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Rectangular bar and no-bar finite elements for three dimensional stress analysis Gantayat, Akhilananda

Abstract

A three dimensional bar cell in the form of a rectangular parallelopiped capable of imitating the action of elastic bodies of any value of Poisson's ratio is devised for three dimensional stress analysis by the finite element method and the stiffness matrix of the cell is derived. Furthermore a rectangular no-bar cell is also formed by extending the idea of linear displacement functions from two dimensional to three dimensional cases and the stiffness matrices of this cell are derived both by the method of virtual work and by statics. Both these types of cells are used to solve three dimensional problems and the results in the form of displacements and stresses are compared with the exact elasticity solutions using different mesh sizes and different values of Poisson's ratio. The stresses found by the Finite element method are calculated in two ways: by the Joint displacement method (using two different procedures) and by the Nodal force method and the quality of solution obtained by these methods is compared. Finally the same examples are also analysed by using the framework models proposed by "Yettram and Robbins". ⁽⁶⁾* The results obtained by these several methods were good, with the ones corresponding to the proposed bar model being consistently the best of the three. The stresses found by both the Joint displacement and the nodal force methods were found comparable in quality. * Numbers signify the references, listed in Bibliography.

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