Figure. Sizing optimization. Design varibles are internal parameters of finite elements.
Optimization of load-carrying structures is usually classified into three main groups, as follows:
In sizing optimization the design parameters are typically internal parameters of finite elements, for example, the cross-section area of a truss element. When these parametrs are optimized, the shape and topology of the FE mesh remain unchanged.
Figure. Sizing optimization. Design varibles are internal parameters of finite elements.
In shape optimization the design parameters are typically some parameters related to the shape of the FE mesh, for example control points of underlying geometrical objects. When these parametrs are optimized, the shape of the structure changes, while the topology of the FE mesh remains unchanged.
Figure. Shape optimization. Design varibles are parameters related to the shape of the FE mesh.
Shape optimization comes in many variations in dependance of what kind of problem is addressed.
In topology optimization the design parameters are typically some parameters related to the presense or absence of material at some location of the FE mesh. When these parametrs are optimized, the topology of the FE mesh changes.
Figure. Topology optimization. Design varibles are parameters related to presence or absence of material in the FE mesh.
The design variables are typically linked to some material function which helps in defining a numerical material that may change continuously from full material to void. The numerical material typically exhibits the same propertis as the actual material, with the exception of a few parameters. Typically, these redefined parameters are the elastic modulus and mass density, for example, as follows:
Numerical elastic modulus = Material function * Actual elastic modulus
Numerical mass density = Material function * Actual mass density
Such relations can be used in a similar sense when various material types are addressed. For example, for an orthotropic material, all elastic moduli can be redefined in this way.
NOTE. CAESS ProTOp is a software package for topology optimization of load-carrying structures. It relies on highly efficient FEA code and ptimizer, both custom developed for maximum performance.