S.Y. Wang^1,2, K.M. Lim^2,3, B.C. Khoo^2,3, M.Y. Wang⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.18, No.3, pp. 155-182, 2007, DOI:10.3970/cmes.2007.018.155

Abstract In this paper, a geometric deformation constrained level set method is presented as an effective approach for structural shape and topology optimization. A level set method is used to capture the motion of the free boundary of a structure. Furthermore, the geometric deformation of the free boundary is constrained to preserve the structural connectivity and/or topology during the level set evolution. An image-processing-based structural connectivity and topology preserving approach is proposed. A connected components labeling technique based on the 4-neighborhood connectivity measure and a binary image is used for the present region identification. The corresponding… More >

S.Y. Wang^1,2, M.Y. Wang³

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.2, pp. 119-148, 2006, DOI:10.3970/cmes.2006.013.119

Abstract In this paper, an implicit free boundary parametrization method is presented as an effective approach for simultaneous shape and topology optimization of structures. The moving free boundary of a structure is embedded as a zero level set of a higher dimensional implicit level set function. The radial basis functions (RBFs) are introduced to parametrize the implicit function with a high level of accuracy and smoothness. The motion of the free boundary is thus governed by a mathematically more convenient ordinary differential equation (ODE). Eigenvalue stability can be guaranteed due to the use of inverse multiquadric… More >

Adnan Ibrahimbegovic¹, Catherine Knopf-Lenoir²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 337-344, 2003, DOI:10.3970/cmes.2003.004.337

Abstract In this work we present an unconventional procedure for combining the optimal shape design and nonlinear analysis in mechanics. The main goal of the presented procedure is to enhance computational efficiency for nonlinear problems with respect to the conventional, sequential approach by solving the analysis and design phases simultaneously. A detailed development is presented for the chosen model problem, the 3d rod undergoing large rotations. More >

H. Okumura¹, M. Kawahara¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 71-78, 2000, DOI:10.3970/cmes.2000.001.231

Abstract This paper presents a new approach to a shape optimization problem of a body located in the unsteady incompressible viscous flow field based on an optimal control theory. The optimal state is defined by the reduction of drag and lift forces subjected to the body. The state equation used is the transient incompressible Navier--Stokes equations. The shape optimization problem can be formulated to find out geometrical coordinates of the body to minimize the performance function that is defined to evaluate forces subjected to the body. The fractional step method with the implicit temporal integration and More >