The Effect of Anisotropy on the Structure Optimization Using Golden-Section Search Algorithm Based on BEM

Aims: A shape optimization technique is developed, using the boundary element method, for two-dimensional anisotropic structures to study the effects of anisotropy on the displacements and stresses, then minimize weight while satisfying certain constraints upon stresses and geometry.

Study Design: Original Research Paper.

Place and Duration of Study: Jamoum University College, Mathematics Department, between June 2016 and July 2017.

Methodology: The shape design sensitivity analysis of a two-dimensional anisotropic structure using a singular formulation of the boundary element method is investigated to study the effects of anisotropy on the displacements and stresses. An Implicit differentiation technique of the discretized boundary integral equations is performed to produce terms that contain derivatives of the fundamental solutions employed in the analysis. This technique allows the coupling between optimization technique and numerical boundary element method (BEM) to form an optimum shape design algorithm that yields shape design sensitivities of the displacement and stress fields for anisotropic materials with very high accuracy. The fundamental solutions of displacements and tractions in terms of complex variables employed in the analysis. The feasible direction method was developed and implemented for use with the golden-section search algorithm based on BEM as a numerical optimization technique for minimizing weight while satisfying all of the constraints.

Results: The proposed method has been verified by using the two-dimensional plate with an elliptical hole as the numerical example. The numerical results show that the proposed method is suitable and effective tool for the computer implementation of the solution.

Conclusion: From the research that has been performed, it is possible to conclude that the optimal shape of the two-dimensional plate with an elliptical hole is crucial when elastic field is sensitive to boundary shape. Also from this knowledge of the effects of anisotropy on the displacements and stresses, we can design various anisotropic structures to meet specific engineering requirements and utilize within which to place new information can be more effective.