Efficient Parametric Optimization For Porous Structure Design

Porous structures are found in many natural organisms,such as woods and bones.Researchers have found that these complex structures themselves give the material excellent physical/chemical performances and inspire the study and development of industrial porous materials.With the rapid development of modern 3D printing technology,the problem of how to manufacture complex porous structures has proved to be an easy task,and consequently raises the issue on how to design porous structures for specific performance requirements.However,the design of porous structures faces many challenges:the structure geometry is too complex to model effectively and lacks an effective control approach;the computational costs of physical simulation are too high;lacking efficient porous structure system design framework.To overcome these challenges,we propose the concept of semiregular porous structures,and correspondingly build an efficient parametric design framework for porous structures,specifically including:the parametric porous structures description,bi-scale simulation techniques and a performance-driven porous structure optimization method.Specifically,the main contributions of the study are:(1)Efficient isotropic porous structure bi-scale parametric optimization and design:To couple the microscopic structure and macroscopic property efficiently,we propose the parametric structure representing method based on representative volume element;and to perform physical simulation directly and efficiently,we introduce homogenization method and combined approximation to deduce the analytical relation between the structure parameters and macroscale performances,and ultimately transform the design problem to optimization problem which is easy to solve.Our approach maintains efficiency and numeric stability even in multi-objective design problem.(2)Efficient anisotropic porous structure parametric design approach:To balance the increasing design degrees of freedom and computational costs in the complex anisotropic structure design problem,we introduce super formula surface to parameterize the porous structure;to satisfy the physical rationality,we improve proper generalized decomposition method to build more accurate relation between structure parameters and performances,and integrate the above methods to form a parametric design approach.The optimization on numeric algorithms and the diversity of anisotropic structures ensure that our approach obtain better performances and capture more physical details.(3)Parametric representing method with reduced dimension and the design optimization of random porous structures:To overcome the disadvantages of classical structure descriptors in extraction speed,structural geometry capture,structure reconstruction speed and accuracy,we propose a novel PCA-based structure parameterization method and reduce the dimension of design space while maintaining geometric characters of random porous structure.Owing to these parameterization method,we form the approach of fast physical simulation and design optimization.With analytical relation of structure parameters and performances and optimization algorithm,our approach can improve computational efficiency while maintaining physical accuracy.