Shape design sensitivity analysis with respect to the positioning of features in composite structures using the boundary element method

• Published in: Engineering analysis with boundary elements Vol. 30; no. 1; pp. 1 - 13
• Main Author: Tafreshi, Azam
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 2006; Elsevier
• Subjects: Anisotropic materials; Boundary element method; Boundary-integral methods; Composites; Computational techniques; Design sensitivity analysis; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; Minimum compliance; Optimum positioning of features; Physics; Shape optimisation; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Design sensitivity analysis; Composites; Optimum positioning of features; Shape optimisation; Minimum compliance; Boundary element method; Anisotropic materials; Geometrical shape; Positioning; Mean field approximation; Hole; Sensitivity analysis; Anisotropic material; Boundary integral method; Modeling; Geometrical model; Optimization; Search algorithm; Cavity; Integral equation; Non linear effect; Structural analysis
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/j.enganabound.2005.08.003

This paper presents the application of the boundary element method to the shape design sensitivity analysis of composite structures with holes and cutouts. A two-dimensional (2D) anisotropic domain, which contains a number of voids of arbitrary shapes will be considered. The objective is to perform the design sensitivity analysis of the structure with respect to the translation and rotation of the voids using the boundary element method. A directly differentiated form of the boundary integral equation, with respect to geometric design variables is used to calculate the shape design sensitivities for anisotropic materials. The response sensitivity analysis, with respect to the design variables such as feature positions and orientations, is achieved by the definition of appropriate design velocity fields for these variables. To find the optimum positions of the features within an anisotropic structure with the highest stiffness, the elastic compliance of the structure has been minimized subject to constraints upon stresses and geometry. Due to the non-linear nature of the mean compliance and stresses, the numerical optimisation algorithm used is the feasible direction method, together with the golden section method for the 1D search. A couple of test cases have been performed to verify the proposed method.