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

✍ Scribed by Michael R. Gosz (Author)

• Publisher: CRC Press
• Year: 2006
• Leaves: 425
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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

✦ Subjects

Engineering & Technology;Mathematics & Statistics for Engineers;Mechanical Engineering;Thermodynamics