Abstract
In this paper, a fourth-order displacement (cubic strain) Serendipity quadrilateral element is presented. The shape functions and integration scheme are introduced, followed by a series of convergence tests, indicating that the element does not have any spurious zero-energy modes, and passes the patch test and single-element tests. Modifications are then made to enable the element's use in effective stress analysis problems. Examples are finally solved using the element and a comparison is made between some computed and closed-form solutions. It is also shown that the cubic strain quadrilateral may be used in conjunction with or as a substitute for the cubic strain triangle when predicting collapse loads for undrained plane or axisymmetric problems in the fully plastic range.
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