An Introduction to Nonlinear Finite
Element Analysis

An Introduction to Nonlinear Finite
Element Analysis

An Introduction to Nonlinear Finite
Element Analysis

One of the most important thing engineers and scientists do is to model natural
phenomena. They develop conceptual and mathematical models to simulate
physical events, whether they are aerospace, biological, chemical, geological,
or mechanical. The mathematical models are developed using laws of physics
and they are often described in terms of algebraic, differential, and/or integral
equations relating various quantities of interest.
A mathematical model can be broadly deÞned as a set of relationships
among variables that express the essential features of a physical system or
process in analytical terms. The relationships that govern the system take the
form of algebraic, differential, and integral equations. Mathematical models of
physical phenomena are often based on fundamental scientiÞclawsofphysics
such as the principle of conservation of mass, the principle of conservation of
linear momentum, and the principle of conservation of energy. Mathematical
models of biological and other phenomena may be based on observations and
accepted theories. Keeping the scope of the present study in mind, we limit
our discussions to engineering systems that are governed by laws of continuum
mechanics.
Mathematical models of engineering systems are often characterized by very
complex equations posed on geometrically complicated regions. Consequently,
many of the mathematical models, until the advent of electronic computation,
were drastically simpliÞed in the interest of analytically solving them. Over
the last three decades, however, the computer has made it possible, with
the help of mathematical models and numerical methods, to solve many
practical problems of science and engineering. There now exists a new and
growing body of knowledge connected with the use of numerical methods and
computers to analyze mathematical models of physical systems, and this body
is known as computational mechanics. Major established industries such as
the automobile, aerospace, chemical, pharmaceutical, petroleum, electronics
and communications, as well as emerging industries such as biotechnology, rely
on computational mechanics—based capabilities to simulate complex systems

J. N. REDDY