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Application of the Finite Element Method in Selected Civil Engineering Problems

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Title: Application of the Finite Element Method in Selected Civil Engineering Problems
Authors: Fujioka, Masanobu
Issue Date: 15 Jan 2014
Publisher: University of Hawaii at Manoa
Abstract: For many engineering problems, an analytical solution is often difficult or impossible. Thus engineers often turn to numerical methods which provide approximate answers of sufficient accuracy to be acceptable. Such a numerical method is the finite element method, one of the newest and most powerful of the numerical methods. The finite element method was developed principally for use in structural mechanics. The wide range of applicability of this method is just beginning to be realized. The general nature of the theory on which it is based will soon lead to applications in many other fields in engineering. The widespread popularity which the method will certainly enjoy will be due to the versatility of the method and the ease with which it can be used. The method is able to handle such difficult problems as nonhomogeneous materials, nonlinear stress-strain behavior, and complicated boundary conditions. Other numerical methods are not able to handle the above complexities.(Desai, 1972) Vigorous mathematical interpretation of the method is not necessary for it's use. The method can be used (especially in structural mechanics where the steps involved have been worked out in almost a cookbook fashion) without knowing the underlying theory behind the formulation of the terms in the basic matrix equation to be solved. This kind of approach is illustrated by a three element cantilever beam problem which is discussed in this thesis. The problem can be handled by merely knowing certain formulas for composing a stiffness matrix for the beam. In solving the problem, the author was able to formulate the stiffness matrix and write a program solving the matrix equation without knowing anything about the energy principles involved. The explanations included in the thesis were composed after the program had been written. The opposite approach is illustrated by the second problem discussed in this thesis. The second problem, dealing with steady state potential flow problems, requires a detailed understanding of the principles involved and of the finite element method. Thus the thesis is composed basically of three parts. The first is a general description of the finite element method. The second is a solution of a simple structural mechanics problem worked out to familiarize the author with the finite element method. The third part is a very detailed explanation of basic principles and finite element techniques required in the solution of steady state potential flow problems. Included are several typical problems using a program written by Richard Cooley and John Peters (Cooley, Peters, 1970) of the Corps of Engineers.
Pages/Duration: 36 pages
URI/DOI: http://hdl.handle.net/10125/32219
Rights: All UHM Honors Projects are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner.
Appears in Collections:Honors Projects for Civil Engineering



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