Topology Optimization

Topology Optimization is a mathematical technique that produces an optimized shape and material distribution for a structure within a given package space. By discretizing the domain into a finite element mesh, OptiStruct calculates material properties for each element. The OptiStruct algorithm alters the material distribution to optimize the user-defined objective under given constraints. Convergence occurs in line with the description provided on the Iterative Solution page.

Beginning in V14.0, an improved Topology Optimization formulation is available that aims at producing more discrete results for all topology runs including manufacturing constraints. This formulation can be activated using OPTPRM,TOPDISC.

The following responses (see Responses for a description) are currently available as the objective or as constraint functions:

Mass	Volume	Volume or Mass Fraction
Center of Gravity	Moment of Inertia	Static Compliance
Static Displacement	Natural Frequency	von Mises Stress on Entire Model (only as constraint)
Buckling Factor (special case)	Frequency Response Displacement, Velocity, Acceleration	Temperature
Weighted Compliance	Weighted Frequency	Combined Compliance Index
Function

Stress Responses for Topology and Free-Size Optimization

DRESP1-based Stress Response

Actual Stress Responses for Topology and Free-Size Optimization are available through corresponding Stress response RTYPE’s on the DRESP1 Bulk Data Entry. The Stress-NORM aggregation is internally used to calculate the Stress Responses for groups of elements in the model.

DTPL-based Stress Response

The von Mises stress constraints may be defined for topology and free-size optimization through the STRESS optional continuation line on the DTPL or the DSIZE card. There are a number of restrictions with this constraint:

•

The definition of stress constraints is limited to a single von Mises permissible stress. The phenomenon of singular topology is pronounced when different materials with different permissible stresses exist in a structure. Singular topology refers to the problem associated with the conditional nature of stress constraints, i.e. the stress constraint of an element disappears when the element vanishes. This creates another problem in that a huge number of reduced problems exist with solutions that cannot usually be found by a gradient-based optimizer in the full design space.

•

Stress constraints for a partial domain of the structure are not allowed because they often create an ill-posed optimization problem since elimination of the partial domain would remove all stress constraints. Consequently, the stress constraint applies to the entire model when active, including both design and non-design regions, and stress constraint settings must be identical for all DSIZE and DTPL cards.

•	The capability has built-in intelligence to filter out artificial stress concentrations around point loads and point boundary conditions. Stress concentrations due to boundary geometry are also filtered to some extent as they can be improved more effectively with local shape optimization.

•	Due to the large number of elements with active stress constraints, no element stress report is given in the table of retained constraints in the .out file. The iterative history of the stress state of the model can be viewed in HyperView or HyperMesh.

•	Stress constraints do not apply to 1D elements.

•	Stress constraints may not be used when enforced displacements are present in the model.

The buckling factor can be constrained for shell topology optimization problems with a base thickness not equal to zero. Constraints on the buckling factor are not allowed in any other cases of topology optimization.

The following responses are currently available as the objective or as constraint functions for elements that do not form part of the design space:

Composite Stress	Composite Strain	Composite Failure Criterion
Frequency Response Stress	Frequency Response Strain	Frequency Response Force