Large-scale Multi-material Topology Optimization for Additive Manufacturing

Graeme Kennedy
2015 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference   unpublished
Advanced manufacturing technologies, such as additive manufacturing, give the engineer greater design freedom by removing geometric and processing constraints that are required by conventional manufacturing methods. Additive manufacturing, therefore, has the potential to enable the design and production of low-weight high-performance structures. However, optimization of such additively-manufactured structures using conventional optimization techniques, such as topology optimization, is
more » ... ng due to the demanding mesh requirements and large size of the design problem. In this paper, we address these difficulties by proposing a scalable approach for analysis and design of large-scale topology and multimaterial optimization problems. This approach includes a multigrid-preconditioned Krylov method for solving large structural finite-element problems, and a parallel interior-point optimization technique for solving large-scale constrained optimization problems. We demonstrate the proposed methods on a large-scale mass-constrained compliance minimization problem for a structure discretized using a 64 × 64 × 256 element mesh, resulting in 3.26 million structural degrees of freedom, 5.24 million design variables and 1.05 million linear constraints. I. Introduction Aerospace vehicles utilize slender, high-aspect ratio structures with small material volume fractions to achieve low structural weight while satisfying structural performance requirements. To meet demanding weight reduction goals, aerospace engineers are increasingly turning to highly-tailored structures fabricated using novel manufacturing processes. New manufacturing technologies, such as additive manufacturing, give the engineer greater design freedom by removing geometric restrictions imposed by conventional manufacturing processes. However, the best way to parametrize such structures for design optimization remains an open question, with various authors suggesting either CAD-based design methods, or topology optimization approaches. Topology optimization techniques offer an attractive solution to the problem of geometry parametrization for additive manufacturing, since these techniques can be used to optimize structures without constraints on structural shape or layout. However, the low volume fraction and high aspect ratios exhibited by many aerospace structures place demanding computational requirements on topology optimization methods. For instance, raster or voxel-based topology methods require near-uniform mesh spacing to resolve detailed structural design features, thereby imposing onerous meshing requirements for three-dimensional problems. Topology optimization techniques based on levelset methods can alleviate this requirement to some degree, since there is only an indirect linkage between the design parametrization and structural discretization. However, high-accuracy structural solutions for refined structural designs still require large structural models. While topology optimization of moderate size problems is now routine, largescale topology optimization is challenging due to the difficulty of both efficiently analyzing large structural models and performing efficient large-scale optimization. These difficulties arise together, since in topology optimization the size of the design problem and analysis problems are proportional. Many authors have developed methods for large-scale topology optimization. Borrvall and Petersson [2] developed techniques for large-scale topology optimization of 3D elastic continua using a regularized intermediate density control. They used parallel computing techniques to solve topology problems with up to 663 000 degrees of freedom. Kim et al. [18] proposed methods to handle large-scale topology optimization problems for eigenvalue-related design problems. Within their framework, the sensitivity analysis and design variable updates were performed with minimal communication amongst subdomains to achieve excellent parallel scalability. Evgrafov et al. [9] discuss the issues that arise when using a finite-element tearing and interconnecting dual-primal (FETI-DP) substructuring iterative solution method for large-scale topology optimization. In particular, the optimal domain decomposition for their solution method is design-dependent, where the best performance is obtained by splitting the domains along solid-void boundaries. More recently, Amir et al. [1] used an algebraic multigrid preconditioner to solve large 3D compliance topology optimization problems involving 400 000 degrees of freedom.
doi:10.2514/6.2015-1799 fatcat:rs6xlanhs5fibbs5mt2scxigwi