MID_A_97W - Midterm Examination 1997 Winter MEAM 305...

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Midterm Examination 1997 Winter MEAM 305 Introduction to Finite Element Methods March 14, 1997 1 . Answer to the following quetions : a) In which yaer was the finite element method introduced ? Who are the authors of the first paper ? The finite element method was first introduced by Turner, Clough, Martin, and Topp in 1956 using the displacement method to derive the stiffness of plane elements, and their paper is regarded as the first paper on the finite element method in engineering, while mathematicians believe that R. Courant introduced the method in 1943 under the name of the generalized finite difference method which is the approximation by 3 node trangular elements. b) Who is the person named the finite element method ? When ? In 1960, Clough named the method as the finite element method . c) Whai is the isoparametric element ? Isoparametric finite elements imples the expression of the element geometry ( that is the transformation of the parametric and local coordinates ) and the displacement approximation using the same shape functions and the nodal coordinates and displacements, respectively. A typical mathematical expression of this isoparametric element is as follows : (geometry) xx N yy N zz N ii i N i N i N eee = (29 = = === ∑∑∑ xxx ,, , ,, ηζ 111 (displacement) uu N N N i i i N i i i N i i i N = (29= (29= (29 Here xyz iii and uuu x i y i z i are the nodal coordinates and displacements, respectively, and N e is the number of node in an element. Functions N i x are the shape functions which are polynomials of the parametric coordinates.
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This note was uploaded on 12/08/2011 for the course CS 525 taught by Professor Gupta during the Spring '08 term at University of Illinois, Urbana Champaign.

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MID_A_97W - Midterm Examination 1997 Winter MEAM 305...

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