Several authors'-5 have discussed the stiffening of isoparametric elements when they are distorted but few have given an alternative. Clough6 compared several elements for threedimensional stress analysis and concluded that the isoparametric element is superior. However, he did not distort the higher order elements and consequently his results are in disagreement with results presented in this note. This note presents numerical results which demonstrate the relative stiffening of several elements when distorted from a rectangular shape.The present results are restricted to the eight node quadrilateral element in a state of plane stress. Three different elements were considered. These include:1. Eight node quadrilateral isoparametric element 2. Eight node quadrilateral consisting of two 6-node L.S.T. elements 3. Eight node quadrilateral consisting of four 6-node L.S.T. elementsThe 2 and 4 L.S.T. configurations give two and ten internal degrees-of-freedom, respectively, which are eliminated by static condensation. Stiffness formation times are: 1. isoparametric (3 X 3 numerical integration) 0.1 1 sec 2. isoparametric (4 X 4 numerical integration) 0.18 sec 3. 2 L.S.T. elements 0.06 sec 4. 4 L.S.T. elements 0.17 sec All computer run times are for the Amdahl470 V/6 computer using the WATFIV compiler. The above times are given for comparison purposes only and will be reduced significantly if a Fortran IV compiler is used.The first comparison consists of checking the eigenvalues of the stiffness matrix. Theoretically, it can be shown that the element providing the lowest eigenvalue trace will yield the least stiff solution. The first three eigenvalues are zero corresponding to rigid body modes. Table I presents the sum of the first ten eigenvalues and all sixteen eigenvalues. Each row in the table has been normalized so that one of the eigenvalue sums is unity. The sum of the first ten eigenvalues is considered a better measure of the relative merit of the elements as only the lower eigenvalues usually contribute to the deformation. Table I shows that for a rectangular element, the 4 element L.S.T. configuration is slightly superior to the isoparametric element and the 2 element L.S.T. configuration is the stiffest. For the distorted elements, both arrays of L.S.T. elements are superior to the isoparametricelement.The next comparison is for the tip deflection of a cantilevered beam with rectangular elements and with distorted elements. The results are presented in Table 11. This rather simple example verifies the results from the eigenvalue study. For the rectangular elements, there is only a slight difference in the results and, as the number of elements is increased, the solution converges towards the strength of materials solution. However for the distorted array of elements, the

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SUMMARYThe prediction of non-linear structural behaviour by the finite element method wherein buckling does not occur has received considerable attention and, with it, reasonable success has been achieved. However, the post-buckling problem has been less actively pursued probably because of the inherent numerical difficulties encountered. This Technical Note reviews very briefly the numerical methods currently being used for preand post-buckling analysis and presents a self-correcting approach based on load and displacement incrementation which is shown to be efficient, reliable, and easy to program. Numerical solutions are presented which demonstrate the effectiveness of the method.