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.

This classic book covers the solution of differential equations in science and engineering in such as way as to provide an introduction for novices before progressing toward increasingly more difficult problems. The Method of Weighted Residuals and Variational Principles describes variational principles, including how to find them and how to use them to construct error bounds and create stationary principles. The book also illustrates how to use simple methods to find approximate solutions, shows how to use the finite element method for more complex problems, and provides detailed information on error bounds. Problem sets make this book ideal for self-study or as a course text.

Unification of Finite Element Methods

The finite difference method (FDM) hasbeen used tosolve differential equation systems for centuries. The FDM works well for problems of simple geometry and was widely used before the invention of the much more efficient, robust finite element method (FEM). FEM is now widely used in handling problems with complex geometry. Currently, we are using and developing even more powerful numerical techniques aiming to obtain more accurate approximate solutions in a more convenient manner for even more complex systems. The meshfree or meshless method is one such phenomenal development in the past decade, and is the subject of this book. There are many MFree methods proposed so far for different applications. Currently, three monographs on MFree methods have been published. Mesh Free Methods, Moving Beyond the Finite Element Method d by GR Liu (2002) provides a systematic discussion on basic theories, fundamentals for MFree methods, especially on MFree weak-form methods. It provides a comprehensive record of well-known MFree methods and the wide coverage of applications of MFree methods to problems of solids mechanics (solids, beams, plates, shells, etc.) as well as fluid mechanics. The Meshless Local Petrov-Galerkin (MLPG) Method d by Atluri and Shen (2002) provides detailed discussions of the meshfree local Petrov-Galerkin (MLPG) method and itsvariations. Formulations and applications of MLPG are well addressed in their book.

This is an advanced modern textbook on thermal stresses. It serves a wide range of readers, in particular, graduate and postgraduate students, scientists, researchers in various industrial and government institutes, and engineers working in mechanical, civil, and aerospace engineering. This volume covers diverse areas of applied mathematics, continuum mechanics, stress analysis, and mechanical design. This work treats a number of topics not presented in other books on thermal stresses, for example: theory of coupled and generalized thermoelasticity, finite and boundary element method in generalized thermoelasticity, thermal stresses in functionally graded structures, and thermal expansions of piping systems. The book starts from basic concepts and principles, and these are developed to more advanced levels as the text progresses. Nevertheless, some basic knowledge on the part of the reader is expected in classical mechanics, stress analysis, and mathematics, including vector and cartesian tensor analysis. This 2nd enhanced edition includes a new chapter on Thermally Induced Vibrations. The method of stiffness is added to Chapter 7. The variational principle for the Green-Lindsay and Green-Naghdi models have been added to Chapter 2 and equations of motion and compatibility equations in spherical coordinates to Chapter 3. Additional problems at the end of chapters were added.