# Computer Aided Structural Analysis: The Finite Element Method

## Abstract

The design process is a complex and tedious one. Within it, the task of design verification appears to require the lion's share of time, effort, and money involved.

The design formulation activity requires creative people, placed in an environment where they are able to formulate ideas which eventually become the manufactured products of an organization. This task takes up comparatively little of the time and effort of the design cycle. Therefore, it would appear that the greatest savings could be made in the design analysis task. Further, if these savings can be made earlier in the design cycle, in the prototype, preprototype, and even the concept ' phases, they would generate even greater savings in time and money. Such savings could then allow analysis of a greater number of design alternatives, and a more optimum design could be selected for the product at an earlier date.

In one form or another, design evaluation involves some form of modeling. Physical models may be of any size ratio with respect to the final product and may be made of whatever material is most suitable for the desired results. In testing, these models are placed in conditions analogous to the conditions which the product is expected to encounter. The use of such physical models involves a considerable number of problems. They require time and money to build; testing them requires more time and money; they are typically built only after the design process has gone some distance from the concept stage; they have a finite and somewhat unpredictable life; the cost per test can be quite high; and they are not usually very portable and must be stored somewhere.

Many, if not all, of these problems could be avoided if a mathematical model of the structure of a product could be used. Such a mathematical model could be built at an early stage in the design cycle, perhaps even the concept stage. It could have a virtually unlimited life and a low per test cost. Such a model could be duplicated easily and could be easily portable. And the time required to set up and perform a test could be less.

This paper will focus on one method for creating and analyzing such mathematical models of structures. The method studied is the Finite Element Method, often known as FEM. Finite element theory has been in existence for almost 20 years (Hamann, 1974, p. 30) and is basically an extension of traditional methods of structural analysis of frames and framed structures. With the proliferation of the high-speed digital computer in the 1960's, the finite element method has become a useful tool for the engineer. Only with the use of a high-speed digital computer can the large number of calculations necessary for the use of the finite element method be performed in a reasonable length of time.

4-1975

Master of Arts

## Department

Department of Industrial Arts and Technology

William E. Luck

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4-1975

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