ABSTRACT
The performance-based optimization (PBO) method for optimal topology and shape designs of continuum structures with displacement constraints has been presented in Chapter 3. Element removal criteria are based on the virtual strain energy densities (VSEDs) of elements. In order to calculate the VSEDs of elements, the structure has to be analyzed for the virtual unit loads, which are applied at the loaded points. An optimal design produced by the PBO method based on displacement performance criteria is in favor of the specific displacements. This means that the optimal design obtained is a maximum stiffness design at minimum weight with respect to the specific displacements. For a structure under only a few point loads, the PBO method for structures with displacement constraints is efficient in generating minimum-weight and maximum stiffness designs. When dealing with the optimization problem of a continuum structure under many concentrated loads and multiple load cases, however, many virtual unit loads have to be applied to the structure in order to calculate the VSEDs of elements and to control the system stiffness performance. This will considerably increase the computational cost. Moreover, practical structures are often designed for overall stiffness performance. To improve the computational efficiency and overall structural performance, a more general approach formulated on the basis of system performance criteria is presented in this chapter.
