Abstract
A novel plane quadratic shape-free hybrid stress-function (HS-F) polygonal element is developed by employing the principle of minimum complementary energy and the fundamental analytical solutions of the Airy stress function. Without construction of displacement interpolation function, the formulations of the new model are much simpler than those of the displacement-based polygonal elements and can be degenerated into triangular or quadrilateral elements directly. In particular, it is quite insensitive to various mesh distortions and even can keep precision when element shape is concave. Furthermore, the element does not show any spurious zero energy modes. Numerical examples show the excellent performance of the new element, denoted by HSF-AP-19β, in both displacement and stress solutions.
Highlights
The conventional triangular and quadrilateral elements are widely used in 2D finite element analyses [1, 2]
Cen et al [39,40,41,42,43,44] proposed a hybrid stressfunction (HS-F) element method based on the principle of minimum complementary energy and the fundamental analytical solutions of Airy stress function
(1) It is simple to build this new element without construction of displacement interpolation functions, which are very complex for polygonal elements compared with quadrilateral elements
Summary
The conventional triangular and quadrilateral elements are widely used in 2D finite element analyses [1, 2]. Beside the Wachspress method, the Laplace functions were utilized to build the interpolation functions for polygonal elements, such as the works proposed by Wang and Li [24] and Sukumar and Tabarraei [25] Another mentionable approach is the barycentric coordinate method [26,27,28] which can be applied to develop both conventional and polygonal elements. Cen et al [39,40,41,42,43,44] proposed a hybrid stressfunction (HS-F) element method based on the principle of minimum complementary energy and the fundamental analytical solutions of Airy stress function They constructed several elements with excellent performance, such as 8node and 12-node plane quadrilateral elements and 4node plane quadrilateral element with drilling degrees of freedom.
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