Research Paper

Structural and Multidisciplinary Optimization

, Volume 32, Issue 2, pp 121-132

First online:

Topology optimization of 2D continua for minimum compliance using parallel computing

  • A. MahdaviAffiliated withDepartment of Mechanical and Nuclear Engineering, The Pennsylvania State University
  • , R. BalajiAffiliated withDepartment of Mechanical and Nuclear Engineering, The Pennsylvania State University
  • , M. FreckerAffiliated withDepartment of Mechanical and Nuclear Engineering, The Pennsylvania State University
  • , E. M. MockensturmAffiliated withDepartment of Mechanical and Nuclear Engineering, The Pennsylvania State University Email author 

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Abstract

Topology optimization is often used in the conceptual design stage as a preprocessing tool to obtain overall material distribution in the solution domain. The resulting topology is then used as an initial guess for shape optimization. It is always desirable to use fine computational grids to obtain high-resolution layouts that minimize the need for shape optimization and postprocessing (Bendsoe and Sigmund, Topology optimization theory, methods and applications. Springer, Berlin Heidelberg New York 2003), but this approach results in high computation cost and is prohibitive for large structures. In the present work, parallel computing in combination with domain decomposition is proposed to reduce the computation time of such problems. The power law approach is used as the material distribution method, and an optimality criteria-based optimizer is used for locating the optimum solution [Sigmund (2001)21:120–127; Rozvany and Olhoff, Topology optimization of structures and composites continua. Kluwer, Norwell 2000]. The equilibrium equations are solved using a preconditioned conjugate gradient algorithm. These calculations have been done using a master–slave programming paradigm on a coarse-grain, multiple instruction multiple data, shared-memory architecture. In this study, by avoiding the assembly of the global stiffness matrix, the memory requirement and computation time has been reduced. The results of the current study show that the parallel computing technique is a valuable tool for solving computationally intensive topology optimization problems.

Keywords

Topology optimization Parallel computing Finite element analysis MPI SIMP Domain decomposition