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

Abstract

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 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 one-dimensional search. A couple of test cases have been performed to verify the proposed method.

Fracture Mechanics Analysis of Composite Structures Using the Boundary Element Shape Sensitivities

“…The advantage of the proposed method was that it can be applied to any geometry, not necessarily regular shapes. However, when entire segments of the boundary or domain were governed by a single variable such as radius, the relevant velocity terms were applied together in the sensitivity analysis with respect to that variable [19] to determine the gradients of the objective function and the constraints. It was shown that, if the entire boundary is governed by a single geometric variable (), such as radius, the material derivative F with respect to the variable can be written as Here, using a similar approach the crack length of arbitrary geometric shape is selected as the shape design variable.…”

“…The objective of the work in Ref. [19] is directed towards the optimal positioning of features in anisotropic structures for maximum stiffness, while the weight remains unchanged. For this purpose, the design sensitivity analysis, with respect to the translation and rotation of the voids of arbitrary shapes using the BEM, was performed.…”

“…The advantage of the proposed method is that it can be applied to any geometry, not just regular shapes. However, when entire segments of the boundary or domain are governed by a single variable such as radius, the relevant velocity terms are applied together in the sensitivity analysis with respect to this variable [19].…”

“…Once J 1 or the derivative of the strain energy with respect to the crack length extension is obtained then K II can be obtained by substituting equation (19) (20) IV.…”

Shape sensitivity analysis of composites in contact using the boundary element method

“…The boundary element method being a surfaceoriented technique is well suited for shape optimization problems [1][2][3][4][5]. Tafreshi, A. Feb. 2009 In : Engineering Analysis with Boundary Elements.…”