Structural optimization is by nature a large-scale constrained optimization, where the number of degrees of freedom (DOF) ranges from 1e4 to more than 1e9 and is solved using gradient-based algorithms.
Despite the qualitative differences between the optimization methods, each method follows the same analytical workflow when performing an analysis, including:
Shape Description: For the Shape Optimization and Topography Optimization methods the shape is explicitly defined using the finite element mesh. The Topology Optimization and Lattice Optimization methods use implicit descriptions through either density fields (Lattice and Solid Isotropic Material with Penalization method (SIMP) topology optimization) or level-set functions (Level Set-based topology optimization).
Shape Evaluation: Methods using implicit shape description require dedicated treatment for finite element analysis.
Shape Derivative Computation: Based on the shape description, the application selects how to best compute the shape derivative, that is, the desired sensitivity for each specified criterion with respect to the corresponding degrees of freedom of the optimization problem.
Shape Update: The application performs final geometry modifications based on the selected shape description.
See the following sections for the shape processing workflows of each method: