Abstract
Nonconvex and nonsmooth optimization problems arise in advanced engineering analysis and structural analysis applications. In fact the set of inequality and complementarity relations that describe the structural analysis problem are generated as optimality conditions by the quasidifferential potential energy optimization problem. Thus new kind of variational expressions arise for these problems, which generalize the classical variational equations of smooth mechanics, the variational inequalities of convex, nonsmooth mechanics and give a solid, computationally efficient explication of hemivariational inequalities of nonconvex, nonsmooth mechanics. Moreover quasidifferential calculus and optimization software make this approach applicable for a large number of problems. The connection of quasidifferential optimization and nonsmooth, nonconvex mechanics is discussed in this paper. A number of representative examples from elastostatic analysis applications are treated in details. Numerical examples illustrate the theory.
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Stavroulakis, G.E., Dem'yanov, V.F. & Polyakova, L.N. Quasidifferentiability in nonsmooth, nonconvex mechanics. J Glob Optim 6, 327–345 (1995). https://doi.org/10.1007/BF01100082
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DOI: https://doi.org/10.1007/BF01100082