Continuum MechanicsThe mechanics of fluids and the mechanics of solids represent the two major areas of physics and applied mathematics that meet in continuum mechanics, a field that forms the foundation of civil and mechanical engineering. This unified approach to the teaching of fluid and solid mechanics focuses on the general mechanical principles that apply to all materials. Students who have familiarized themselves with the basic principles can go on to specialize in any of the different branches of continuum mechanics. This text opens with introductory chapters on matrix algebra, vectors and Cartesian tensors, and an analysis of deformation and stress. Succeeding chapters examine the mathematical statements of the laws of conservation of mass, momentum, and energy as well as the formulation of the mechanical constitutive equations for various classes of fluids and solids. In addition to many worked examples, this volume features a graded selection of problems (with answers, where appropriate). Geared toward undergraduate students of applied mathematics, it will also prove valuable to physicists and engineers. Book jacket. |
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A₁ A2 and A3 axis B₁ base vectors cartesian tensors Cijk column matrices constants constitutive equation continuum mechanics coordinate system coordinates XR D₁ defined deformation denote dyadic product e₁ eigenvalues eigenvectors example ƏXR ƏXS function given Hence I₁ incompressible infinitesimal strain invariants isotropic isotropic tensor linear elastic magnitude material line element matrix of components nents normal orthogonal matrix orthogonal tensor outer product particle plane polar decomposition position vector positive definite principal axes principal directions principal stretches principal values proper orthogonal quantities reference configuration relation rigid-body motion rotation scalar second-order tensor Section simple shearing spherical polar coordinates square matrix strain tensor stress components stress tensor summation convention Suppose symmetric tensor system with base T₁ T₁₁ tensor of order theorem theory tion transform unit vector v₁ v₂ vectors ē velocity viscoelasticity x-axis x₁ X₂ zero ди диз дх მა