## Classical and Advanced Theories of Thin Structures: Mechanical and Mathematical Aspects (Google eBook)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. |

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Anal assume assumptions asymptotic analysis body boundary conditions bounded Calculus of Variations Christoffel symbols constant contravariant convergence convex covariant components covariant derivatives curvature curve curvilinear coordinates daa3 daap defined definition deformation denote displacement field domain Dret elastic shell elasticity tensor energy functional equations equilibrium exists Figure finite Fonseca G H1 G uj Gaufi given gradient Hence immersion implies internal constraints Koiter Korn's inequality Lemma lim sup liminf linearized elasticity linearly lower semicontinuity LP(Q Math Mathematical matrix Mech mechanics membrane method Miara middle surface nonlinear norm open subset P.G. Ciarlet Paroni plate theory Podio-Guidugli problem proof quasiconvex Radon measure reactive stress reference configuration Reissner-Mindlin respect satisfies scaling second fundamental forms solution space stored-energy stress field symmetric symmetric matrix tangent plane Theorem thin films thin structures three-dimensional two-dimensional unique vector field Young measures