The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are: (1) Weighted residual methods and Galerkin approximations, (2) A model problem for one-dimensional linear elastostatics, (3) Weak formulations in one dimension, (4) Minimum principles in one dimension, (5) Error estimation in one dimension, (5) Construction of Finite Element basis functions in one dimension, (6) Gaussian Quadrature, (7) Iterative solvers and element by element data structures, (8) A model problem for three-dimensional linear elastostatics, (9) Weak formulations in three dimensions, (10) Basic rules for element construction in three-dimensions, (11) Assembly of the system and solution schemes, (12) Assembly of the system and solution schemes, (13) An introduction to time-dependent problems and (14) A brief introduction to rapid computation based on domain decomposition and basic parallel processing.

The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are: • Weighted residual methods and Galerkin approximations, • A model problem for one-dimensional linear elastostatics, • Weak formulations in one dimension, • Minimum principles in one dimension, • Error estimation in one dimension, • Construction of Finite Element basis functions in one dimension, • Gaussian Quadrature, • Iterative solvers and element by element data structures, • A model problem for three-dimensional linear elastostatics, • Weak formulations in three dimensions, • Basic rules for element construction in three-dimensions, • Assembly of the system and solution schemes, • An introduction to time-dependent problems and • An introduction to rapid computation based on domain decomposition and basic parallel processing. The approach is to introduce the basic concepts first in one-dimension, then move on to three-dimensions. A relatively informal style is adopted. This primer is intended to be a “starting point”, which can be later augmented by the large array of rigorous, detailed, books in the area of Finite Element analysis. In addition to overall improvements to the first edition, this second edition also adds several carefully selected in-class exam problems from exams given over the last 15 years at UC Berkeley, as well as a large number of take-home computer projects. These problems and projects are designed to be aligned to the theory provided in the main text of this primer.

Annotation This book fills a gap within the finite element literature by addressing the challenges and developments in multidiscipli-nary analysis. Current developments include disciplines of structural mechanics, heat transfer, fluid mechanics, controls engineering and propulsion technology, and their interaction as encountered in many practical problems in aeronautical, aerospace, and mechanical engineering, among others. These topics are reflected in the 15 chapter titles of the book. Numerical problems are provided to illustrate the applicability of the techniques. Exercises may be solved either manually or by using suitable computer software. A version of the multidisciplinary analysis program STARS is available from the author. As a textbook, the book is useful at the senior undergraduate or graduate level. The practicing engineer will find it invaluable for solving full-scale practical problems.

The primary goal of Introduction to Finite Element Analysis Using SOLIDWORKS Simulation 2015 is to introduce the aspects of Finite Element Analysis (FEA) that are important to engineers and designers. Theoretical aspects of FEA are also introduced as they are needed to help better understand the operation. The primary emphasis of the text is placed on the practical concepts and procedures needed to use SOLIDWORKS Simulation in performing Linear Static Stress Analysis and basic Modal Analysis. This text covers SOLIDWORKS Simulation and the lessons proceed in a pedagogical fashion to guide you from constructing basic truss elements to generating three-dimensional solid elements from solid models. This text takes a hands-on, exercise-intensive approach to all the important FEA techniques and concepts. This textbook contains a series of fourteen tutorial style lessons designed to introduce beginning FEA users to SOLIDWORKS Simulation. The basic premise of this book is that the more designs you create using SOLIDWORKS Simulation, the better you learn the software. With this in mind, each lesson introduces a new set of commands and concepts, building on previous lessons.

A novel computational procedure called the scaled boundary finite-element method is described which combines the advantages of the finite-element and boundary-element methods : Of the finite-element method that no fundamental solution is required and thus expanding the scope of application, for instance to anisotropic material without an increase in complexity and that singular integrals are avoided and that symmetry of the results is automatically satisfied. Of the boundary-element method that the spatial dimension is reduced by one as only the boundary is discretized with surface finite elements, reducing the data preparation and computational efforts, that the boundary conditions at infinity are satisfied exactly and that no approximation other than that of the surface finite elements on the boundary is introduced. In addition, the scaled boundary finite-element method presents appealing features of its own : an analytical solution inside the domain is achieved, permitting for instance accurate stress intensity factors to be determined directly and no spatial discretization of certain free and fixed boundaries and interfaces between different materials is required. In addition, the scaled boundary finite-element method combines the advantages of the analytical and numerical approaches. In the directions parallel to the boundary, where the behaviour is, in general, smooth, the weighted-residual approximation of finite elements applies, leading to convergence in the finite-element sense. In the third (radial) direction, the procedure is analytical, permitting e.g. stress-intensity factors to be determined directly based on their definition or the boundary conditions at infinity to be satisfied exactly. In a nutshell, the scaled boundary finite-element method is a semi-analytical fundamental-solution-less boundary-element method based on finite elements. The best of both worlds is achieved in two ways: with respect to the analytical and numerical methods and with respect to the finite-element and boundary-element methods within the numerical procedures. The book serves two goals: Part I is an elementary text, without any prerequisites, a primer, but which using a simple model problem still covers all aspects of the method and Part II presents a detailed derivation of the general case of statics, elastodynamics and diffusion.

Designed for students without in-depth mathematical training, this text includes a comprehensive presentation and analysis of algorithms of time-dependent phenomena plus beam, plate, and shell theories. Solution guide available upon request.

Highlights of the book: Discussion about all the fields of Computer Aided Engineering, Finite Element Analysis Sharing of worldwide experience by more than 10 working professionals Emphasis on Practical usuage and minimum mathematics Simple language, more than 1000 colour images International quality printing on specially imported paper Why this book has been written ... FEA is gaining popularity day by day & is a sought after dream career for mechanical engineers. Enthusiastic engineers and managers who want to refresh or update the knowledge on FEA are encountered with volume of published books. Often professionals realize that they are not in touch with theoretical concepts as being pre-requisite and find it too mathematical and Hi-Fi. Many a times these books just end up being decoration in their book shelves ... All the authors of this book are from IIT€™s & IISc and after joining the industry realized gap between university education and the practical FEA. Over the years they learned it via interaction with experts from international community, sharing experience with each other and hard route of trial & error method. The basic aim of this book is to share the knowledge & practices used in the industry with experienced and in particular beginners so as to reduce the learning curve & avoid reinvention of the cycle. Emphasis is on simple language, practical usage, minimum mathematics & no pre-requisites. All basic concepts of engineering are included as & where it is required. It is hoped that this book would be helpful to beginners, experienced users, managers, group leaders and as additional reading material for university courses.

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​

Designed for a one-semester course in Finite Element Method, this compact and well-organized text presents FEM as a tool to find approximate solutions to differential equations. This provides the student a better perspective on the technique and its wide range of applications. This approach reflects the current trend as the present-day applications range from structures to biomechanics to electromagnetics, unlike in conventional texts that view FEM primarily as an extension of matrix methods of structural analysis. After an introduction and a review of mathematical preliminaries, the book gives a detailed discussion on FEM as a technique for solving differential equations and variational formulation of FEM. This is followed by a lucid presentation of one-dimensional and two-dimensional finite elements and finite element formulation for dynamics. The book concludes with some case studies that focus on industrial problems and Appendices that include mini-project topics based on near-real-life problems. Postgraduate/Senior undergraduate students of civil, mechanical and aeronautical engineering will find this text extremely useful; it will also appeal to the practising engineers and the teaching community.