Chengwan Zhang¹, Kai Long^1,*, Zhuo Chen^1,2, Xiaoyu Yang¹, Feiyu Lu¹, Jinhua Zhang³, Zunyi Duan⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.1, pp. 369-390, 2024, DOI:10.32604/cmes.2023.029876

Abstract This paper aims to propose a topology optimization method on generating porous structures comprising multiple materials. The mathematical optimization formulation is established under the constraints of individual volume fraction of constituent phase or total mass, as well as the local volume fraction of all phases. The original optimization problem with numerous constraints is converted into a box-constrained optimization problem by incorporating all constraints to the augmented Lagrangian function, avoiding the parameter dependence in the conventional aggregation process. Furthermore, the local volume percentage can be precisely satisfied. The effects including the global mass bound, the influence radius and local volume percentage… More >

S.R. Santos¹, L.C. Matioli², A.T. Beck³

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.1, pp. 23-56, 2012, DOI:10.3970/cmes.2012.083.023

Abstract Solution of structural reliability problems by the First Order method require optimization algorithms to find the smallest distance between a limit state function and the origin of standard Gaussian space. The Hassofer-Lind-Rackwitz-Fiessler (HLRF) algorithm, developed specifically for this purpose, has been shown to be efficient but not robust, as it fails to converge for a significant number of problems. On the other hand, recent developments in general (augmented Lagrangian) optimization techniques have not been tested in aplication to structural reliability problems. In the present article, three new optimization algorithms for structural reliability analysis are presented. One algorithm is based on… More >

J.C. Michel¹, H. Moulinec, P. Suquet

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 79-88, 2000, DOI:10.3970/cmes.2000.001.239

Abstract An iterative numerical method based on Fast Fourier Transforms has been proposed by \cite{MOU98} to investigate the effective properties of periodic composites. This iterative method is based on the exact expression of the Green function for a linear elastic, homogeneous reference material. When dealing with linear phases, the number of iterations required to reach convergence is proportional to the contrast between the phases properties, and convergence is therefore not ensured in the case of composites with infinite contrast (those containing voids or rigid inclusions or highly nonlinear materials). It is proposed in this study to overcome this difficulty by using… More >