Classical and Advanced Theories of Thin Structures

The book presents an updated state-of-the-art overview of the general aspects and practical applications of the theories of thin structures, through the interaction of several topics, ranging from non-linear thin-films, shells, junctions, beams of different materials and in different contexts (elasticity, plasticity, etc.). Advanced problems like the optimal design and the modeling of thin films made of brittle or phase-transforming materials will be presented as well.

Inhalt

Strain, stress and linearized elasticity.- Constitutive equations and variational elasticity.- An introduction to ?-convergence methods for thin structures.- Concepts in the mechanics of thin structures.- A brief introduction to mathematical shell theory.- Non-Brittle and Brittle Thin Films - Lectures I, II.- A Young measure approach to a nonlinear membrane model - Lecture III.- Bending moment and higher order membrane models-lecture IV.- 3D-2D asymptotic analysis for inhomogeneous thin films - lectures V, VI.