8-node and 12-node plane elements based on assumed stress quasi-conforming method immune to distorted mesh

Purpose Severe accuracy loss may occur when finite element comes to the distorted mesh model, and the calculation may fail when element mesh degenerates into concave quadrangle or the element boundary is curved. This is a valuable research topic, and many efforts have been made to develop new finite element models. This paper aims to propose two quasi-conforming membrane elements based on the assumed stress quasi-conforming method and fundamental analytical solutions to overcome the difficulties. Design/methodology/approach First, the fundamental analytical solutions which satisfied both the equilibrium and the compatibility relations of plane stress problem are used as the initial assumed stress of both elements. Then, the stress-function matrices are used as the weighted functions to weaken the strain-displacement equations, which makes only string-net functions on the boundary of the elements are needed in the process of strain integration. Finally, boundary interpolation functions expressed by unknown nodal displacement parameters are adopted to the process of strain integration. Findings The formulations of both elements are simple and concise, and the elements are immune to the distorted mesh, which can be used to the mesh shape degenerates into a triangle or concave quadrangle and curved-side element. The results of the numerical tests have proven that the new models possess high accuracy. Originality/value New formulations of quasi-conforming method are described is detail, and the new strategy exhibits advantages of both analytical and discrete methods.

A Novel Shape-Free Plane Quadratic Polygonal Hybrid Stress-Function Element

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.

A Thick/Thin Plate Element Based on the Area Coordinate Analytical Trial Functions

In this paper, a generalized conforming thick/thin plate element based on the quadrilateral area coordinate system called AATF-PQ4 is developed. Based on the governing equations of Mindlin-Reissner plate theory, the fundamental analytical solutions are first derived, then using this trial functions to formulate element AATF-PQ4. In the case of thin plate, this thick/thin plate element is degraded into corresponding thin plate element automatically and is free from shear locking. Numerical examples show that the proposed element, AATF-PQ4, has a good precision for thick and thin plate.

A Four-Node Hybrid-Trefftz Plane Elasticity Element with Fundamental Analytical Solutions

A new four-node hybrid-Trefftz element is developed for plane elasticity problems. From the Airy stress function, the fundamental analytical solutions of the governing equation are derived as Trefftz functions for the intra-element (Trefftz) displacement field. Together with an independent frame displacement field along the element boundary, the element formulation is then constructed following the modified variational functional. Several numerical examples indicate that the proposed element exhibits good performance.