A First Course in the Finite Element Method

A First Course in the Finite Element Method

TThe finite elent~t method' is a mnnerical method for solving problems of engineering

and mathematical physics. Typical problem areas of interest in engineering and math-
ematical physics that are solvable by use of the finite element method include struc-
tural analysis) heat transfer, fluid flow, mass transport, and electromagnetic potential.

For problems involving complicated geometries, loadings, and material proPer-
ties, it is generally not possible to obtain an3Jytical mathematical solutions. Analytical

solutions are those given by a mathematical expression that yields the values of the
desired ~known quantities at any location in a body (bere total structure or physical
system of interest) and are thus valid for an infinite nwnber of locations in the body.

These analytical solutions generally require the solution of ordinary O,f partial differ-
ential equations, which, because of the complicated gt;Ometries, lcadings, and material

prcperties, are nct usually obtainable. Hence we need to rely on numerical methods,

such as the finite element method, for acceptable solutions.

The book proceeds from basic to advanced topics and can be suitably used in a
two-course sequence. Topics include basic treatments of (1) simple springs and bars,
leading to two· and three-dimensional truss analysis; (2) beam bending, leading to
plane frame and grid analysis and space frame analysis; (3) elementary plane stress/strain
elements> leading to more advanced plane stress/strain elements; (4) axisymmetric
stress; (5) isoparametric formulation of the finite element method; (6) three-dimensional
stress; (7) plate bending; (8) heat transfer and fluid mass transport; (9) basic
fluid mechanics; (10) tennal stress; and (11) time.dependent stress and heat transfer.
Additional features include how to handle inclined or skewed supports, beam
element with nodal hinge, beam element arbitrarily located in space, and the concept
of substructure analysis.


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