An Introduction to Linear and Nonlinear Finite Element Analysis: A Computational Approach [Hardcover]

Modern finite element analysis has grown into a basic mathematical tool for almost every field of engineering and the applied sciences. This introductory textbook fills a gap in the literature, offering a concise, integrated presentation of methods, applications, software tools, and hands-on projects. Included are numerous exercises, problems, and Mathematica/Matlab-based programming projects. The emphasis is on interdisciplinary applications to serve a broad audience of advanced undergraduate/graduate students with different backgrounds in applied mathematics, engineering, physics/geophysics. The work may also serve as a self-study reference for researchers and practitioners seeking a quick introduction to the subject for their research.Preface.- Notation.- 1 Introduction.- 1.1 Historical Sketch.- 1.2 Euler-Lagrange Equations.- 1.3 Weak Variational Form.- 1.4 Galerkin Method.- 1.5.- 1.6.- 2 One-Dimensional Shape Functions.- 2.1 Local and Global Linear Shape Functions.- 2.2 Local and Global Quadratic Shape Functions.- 2.3 Parametric Coordinates.- 2.4 Hermite Shape Functions.- 2.5 Exercises.- 3 One-Dimensional Second-Order Equation.- 3.1 Galerkin Finite Element Method.- 3.2 Two Dependent Variables.- 3.3 Exercises.- 4 One-Dimensional Fourth-Order Equation.- 4.1 Euler-Bernoulli Beam Equation.- 4.2 Exercises.- 5 Two-Dimensional Elements.- 5.1 Linear Three-Node Triangular Elements.- 5.2 Bilinear Four-Node Rectangular Elements.- 5.3 Global Shape Functions.- 5.4 Triangular Coordinates.- 5.5 Shape Functions on the Sides of a Triangle.- 5.6 Exercises.- 6 Two-Dimensional Problems.- 6.1 Single Dependent Variable Problems.- 6.2 Exercises.- 7 More Two-Dimensional Problems.- 7.1 Heat Transfer.- 7.2 Torsion.- 7.3 Seepage.- 7.4 Fluid Flows.- 7.5 Exercises.- 8 Axisymmetric Heat Transfer.- 8.1 Radial Symmetry.- 8.2 Linear Elements.- 8.3 Linear Elements for Heat Transfer in Fluids.- 8.4 Nonlinear Heat Transfer.- 8l“©