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A structural optimization technique for minimum sensitivity with uncertain parameters uses a nested optimization procedure to directly minimize optimum sensitivity derivatives (OSD) with respect to fixed design parameters. The procedure involves two nested optimization loops with the inner loop containing the primary optimization procedure. The outer loop minimizes an objective function and a sequential quadratic programing procedure gives the Lagrange multipliers for OSD calculation. The technique is demonstrated for a bimetallic beam design and validated through parametric studies.

The application of infeasible path sequential quadratic programming methods in aerodynamics leads to the shape optimization of airfoils. The optimization strategy constitutes physical systems based on nonlinear boundary value problems. During the optimization process, the infeasible path methods require the solution of two or three linear systems. In these systems, the coefficient matrix represents the Jacobian matrix of the flow equations.

A quadratic programming strategy, based on the boundary element method for studying contact of deformable bodies, was found versatile in assessing contact discrepancies, even in cases of multiple loading and gap conditions. The methodology pertains solely to unknown contact fractions, thereby providing for the compactness of the resulting numerical model.