A novel minimum weight formulation of topology optimization implemented with reanalysis approach

Abstract

In this paper, we develop an efficient diagonal quadratic optimization formulation for minimum weight design problem subject to multiple constraints. A high-efficiency computational approach of topology optimization is implemented within the framework of approximate reanalysis. The key point of the formulation is the introduction of the reciprocal-type variables. The topology optimization seeking for minimum weight can be transformed as a sequence of quadratic program with separable and strictly positive definite Hessian matrix, thus can be solved by a sequential quadratic programming approach. A modified sensitivity filtering scheme is suggested to remove undesirable checkerboard patterns and mesh dependence. Several typical examples are provided to validate the presented approach. It is observed that the optimized structure can achieve lighter weight than those from the established method by the demonstrative numerical test. Considerable computational savings can be achieved without loss of accuracy of the final design for 3D structure. Moreover, the effects of multiple constraints and upper bound of the allowable compliance upon the optimized designs are investigated by numerical examples. KEYWORDS approximate reanalysis, multigrid preconditioned conjugate gradients, preconditioned conjugate gradient, sequential quadratic programming, topology optimization INTRODUCTIONStructural topology optimization spawns from the seminal work by Bendsøe and Kikuchi. 1 In the past few decades, density-based topology optimization method has gained significant progress in a wide range of engineering fields and disciplines. The available state-of-the-art reviews on the latest developments in this field can be found in related works 2-4 and the references therein.Despite tremendous advances in computer performance, large-scale topology optimizations is still a challenge involving intensive computational cost. Reduction of computational effort in topology optimization has been investigated from various standpoints. One of the possible trajectories is the introduction of high-resolution with lower computational cost, thus circumventing the burn of solving the FE equation on a fine mesh. Kim and Yoon initially presented the new concept, Int J Numer Methods Eng. 2019;120:567-579.wileyonlinelibrary.com/journal/nme

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