task. However, the Optimization module allows you refer to a different coordinate system when you are defining a design response.
Supported element types
The Abaqus elements that are supported as design elements by topology and shape optimization are listed in Table 13.2.3–1 through Table 13.2.3–4. The tables also list the Abaqus elements that support the reaction and internal force design responses. The shell elements that are supported as design elements by sizing and bead optimization are listed in Table 13.2.3–5 and Table 13.2.3–6, respectively. Unsupported elements are ignored during optimization and remain unchanged. Structural optimization does not place any restrictions on the type of elements that you use outside the design area.
Supported two-dimensional solid elements
Topology optimization (both condition-based and general) and shape optimization support the two-dimensional solid elements listed in Table 13.2.3–1.
Table 13.2.3–1 Supported two-dimensional solid elements.
| CPE3 $^{1}$ , CPE3H, CPE4 $^{1}$ , CPE4H, CPE4I, CPE4IH, CPE4R $^{1}$ , CPE4RH, |
| CPE6H, CPE6M, CPE6MH |
| CPE8 $^{1}$ , CPE8H, CPE8R $^{1}$ , CPE8RH |
| CPS3 $^{1}$ , CPS4 $^{1}$ , CPS4I, CPS4R $^{1}$ , CPS6 $^{1}$ , CPS6M, CPS6MT, CPS8 $^{1}$ . CPS8R $^{1}$ |
| CPEG3, CPEG3H, CPEG4, CPEG4H, CPEG4I, CPEG4IH, CPEG4R, CPEG4RH, CPEG6, CPEG6H, CPEG6M, CPEG6MH, CPEG8, CPEG8H, CPEG8R, CPEG8RH |
| CPE3T, CPE4T, CPE4HT, CPE4RT, CPE4RHT, CPE6MT, CPE6MHT, CPE8T, CPE8HT, CPE8RT, CPE8RHT |
| CPS3T, CPS4T, CPS4RT, CPS8T, CPS8RT |
| CPEG3T, CPEG3HT, CPEG4T, CPEG4RT, CPEG4RHT, CPEG6MT, CPEG6MHT, CPEG8T, CPEG8HT, CPEG8RHT |
| $^{1}$ Can include reaction and internal force design responses. |
Supported three-dimensional solid elements
Topology optimization (both condition-based and general) and shape optimization support the threedimensional solid elements listed in Table 13.2.3–2.
Table 13.2.3–2 Supported three-dimensional solid elements.
| C3D4 $^{1}$ , C3D4H, C3D8 $^{1}$ |
| C3D6 $^{1}$ , C3D6H |
| C3D8H, C3D8I, C3D8IH, C3D8R $^{1}$ , C3D8RH |
| C3D10 $^{1}$ , C3D10H, C3D10M, C3D10MH |
| C3D15 $^{1}$ , C3D15H |
| C3D20 $^{1}$ , C3D20H, C3D20R $^{1}$ , C3D20RH |
| C3D4T, C3D6T, C3D8T, C3D8HT, C3DHRT, C3D8RHT, C3D10MT, C3D10MHT, C3D20T, C3D20HT, C3D20RT, C3D20RHT |
| $^{1}$ Can include reaction and internal force design responses. |
Supported axisymmetric solid elements
Topology optimization (both condition-based and general) and shape optimization support the axisymmetric solid elements listed in Table 13.2.3–3.
Table 13.2.3–3 Supported axisymmetric solid elements.
| CAX31, CAX3H, CAX41, CAX4H, CAX4I, CAX4IH, CAX4R1, CAX4RH |
| CAX81, CAX8H, CAX8R1, CAX8RH |
| CGAX3, CGAX3H, CGAX4, CGAX4H, CGAX4R, CGAX4RH, CGAX8, CGAX8H, CGAX8R, CGAX8RH |
| CAX3T, CAX4T, CAX4HT, CAX4RT, CAX4RHT, CAX8T, CAX8HT, CAX8RT, CAX8RHT |
| CGAX3T, CGAX3HT, CGAX4T, CGAX4HT, CGAX4RT, CGAX4RHT, CGAX8T, CGAX8HT, CGAX8RT, CGAX8RHT |
| 1 Can include reaction and internal force design responses. |
Additional supported elements
Table 13.2.3–4 lists the general membrane, three-dimensional conventional shell, and beam elements that are supported by optimization.
Table 13.2.3–4 Additional supported elements
| General membrane elements (topology and shape optimization) | M3D3 $^{1}$ , M3D4 $^{1}$ , M3D4R $^{1}$ , M3D6 $^{1}$ , M3D8 $^{1}$ , M3D8R $^{1}$ |
| Three-dimensional conventional shell elements (topology optimization only) | STRI3, S3, S3R, STRI65, S4, S4R, S4R5, S8R, S8R5, S8RT |
| Three-dimensional conventional shell elements (shape optimization only) | STRI3 $^{1}$ , S3 $^{1}$ , S3R $^{1}$ , S4 $^{1}$ , S4R $^{1}$ , S8R $^{1}$ |
| Beam elements (shape optimization only) | B21 $^{2}$ , B21H $^{2}$ , B31 $^{2}$ , B31H $^{2}$ |
| $^{1}$ Can include reaction and internal force design responses. | |
| $^{2}$ You can include beam elements in shape optimization only to define a neighboring component that is used to restrict the movement of nodes in the optimized region. | |
Supported three-dimensional conventional shell elements
Sizing optimization supports only the three-dimensional conventional shell elements listed in Table 13.2.3–5.
Table 13.2.3–5 Supported three-dimensional conventional shell elements for sizing optimization.
| S3, S3R, S4, S4R, S8R |
| $STRI65^1$ |
| $^1$ You must request that rotational degrees of freedom be written to the output database. |
Condition-based bead optimization supports all Abaqus plate and shell elements. However, general bead optimization supports only the three-dimensional conventional shell elements listed in Table 13.2.3–6.
Table 13.2.3–6 Supported three-dimensional conventional shell elements for general bead optimization.
| S3, S3R |
| STRI3 |
| S4, S4R |
| S8R |
14. Eulerian Analysis
Eulerian analysis
14.1