Quasidifferentiability in nonsmooth, nonconvex mechanics
The modern structural analysis and engineering applications require the study of structures with material laws which involve complete ascending or descending vertical branches with monotone and generally nonmonotone graphs. Adhesive contact mechanics, softening and locking effects in concrete and geomaterials, tension cracking effects in masonry structures belong to category of problems where methods of nonsmooth structural analysis are used. The general scheme used in structural analysis and computational mechanics consists of defining a potential energy function and producing the governing equations and inequalities as well as optimality conditions for this potential function, taking into account equality or inequality constraints. The aim of this paper is to review the development of solution methods for such problems. The methods considered employ nonsmooth nonconvex mechanics and quasidifferentiable and codifferentiable optimization of problems involving variational inequalities. Remark. The concept of quasidifferential was given by \textit{V. F. Dem'yanov}, \textit{L. N. Polyakova} and \textit{A. M. Rubinov} in the work [On one generalization of the concept of subdifferential, All Union Conf. on Dynamic Control, 79-84, Sverdlovsk (1979)].
quasidifferentiable and codifferentiable optimization
scientific article; zbMATH DE number 836793
scientific article