Chapter 1 - The Standard Discrete System and Origins of the Finite Element Method

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Abstract

This chapter describes discrete systems and their mathematical representation by what we define as a standard discrete system. The system is defined by components we call elements which are joined together at discrete points we call nodes. Today, discrete problems can generally be solved using computers even if the number of elements is very large. Systems which are continuous are often defined using differential equations or equivalent statements which imply an infinite number of elements. Engineering solutions to continuous problems can be attained using discretization methods. This volume presents a view of the finite element method as a general discretization procedure of continuous systems.

Finite element analyses follow a standard pattern which is universally adaptable to all discrete systems. The goal of this volume is to show how finite element methods lead to a standard discrete system. This chapter is primarily concerned with establishing the processes applicable to such systems.

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