Shape and Topology Structural Redesign by Large Perturbations

Abstract

The ultimate goal in concurrent engineering of structures is to achieve simultaneously in the design stage the following objectives: (1) A shape that performs itsfunction, conforms with the boundary conditions,and can support the external loads. (2) A product with structural integrity, i.e. with stress levels remaining below acceptable limits. (3) A product with acceptable performance, e.g. modal dynamics, i.e. with natural frequencies and mode shapes that do not amplify external dynamic loads; and static, i.e. acceptable deflection. (4) A composite microstructure that can optimally satisfy the above topology/ shape, load, and performance constraints. (5) A microstructurefabrication process that efficiently produces the above optimal structure. The purpose of our ONR funded project is to address the complete problem in concurrent structural design by further developing the LargE Admissible Perturbations (LEAP) theory which is being developed at the University of Michigan since 1983, and combiningit with micromechanicsconstitutive equations. At the fabrication end, the Selective Laser Sintering (SLS) process will be simulated so that the SLS variables are defined as the final product of the concurrent structuraLdesign optimization process. LEAP theory -- as implemented in Code RESTRUCT (REdesign of STRUCTures) -- produces the final design without trial and error or repeated Finite Element Analyses (FEAs), thus, shortening the redesign process and contributing to rapid prototyping.