A First Course in Finite Elements - Ko231; Hastanesi（第一次在有限元素ko 231;Hastanesi）.pdf

A First Course in Finite Elements Introduction The finite element method has become a powerful tool for the numerical so- lution of a wide range of engineering problems. Applications range from deforma- tion and stress analysis of automotive, aircraft, building, and bridge structures to field analysis of heat flux, fluid flow, magnetic flux, seepage, and other flow prob- lems. With the advances in computer technology and CAD systems, complex prob- lems can be modeled with relative ease. Several alternative configurations can be tried out on a computer before the first prototype is built. All of this suggests that we need to keep pace with these developments by understanding the basic theory, modeling techniques, and computational aspects of the finite element method. In this method of analysis, a complex region defining a continuum is discre- tized into simple geometric shapes called finite elements. The material proper- ties and the governing relationships are considered over these elements and ex- pressed in terms of unknown values at element corners. An assembly process, duly considering the loading and constraints, results in a set of equations. Solu- tion of these equations gives us the approximate behavior of the continuum. Historical Background Basic ideas of the finite element method originated from advances in aircraft structural analysis. In 1941, Hrenikoff presented a solution of elasticity problems using the “frame work method.” Courant’s paper, which used piecewise polyno- mial interpolation over triangular subregions to model torsion problems, appeared in 1943. Turner et al. derived stiffness matrices for truss, beam, and other ele- ments and presented their findings in 1956. The term finite element was first coined and used by Clough in 1960. In the early 1960s, engineers used the method for approximate solution of problems in stress analysis, fluid flow, heat transfer, and other areas. A book by