Finite Element Applications

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.

This volume on some recent aspects of finite element methods and their applications is dedicated to Ulrich Langer and Arnd Meyer on the occasion of their 60th birthdays in 2012. Their work combines the numerical analysis of finite element algorithms, their efficient implementation on state of the art hardware architectures, and the collaboration with engineers and practitioners. In this spirit, this volume contains contributions of former students and collaborators indicating the broad range of their interests in the theory and application of finite element methods.

This book provides several applications of the finite element method (FEM) for solving real-world problems. This book describes the development of FEM and discusses and illustrates its specific applications.

This textbook demonstrates the application of the finite element philosophy to the solution of real-world problems and is aimed at graduate level students, but is also suitable for advanced undergraduate students. An essential part of an engineer’s training is the development of the skills necessary to analyse and predict the behaviour of engineering systems under a wide range of potentially complex loading conditions. Only a small proportion of real-life problems can be solved analytically, and consequently, there arises the need to be able to use numerical methods capable of simulating real phenomena accurately. The finite element (FE) method is one such widely used numerical method.

The Finite Element Method and Applications with ANSYS® provides the reader with theoretical and practical knowledge of the finite element method and with the skills required to analyze engineering problems with ANSYS®, a commercially available FEA program. This self-contained, introductory text minimizes the need for additional reference material, covering the fundamental topics in finite element methods, as well as advanced topics concerning modeling and analysis with ANSYS®.

This book serves as a practical guide to simulation of 3D deformable solids using the Finite Element Method (FEM). It reviews a number of topics related to the theory and implementation of FEM approaches: measures of deformation, constitutive laws of nonlinear materials, tetrahedral discretizations, and model reduction techniques for real-time simulation.

In teaching an introduction to the finite element method at the undergraduate level, a prudent mix of theory and applications is often sought. In many cases, analysts use the finite element method to perform parametric studies on potential designs to size parts, weed out less desirable design scenarios, and predict system behavior under load. In this book, we discuss common pitfalls encountered by many finite element analysts, in particular, students encountering the method for the first time. We present a variety of simple problems in axial, bending, torsion, and shear loading that combine the students' knowledge of theoretical mechanics, numerical methods, and approximations particular to the finite element method itself.