The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical solution of the equations governing the discrete model. Though the theory and methods are sufficiently general to be applied to any nonlinear problem, emphasis has been placed on problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity. Problems in rarefied gas dynamics and nonlinear partial differential equations are also examined.
Other topics include topological properties of finite element models, applications to linear and nonlinear boundary value problems, and discrete models of nonlinear thermomechanical behavior of dissipative media. This comprehensive text is valuable not only to students of structural analysis and continuum mechanics but also to professionals researching the numerical analysis of continua 目录
I. Preliminary Discussions
  1. Introduction
  2. The Finite-Element Concept
  3. Mechanics of Continua
  4. Kinematic Preliminaries
  5. Kinetic Preliminaries
II. Theory of Finite Elements
  6. Introduction to the Concept of Finite Elements
  7. Finite-Element Models of General Functions
  8. Higher-Order Representations
  9. Theory of Conjugate Approximations
  10. Finite Elements and Interpolation Functions
  11. Selected Applications
III. Thermomechanical Behavior of Finite Elements of Continuous Media
  12. Thermodynamic Preliminaries
  13. Thermomechanics of a Finite Element
  14. Constitutive Equations
IV. Finite Elasticity
  15. Foundations of the Theory of Elasticity
  16. Finite Elements of Elastic Bodies
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