Keywords

Finite element method, Structural analysis (Engineering)

Abstract

Any structural analysis which gives stresses and displacements for some predefined structure is governed by some physical domain of loading, geometry and boundary conditions. Let this domain be called the structures "problem space." In applying finite element analysis, the solution to any one problem space may be one of many admissible solutions all of which satisfy some given set of boundary conditions. Admissibility is determined by the stated problem with its boundary conditions along with computer storage capacity considerations. Obtaining the most exact approximate solutions is one of major concern to insure adequate results. This problem has been approached from a number of viewpoints [4-9] all of which employ some version of minimum potential energy [5, 10]. This report is a study of current approaches to this problem and their effect on finite element grid optimizations. Selected optimizations [4-9] are shown to be effective in producing better solutions but it is noted that the implementation of these optimizations may be difficult. To survey the situation two fixed problem spaces of a tapered beam and a cantilever beam are chosen for investigation. Conclusions based on this study display that optimizations methods applied to a finite element model give an optimum space arrangement that is a function of the selected element geometry and displacement function. When changes in the element geometry are introduced a new optimum results. Comparing test problem results leads to some speculation employing uniform strain energy as a better guide to "first guess" grid arrangement and a recommendation for further investigation in this direction.

Notes

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Graduation Date

1973

Degree

Master of Science (M.S.)

College

College of Engineering

Format

PDF

Pages

v, 23 pages

Language

English

Rights

Public Domain

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

Identifier

DP0012254

Subjects

Finite element method, Structural analysis (Engineering)

Collection (Linked data)

Retrospective Theses and Dissertations

Included in

Engineering Commons

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