Sensitivity Analysis of Problems of Elasticity with Unilateral Constraints*

ABSTRACT A unified approach is developed for sensitivity analyses of unilateral problems for discrete and continuous elastic structures. Sensitivity analyses are crucial in problems of redesign or optimization of structures. The topic covers, in this paper, the problem of determining the variation of structural response, subject to variations of ihe design, material, and loading. This type of problem is inherently nonlinear and nondifFerentiable for structures with unilateral constraints and, in general, only directional sensitivities can be obtained. Employing modern methods of functional analysis and the principle of minimum potential energy, a general result is presented for determination of sensitivities, and the implications for discrete or discretized structures are discussed in some detail. Four example problems are used to illustrate different aspects of the sensitivity analysis and to show how to handle variations of unilateral constraints.