Contents



Preface

The finite element method (FEM) is a widely used technique for numerical simulations in many areas of science and engineering. The method has gained increased popularity over the years for the solution of complex mathematical problems. It is now a powerful and popular numerical method for solving partial differential equations, with flexibility in dealing with complex geometric domains and various boundary conditions. Although the method has been extensively used in the field of structural mechanics, it has also been successfully applied to solve several other types of engineering problems, such as heat conduction, fluid dynamics, seepage flow, and electric and magnetic fields. In particular, FEM has been successfully applied to fluid-structure interaction, thermomechanical, thermochemical, and thermo-chemo-mechanical problems, biomechanics, biomedical engineering, piezoelectricity, ferroelectricity, electromagnetics, and

An important advantage of FEM, and the main reason for its popularity among academics and industrial developers, is the ability to handle mathematical problems on domains with arbitrary geometry. An attractive feature is the ability to generate solutions to problems governed by linear and nonlinear differential equations. Moreover, FEM enjoys a firm theoretical foundation that is mostly free of ad hoc schemes and heuristic numerical approximations, thereby inspiring confidence in

This book provides several applications of FEM for solving real-world problems. It is a useful resource for students in science and engineering, researchers with diverse educational background, practicing scientists and engineers, computational

Chapter 1 introduces the method for several one-dimensional and two-dimensional model problems. The remaining chapters consider applications of FEM to several problems. These applications include fluid problems, magnetostatic and magnetodynamic problems, stress predictions of early-age concrete members, application on cell migration, dentistry, nanotechnology research, ship composite-based on aluminum, and nonlinear solid mechanics. The emphasis of the text is on the simulation of several physical phenomena of FEM, but many mathematical and

Chapter 1 provides a summary of FEM. Since the remaining chapters of this textbook are based on FEM, we present it in the first chapter as a general method for approximating solutions of ordinary differential equations (ODEs) and partial differential equations (PDEs). To be more specific, we use simple one-dimensional

Chapter 2 studies the pulsatile flow of blood with different physiological pressure conditions and altered gravity. It summarizes the investigation on the effects of hypertension in comparison with normal blood pressure on normal and stenosed carotid artery bifurcation. In addition, it discusses the effects of

more.

the physical relevance of the solution.

scientists, and applied mathematicians.

numerical aspects to important problems are also given.

and two-dimensional model problems to introduce FEM.
