Optimal Bi-scale Design Of Anisotropic Porous Structures

Porous structures are widely found in natural objects such as bones,wood,cork,bird beaks and so on,and manifest many appealing properties to solid counterparts,such as light weight,larger internal surface areas,higher strength-to-weight ratios,and many multi-function properties.It is widely accepted that the supreme property of porous structures come from its various degrees of structural heterogeneity and anisotropy.In spite of these attracting properties,optimally designing heterogeneous and anisotropic structures is a very challenging task seldom addressed before,and previous studies mainly focus on building homogeneous and isotropic porous structures.This is partly due to the limited traditional fabrication abilities,and partly due to the complex and challenging controlling task on the pore sizes and pore distributionsThe study focuses on the parametric modeling of porous structures,and also proposes a design optimization approach built on it.The porous structures containing elliptic holes are first studied,and then a novel porous structure built from the newly elliptic triply periodic minimal surface(ETPMS)is introduced.Designing the porous structure is here formulated as a bi-scale compliance minimization problem,or equivalently stifness maximization,under constraints on volume fraction.In summary,the contributions of the study are summarized as follows:Firstly,a novel bi-scale method is introduced for heterogeneous and anisotropic porous structure design optimization,which ultimately builds an interconnected porous structure of maximal stiffness under certain constraint on material usage.Such anisotropic structure design problem is seldom addressed in previous studies.Secondly,a novel ETPMS is introduced for heterogeneous anisotropic porous structure modeling,which allows for building an interconnected porous structure of different material property various along different axis directions at different locations.Traditional TPMS can only model homogeneous and anisotropic porous structures.Lastly,the model reduction approach of PGD is further extended to computing offline a parametric material property description for different parametric microstructures.It thus greatly reduce the efforts on performing numerical homogenization for each porous microstructure,and greatly reduces the computational costs.