Comparison of shape design sensitivity analysis formulations via material derivative-adjoint variable and implicit differentiation techniques for 3-D and 2-D curved boundary element

This paper reviews and compares two different approaches to continuum structural shape design sensitivity analysis: the material derivative-adjoint variable method and the implicit differentiation method using 3-D and 2-D BEM. Employing identical BEA models, curved element technology, numerical integration and equation solving techniques, the similarities and differences of both methods are highlighted. Significant theoretical and computational aspects associated with both methods are presented and accuracy and computational efficiency characteristics are demonstrated. Advantages and disadvantages of both techniques are identified. The characterization provided can aid in the prudent selection between these sensitivity analysis techniques, based on the characteristics of the proposed application.