Finite and Boundary Element Methods in Engineering

O.P. Gupta

• Verlag: Routledge
• Jahr: 2022
• ISBN:
  9781351448635
• Auflage: 1
• Thema: Technik & Maschinenbau
• Thema: Elektrotechnik & Telekommunikation

The interest in finite element method as a solution technique of the computer age is reflected in the availability of many general and special purpose software based on this technique. This work aims to provide a complete and detailed explanation of the basics of the application areas.

Chapter 1 INTRODUCTION AND BASIC CONCEPTS

DOI: 10.1201/9780203756041-1

1.1 INTRODUCTION

The finite element method (FEM) has now become a very important tool of engineering analysis. Its versatility is reflected in its popularity among engineers and designers belonging to nearly all the engineering disciplines. Whether a civil engineer designing bridges, dams, harbours or a mechanical engineer designing auto engines, rolling mills, machine tools or an aerospace engineer interested in analysis of dynamics of an aeroplane or temperature rise in the heat shield of a space shuttle or a metallurgist concerned about the influence of a rolling operation on the microstructure of a rolled product or an electrical engineer interested in analysis of the electromagnetic field in electrical machinery—all find the finite element method quite handy and useful. It is not that these problems remained unproved before the finite element method came into vogue; rather this method has become popular due to its relative simplicity of approach and accuracy of results. Before going into detail we shall look at the limitations of the traditional approach to design and analysis and then see how neatly FEM overcomes them. The boundary element method is a sister technique inheriting many advantages of FEM.

Traditional methods of engineering analysis, while attempting to solve an engineering problem mathematically, always try for simplified formulation in order to overcome the various complexities involved in exact mathematical formulation. Here we consider some examples which illustrate the approach generally followed for solution of some engineering problems.

The behaviour of an engineering system or its components is governed by various laws of nature, such as Newton’s laws of motion for study of dynamic behaviour of moving bodies, Fourier law of heat conduction for analysis of temperature distribution in solids, Stokes’ law or the Navier-Stokes’ equation for study of motion of viscous fluids, Young’s law or various forms of force-stress-strain relationship for study of load-bearing capabilit...