The high-order Serendipity elements have internal nodes,which is not convenient for grid division and practical use.There are few publications discussing their implementation and actual performance.This paper introduces the shape function of the 32-node sextic element Q32,and discusses two integration schemes of element stiffness matrix:Gaussian integration and complete polynomial integration.The latter has fewer integration points than the former.Taking the transverse bending of a cantilever beam as an example,the results show that the integration scheme for Q32 can be 6×6(36-point)Gaussian integration or various 11-order complete polynomial integrations.The 25-point symmetrical integration can be used in practice:its accuracy is comparable to that of 6×6 Gaussian integration,but its calculation workload is about 69％of the latter.Q32 can simulate a cubic displacement field quite accurately even if the mesh is seriously distorted.
Serendipity elementsextic element Q32quadrilateral elementhigh-order elementcomplete polynomial integration
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