Multiscale Design and Optimization of Bi-Material Laminated Structures

Two-scale structural design optimization for the simultaneous design of material and structure, has been a topic of research interest during the last decade. This paper is based on the approach presented in [1] and considers two scales, macro and micro, identified with the design domains of the structure and its material (cellular or composite material), respectively. Structure and material evolve for their optimal layouts as a result of updating the density based design variables such that the global compliance is minimized and a global resource volume constraint is satisfied. Here the class of cellular or composite materials, is restricted to single scale periodic materials, with the unit cell topology locally optimized for the given objective function and constraints. Asymptotic homogenization theory is used to compute equivalent elastic properties at the macroscopic level [2]. The design model may include local constraints for the material microstructure depending on the applications. For instance, some constraints may be related with material manufacture requirements as minimum thicknesses as well as mass transport properties and so forth [3]. Paper 39