The finite element method is a generally applicable method for getting numerical solutions. Problems of stress analysis, heat transfer, fluid flow, electric fields, and others have been solved by finite elements. This book emphasizes stress analysis and structural mechanics. Other areas are treated in a way that is easy for stress analysts to understand. The formulation and computation procedures of finite elements are much the same in all areas of application.
This text is introductory and is inclined toward practical application. Theory is presented as needed. The book contains enough material for a two-semester course sequence. By studying this book, an engineer can learn to use finite elements with confidence and effectiveness, and those who want to do advanced work will have a sound physical understanding from which to proceed.
The background for the book is as follows. Undergraduate courses in statics,
dynamics, and mechanics of materials must be mastered. Mathematically, little is needed but the ability to differentiate and integrate sines, cosines, and polynomials. I presume knowledge of matrix operations such as multiplication, transposition, differentiation, and the meaning of an inverse (the calculation procedure for inversion is not essential). Students should be competent in Fortran programming, to the extent of being able to use subroutines, COMMON blocks, and storage such as disc files. Other areas–theory of elasticity, plates and shells, energy methods, numerical analysis–are desirable but not essential. Fortunately, we seldom call on these areas and, when we do, it is usually for their elementary concepts.