Written for engineers and students alike, the aim of the book is to provide the necessary theories and techniques of the FEM for readers to be able to use a commercial FEM package to solve primarily linear problems in mechanical and civil engineering with the main focus on structural mechanics and heat transfer.
Fundamental theories are introduced in a straightforward way, and state-of-the-art techniques for designing and analyzing engineering systems, including microstructural systems are explained in detail. Case studies are used to demonstrate these theories, methods, techniques and practical applications, and numerous diagrams and tables are used throughout. Full sets of PowerPoint slides developed by the authors for their course on FEM are available as a free download from a companion website.
I have little experience working with CFD and elect. Typical problem areas of interest include structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The analytical solution of these problems generally require the solution to boundary value problems for partial differential equations. The finite element method formulation of the problem results in a system of algebraic equations.
The method approximates the unknown function over the domain. To solve the problem, it subdivides a large system into smaller, simpler parts that are called finite elements.
The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function.
Using the transport equation for heat transfer as the foundation for the governing equations, this new edition demonstrates the versatility of the method for a wide range of applications, including structural analysis and fluid flow. Much attention is given to the development of the discrete set of algebraic equations, beginning with simple one-dimensional problems that can be solved by inspection, continuing to two- and three-dimensional elements, and ending with three chapters describing applications.
The increased number of example problems per chapter helps build an understanding of the method to define and organize required initial and boundary condition data for specific problems. In addition to exercises that can be worked out manually, this new edition refers to user-friendly computer codes for solving one-, two-, and three-dimensional problems. This textbook is valuable for senior level undergraduates in mechanical, aeronautical, electrical, chemical, and civil engineering.
Useful for short courses and home-study learning, the book can also serve as an introduction for first-year graduate students new to finite element coursework and as a refresher for industry professionals.
Volume1 presents the basis of the FEM for structural analysis and a detailed description of the finite element formulation for axially loaded bars, plane elasticity problems, axisymmetric solids and general three dimensional solids.
Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems. The book includes a chapter on miscellaneous topics such as treatment of inclined supports, elastic foundations, stress smoothing, error estimation and adaptive mesh refinement techniques, among others. The text concludes with a chapter on the mesh generation and visualization of FEM results.
The book will be useful for students approaching the finite element analysis of structures for the first time, as well as for practising engineers interested in the details of the formulation and performance of the different finite elements for practical structural analysis.
The first volume focuses on the use of the method for linear problems. A general procedure is presented for the finite element analysis FEA of a physical problem, where the goal is to specify the values of a field function. First, the strong form of the problem governing differential equations and boundary conditions is formulated. Subsequently, a weak form of the governing equations is established. Finally, a finite element approximation is introduced, transforming the weak form into a system of equations where the only unknowns are nodal values of the field function.
Important concepts for finite element computations, such as isoparametric elements for multi-dimensional analysis and Gaussian quadrature for numerical evaluation of integrals, are presented and explained. Practical aspects of FEA and advanced topics, such as reduced integration procedures, mixed finite elements and verification and validation of the FEM are also discussed.
Provides detailed derivations of finite element equations for a variety of problems. Incorporates quantitative examples on one-dimensional and multi-dimensional FEA. Provides an overview of multi-dimensional linear elasticity definition of stress and strain tensors, coordinate transformation rules, stress-strain relation and material symmetry before presenting the pertinent FEA procedures.
Discusses practical and a. This book presents all of the theoretical aspects of FEM that students of engineering will need. It eliminates overlong math equations in favour of basic concepts, and reviews of the mathematics and mechanics of materials in order to illustrate the concepts of FEM. It introduces these concepts by including examples using six different commercial programs online.
The all-new, second edition of Introduction to Finite Element Analysis and Design provides many more exercise problems than the first edition. It includes a significant amount of material in modelling issues by using several practical examples from engineering applications. The book features new coverage of buckling of beams and frames and extends heat transfer analyses from 1D in the previous edition to 2D.
It also covers 3D solid element and its application, as well as 2D.
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