1st Edition

Finite Element Method Applications in Solids, Structures, and Heat Transfer

By Michael R. Gosz Copyright 2006
    426 Pages 163 B/W Illustrations
    by CRC Press

    The finite element method (FEM) is the dominant tool for numerical analysis in engineering, yet many engineers apply it without fully understanding all the principles. Learning the method can be challenging, but Mike Gosz has condensed the basic mathematics, concepts, and applications into a simple and easy-to-understand reference.

    Finite Element Method: Applications in Solids, Structures, and Heat Transfer navigates through linear, linear dynamic, and nonlinear finite elements with an emphasis on building confidence and familiarity with the method, not just the procedures. This book demystifies the assumptions made, the boundary conditions chosen, and whether or not proper failure criteria are used. It reviews the basic math underlying FEM, including matrix algebra, the Taylor series expansion and divergence theorem, vectors, tensors, and mechanics of continuous media.

    The author discusses applications to problems in solid mechanics, the steady-state heat equation, continuum and structural finite elements, linear transient analysis, small-strain plasticity, and geometrically nonlinear problems. He illustrates the material with 10 case studies, which define the problem, consider appropriate solution strategies, and warn against common pitfalls. Additionally, 35 interactive virtual reality modeling language files are available for download from the CRC Web site.

    For anyone first studying FEM or for those who simply wish to deepen their understanding, Finite Element Method: Applications in Solids, Structures, and Heat Transfer is the perfect resource.

    INTRODUCTION
    MATHEMATICAL PRELIMINARIES
    Matrix Algebra
    Vectors
    Second-Order Tensors
    Calculus
    Newton's Method
    Kinematics of Motion
    Problems
    ONE-DIMENSIONAL PROBLEMS
    The Weak Form
    Finite Element Approximations
    Plugging in the Trial and Test Functions
    Algorithm for Matrix Assembly
    One-Dimensional Elasticity
    Problems
    LINEARIZED THEORY OF ELASTICITY
    Cauchy's Law
    Principal Stresses
    Equilibrium Equation
    Small-Strain Tensor
    Hooke's Law
    Axisymmetric Problems
    Weak Form of the Equilibrium Equation
    Problems
    STEADY-STATE HEAT CONDUCTION
    Derivation of the Steady-State Heat Equation
    Fourier's Law
    Boundary Conditions
    Weak Form of the Steady-State Heat Equation
    Problems
    CONTINUUM FINITE ELEMENTS
    Three-Node Triangle
    Development of an Arbitrary Quadrilateral
    Four-Node Tetrahedron
    Eight-Node Brick
    Element Matrices and Vectors
    Gauss Quadrature
    Bending of a Cantilever Beam
    Analysis of a Plate with Hole
    Thermal Stress Analysis of a Composite Cylinder
    Problems
    STRUCTURAL FINITE ELEMENTS
    Space Truss
    Euler-Bernoulli Beams
    Mindlin-Reissner Plate Theory
    Deflection of a Clamped Plate
    Problems
    LINEAR TRANSIENT ANALYSIS
    Derivation of the Equation of Motion
    Semi-Discrete Equations of Motion
    Central Difference Method
    Trapezoidal Rule
    Unsteady Heat Conduction
    Problems
    SMALL-STRAIN PLASTICITY
    Basic Concepts
    Yield Condition
    Flow and Hardening Rules
    Derivation of the Elastoplastic Tangent
    Finite Element Implementation
    One-Dimensional Elastoplastic Deformation of a Bar
    Elastoplastic Analysis of a Thick-Walled Cylinder
    Problems
    TREATMENT OF GEOMETRIC NONLINEARITIES
    Large-Deformation Kinematics
    Weak Form in the Original Configuration
    Linearization of the Weak Form
    Snap-Through Buckling of a Truss Structure
    Uniaxial Tensile Test of a Rubber Dog-Bone Specimen
    Problems
    BIBLIOGRAPHY
    INDEX

    Biography

    Michael R. Gosz

    ". . . extremely clearly written, so much so that it could easily be used for self-study . . . achieves an excellent balance between the presentation of fundamental building blocks and the further development and implementation of the theory in the context of specific applications . . . is indeed a very useful addition to the literature on the subject, at the introductory level."

    – Batmanathan D. Reddy, in Zentralblatt Math, 2006, Vol. 1095, No. 21