Implementation of Some Methods of Shape Design for Variational Inequalities (Journal of Partial Differential Equations, 2013)
In this paper we present some results concerning the optimal shape design problem governed by the fourth-order variational inequalities. The problem can be considered as a model example for the design of the shapes for elastic-plastic problem. The computations are done by finite element method, and the performance criterion is minimized by the material derivative method. We also discuss the error estimates in the appropriate norm and present some numerical results. An example is used to clearly illustrate the essential elements of shape design problems.
Keywords: Sobolev space; convexity; optimal shape design; variational inequalities; approximation; optimization techniques; finite element method; material derivative method