Handbook of Continuum Mechanics: General Concepts, Thermoelasticity

I. Modelling the Continuum.- II. Deformation.- III. Kinematics.- IV. The Virtual Work Approach to the Modelling of Forces.- V. Modelling Forces in Continuum Mechanics.- VI. Local Analysis of Stresses.- VII. Thermoelasticity.- VIII. Thermoelastic Processes and Equilibrium.- IX. Classic Topics in Three-Dimensional Elasticity.- X. Variational Methods in Linearised Thermoelasticity.- XI. Statics of One-Dimensional Media.- XII. Thermoelastic Structural Analysis.- Appendices.- I. Element of Tensor Calculus.- 1 Tensors on a Vector Space.- 1.1 Definition.- 1.2 First Rank Tensors.- 1.3 Second Rank Tensors.- 2 Tensor Product of Tensors.- 2.1 Definition.- 2.2 Examples.- 2.3 Product Tensors.- 3 Tensor Components.- 3.1 Definition.- 3.2 Change of Basis.- 3.3 Mixed Second Rank Tensors.- 3.4 Twice Contravariant or Twice Covariant Second Rank Tensors.- 3.5 Components of a Tensor Product.- 4 Contraction.- 4.1 Definition of the Contraction of a Tensor.- 4.2 Contracted Multiplication.- 4.3 Doubly Contracted Product of Two Tensors.- 4.4 Total Contraction of a Tensor Product.- 4.5 Defining Tensors by Duality.- 4.6 Invariants of a Mixed Second Rank Tensor.- 5 Tensors on a Euclidean Vector Space.- 5.1 Definition of a Euclidean Space.- 5.2 Application: Deformation in a Linear Mapping.- 5.5 First Rank Euclidean Tensors and the Contracted Product.- 5.6 Second Rank Euclidean Tensors of Simple Product Form and their Contracted Products.- 5.7 Second Rank Euclidean Tensors.- 5.10 Principal Axes and Principal Values of a Real Symmetric Second Rank Euclidean Tensor.- 6 Tensor Fields.- 6.1 Definition.- 6.2 Derivative and Gradient of a Tensor Field.- 6.3 Divergence of a Tensor Field.- 6.4 Curvilinear Coordinates.- Summary of Main Formulas.- II. Differential Operators: Basic Formulas.- 1 Orthonormal Cartesian Coordinates.- 1.1 Coordinates.- 1.2 Vector Field.- 1.3 Scalar Function.- 1.4 Second Rank Tensor Field.- 2 General Cartesian Coordinates.- 2.1 Coordinates.- 2.2 Vector Field.- 2.3 Scalar Function.- 2.4 Second Rank Tensor Field.- 3 Cylindrical Coordinates.- 3.1 Parametrisation.- 3.2 Vector Field.- 3.3 Scalar Function.- 3.4 Symmetric Second Rank Tensor Field.- 4 Spherical Coordinates.- 4.1 Parametrisation.- 4.2 Vector Field.- 4.3 Scalar Function.- 4.4 Symmetric Second Rank Tensor Field.- III. Elements of Plane Elasticity.- 1 Plane Problems.- 2 Plane Strain Thermoelastic Equilibrium.- 2.1 Plane Linearised Strain Tensor.- 2.2 Plane Strain Displacement Field.- 2.3 Plane Strain Thermoelastic Equilibrium in a Homogeneous and Isotropic Material.- 2.4 Solution by the Displacement Method.- 2.5 Solution by the Stress Method.- 2.6 Remarks on the Plane Strain Two-Dimensional Problem.- 2.7 Two-Dimensional Beltrami-Michell Equation.- 2.8 Body Forces Deriving from a Potential. Airy Function.- 2.9 Cylindrical Tube Under Pressure.- 3 Plane Stress Thermoelastic Equilibrium.- 3.1 Plane Stress Tensor.- 3.2 Plane Stress Field.- 3.3 Plane Stress Thermoelastic Equilibrium in a Homogeneous and Isotropic Material.- 3.4 Solution.- 3.5 Cylindrical Tube Under Pressure.- Summary of Main Formulas.