The analytical formulation of accurate and efficient techniques for obtaining structural design sensitivities of three-dimensional solid objects using the boundary element approach will be developed. A new design sensitivity analysis (DSA) will be formulated by performing implicit differentiation of the three-dimensional boundary integral system equations. This efficient DSA will be developed to allow the use of the same triangular factors of the system matrix that are formed in a previous stress analysis step. The right-hand side vectors required in this approach will be derived by two different strategies and their respective performances will be investigated. A semi- analytical univariate perturbation/finite difference algorithm and a formulation involving differentiating boundary integrals will be developed. Algorithms for recognition and exploitation of significant matrix sparsity that occurs in DSA of objects with geometrically insensitive regions will be developed. Accurate numerical integration algorithms using appropriate orders for efficient evaluation will be developed for the new matrices associated with three-dimensional DSA. A formulation for the efficient calculation of sensitivities of all components of the stress tensor on the surface of an object will also be developed. This approach will use boundary displacement and traction solutions and avoid the need for any additional numerical integrations. The above developments will be integrated in a unified systems for DSA research for complex three-dimensional components.
