Integrodifferential Relations in Linear Elasticity (Studies in Mathematical Physics)

Hardcover, x + 280 pages, NOT ex-library. Clean and bright interior with unmarked text, free of inscriptions and stamps, firmly bound. Two small scuffed areas on the front board; some gentle indentations to edges. Issued without a dust jacket. -- Deformations of elastic bodies are encountered in many areas in science, engineering and technology. In the last decades, various numerical approaches using the finite element technique have been developed, but many are not adequate to address the full complexity. This work treats the elasticity of deformed bodies, including the resulting interior stresses and displacements. Other than comparable books, this work also takes into account that some of constitutive relations can be considered in a weak form. To discuss this problem properly, the method of integrodifferential relations is used, and an advanced numerical technique for stress-strain analysis is presented and evaluated using various discretization techniques. The methods presented in this book are of importance for almost all elasticity problems in materials science and mechanical engineering. -- Contents: 1 Introduction 2 Basic concepts of the linear theory of elasticity: - Stresses - Linear strains - Constitutive relations - Boundary value problems [Static statements; Dynamic problems] - Simplified models [Elastic rods and strings; Beam models; Membranes; Plane stress and strain states] 3 Conventional variational principles: - Classical variational approaches [Energy relations; Direct principles; Complementary principles] - Variational principles in dynamics - Generalized variational principles [Relations among variational principles; Semi-inverse approach] - Finite dimensional discretization [Ritz method; Galerkin method; Finite element method; Boundary element method] 4 The method of integrodifferential relations: - Basic ideas [Analytical solutions in linear elasticity; Integral formulation of Hooke's law] - Family of quadratic functionals - Ritz method in the MIDR [Algorithm of polynomial approximations; 2D clamped plate - static case] - 2D natural vibrations [Eigenvalue problem; Free vibrations of circular and elliptic membranes] 5 Variational properties of the integrodifferential statements: - Variational principles for quadratic functionals - Relations with the conventional principles - Bilateral energy estimates - Body on an elastic foundation [Variational principle for the energy error functional; Bilateral estimates] 6 Advance finite element technique: - Piecewise polynomial approximations - Smooth polynomial splains [Argyris triangle; Stiffness matrix for the Argyris triangle; E2 approximations for a triangle element] - Finite element technique in linear elasticity problems - Mesh adaptation and mesh refinement 7 Semi-discretization and variational technique: - Reduction of PDE system to ODEs [Beam-oriented notation; Semi-discretization in the displacements; Semi-discretization in the stresses] - Analysis of beam stress-strain state - 2D elastic beam vibrations 8 An asymptotic approach: - Classical variational approach - Integrodifferential approach [Basic ideas of asymptotic approximations; Beam equations - general case of loading] - Elastic beam vibrations [Statement of an eigenvalue problem; Longitudinal vibrations; Lateral vibrations] - 3D static problem 9 A projection approach: - Projection formulation of linear elasticity problems - Projections vs. variations and asymptotics 10 3D static beam modeling: - Projection algorithms - Cantilever beam with the triangular cross section - Projection beam model - Characteristics of a beam with the triangular cross section 11 3D beam vibrations: - Integral projections in eigenvalue problems - Natural vibrations of a beam with the triangular cross section - Forced vibrations of a beam with the triangular cross section; A. Vectors and tensors B. Sobolev spaces; Bibliography; Index.…