Unilateral problems for nonlinearly elastic plates. (Q2748475)

In the mechanics of structures, there appear problems concerning the deformations of thin elastic plates subjected to bending and buckling and coming in contact with adjacent supports. These problems are strongly nonlinear due to the presence of nonlinear fourth-order differential operators. Multiple solutions can occur which implies the use of the bifurcation theory. Here the author treats such problems theoretically and numerically by using variational or hemivariational inequalities and nonconvex optimization of pseudomonotone operators.NEWLINENEWLINENEWLINEThe following chapter headings reflect in detail the material covered in the book: 1. Mechanical motivations -- the model of von Kármán plates; existence and bifurcations; 2. Topological degrees of generalized monotone operators; 3. Coercive variational inequalities in von Kármán's theory of plates; 4. Noncoercive variational inequalities in von Kármán's theory of plates; 5. Hemivariational inequalities in von Kármán's theory of plates.NEWLINENEWLINENEWLINEA rich bibliography (129 titles) contains many contributions of the author. Any item is presented from three points of view: mechanical, variational and topological. Taking into account many original mathematical results presented in the book, the reviewer believes that the volume is a valuable contribution to the theory of elastic plates.