http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Applications in Solids, Structures, and Heat Transfer
Cover; Half Title; Title Page; Copyright Page; Dedication; Preface; Table of Contents; 1: Introduction; 2: Mathematical Preliminaries; 2.1 Matrix algebra; 2.1.1 Multiplication of a matrix by a scalar; 2.1.2 Transpose of a matrix; 2.1.3 Matrix multiplication; 2.1.4 The identity matrix; 2.1.5 Determinant of a matrix; 2.1.6 Inverse of a matrix; 2.1.7 Linear algebraic equations; 2.1.8 Integration of matrices; 2.2 Vectors; 2.2.1 Vector dot product; 2.2.2 Vector cross product; 2.2.3 Vector transformation; 2.3 Second-order tensors; 2.3.1 Tensor transformation
2.3.2 Eigenvalues and eigenvectors of second-order tensors2.3.3 Common operations with vectors and tensors; 2.4 Calculus; 2.4.1 Fundamental theorem of calculus; 2.4.2 Integration by parts; 2.4.3 Taylor series expansion; 2.4.4 Gradient and divergence; 2.4.5 The level surface; 2.4.6 Divergence theorem; 2.5 Newton's method; 2.5.1 Nonlinear equations of several variables; 2.6 Kinematics of motion; 2.7 Problems; 3: One-Dimensional Problems; 3.1 The weak form; 3.2 Finite element approximations; 3.2.1 The linear-u element; 3.2.2 The quadratic-u element; 3.3 Plugging in the trial and test functions
3.4 Algorithm for matrix assembly3.5 One-dimensional elasticity; 3.5.1 Strain and stress calculation; 3.5.2 Finite element results; 3.6 Problems; 4: Linearized Theory of Elasticity; 4.1 Cauchy's law; 4.2 Principal stresses; 4.3 Equilibrium equation; 4.4 Small-strain tensor; 4.4.1 Relative stretch; 4.4.2 Angle change; 4.4.3 Small-displacement gradients; 4.5 Hooke's law; 4.5.1 Engineering constants; 4.5.2 Hooke's law for plane stress and plane strain; 4.5.3 Hooke's law for thermal stress problems; 4.6 Axisymmetric problems; 4.7 Weak form of the equilibrium equation; 4.8 Problems
5: Steady-State Heat Conduction5.1 Derivation of the steady-state heat equation; 5.2 Fourier's law; 5.3 Boundary conditions; 5.4 Weak form of the steady-state heat equation; 5.5 Problems; 6: Continuum Finite Elements; 6.1 Three-node triangle; 6.1.1 The B-matrix; 6.2 Development of an arbitrary quadrilateral; 6.2.1 Compatibility issues; 6.2.2 The bi-unit square; 6.2.3 The parent domain; 6.2.4 The B-matrix; 6.2.5 Derivatives of the shape functions; 6.2.6 Area change; 6.3 Four-node tetrahedron; 6.3.1 The B-matrix; 6.4 Eight-node brick; 6.4.1 The B-matrix; 6.4.2 Volume change
6.5 Element matrices and vectors6.6 Gauss quadrature; 6.7 Bending of a cantilever beam; 6.8 Analysis of a plate with hole; 6.9 Thermal stress analysis of a composite cylinder; 6.9.1 Heat conduction analysis; 6.9.2 Thermal stress analysis; 6.9.3 Results; 6.10 Problems; 7: Structural Finite Elements; 7.1 Space truss; 7.1.1 Strain-displacement relationship; 7.1.2 Element matrix; 7.1.3 Element vector; 7.2 Euler-Bernoulli beams; 7.2.1 Kinematic assumptions; 7.2.2 Finite element approximations; 7.2.3 Element matrix; 7.2.4 Element vector; 7.3 Mindlin-Reissner plate theory; 7.3.1 Assumptions
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