A generalized evolutionary method for numerical topology optimization of structures under static loading conditions

Generalized evolutionary methods, which successively construct and solve static equilibrium problems with progressive mesh adaptation, are useful tools for defining structures that utilize their construction material to greatest effect in the finite element sense. By basing the successive element erosion upon (i) the contribution of an element to the strain energy of a structure and (ii) a certain material efficiency indicator of a structure, several weaknesses associated with previous methods have been overcome. Under static loading conditions, the strain energy contribution of an element is determined solely by the related stiffness and displacement vector. Consequently, the method is effective, and efficient when applied to problems involving such loading conditions. The efficacy of the method is demonstrated through numerical applications to the problem of optimizing the topologies of two structures, a cantilever structure and a Michell structure