Eight‐node membrane element with drilling degrees of freedom for analysis of in‐plane stiffness of thick floor plates

Abstract

SUMMARYThe development of eight-node arbitrary quadrilateral membrane elements with drilling degrees of freedom is presented using the compatible displacement interpolation within the element. The element is considered to develop specifically for analysing the in-plane stiffness of thick floor plates in building systems, particularly the transfer plates in tall buildings as well as pile caps. With a new set of shape functions and following the displacement-based element procedure, the element stiffness and force vector are derived and nodal displacements are obtained after solving the simultaneous equations; the element stresses are then determined. A wide range of patch tests is conducted to evaluate the consistency and stability of the proposed element. The test results show very good agreement with the exact solutions of the beam theory. Numerical investigations are carried out, showing that the analyses using the proposed elements provide better results than those from the existing methods.

A new enhanced assumed strain quadrilateral membrane element with drilling degree of freedom and modified shape functions

“…The same element with full numerical integration is compared with the present element with full numerical integration in Appendix A Tab A.2, Tab A.4, Tab A.5, Tab A.6,Tab A.7 and Tab A.9. These eight-node elements are listed in the following: DB-8-node: A displacement-based eight-node element with drilling DOF [55]. HQ8-13ˇ: A mixed isostatic 16 DOF quadrilateral eight-node membrane element with drilling rotations, based on Airy stresses [56].…”

A mixed isostatic 16 dof quadrilateral membrane element with drilling rotations, based on Airy stresses

“…Zhang [16] HBQ8 [31] DOFs ratio 6/5 9/5 4.2857 5.2506 λ 10 7.8688 -λ 11 9.3283 -λ 12 9.3284 -λ 13 11.9951 - fξ; ηg is implicitly defined by…”

“…Cook's cantilever. Convergence graphs for displacement u y at point A. HQ4-9β [2], S8R (Abaqus) [38], Allman [19], M-type [39], Pimpinelli [42], Choi [41], Choo [40], Zhang [16], HS-A7 [8], US-ATFQ8 [5] and HSF-Q8-15β [3] results are compared. …”

“…The results from a numerical benchmarking will be discussed here to show the performance of the proposed element HQ8-13β in comparison with the elements available in the literature, including the assumed displacement shell element with reduced integration, called S8R, implemented in ABAQUS [38], the classical elements AQD4 and M-Type by Allman [19] and Ibrahimbegovic [39] respectively, the elements based on the hybrid Trefftz method by Choo and Choi [40,41], the assumed strain quadrilateral with drilling rotation by Pimpinelli [42] and the eight-node with drilling rotation by Zhang and Kuang [16], the recent membrane element by Rezaiee-Pajand and Karkon [8] based on analytical solution, the US-ATFQ8 element [5] based on the unsymmetrical trial function method, the eight node HSF-Q8-15β proposed by Cen et al [3] and based on Airy stress functions and the HQB8 element proposed by Darilmaz et al [31]. Stress recovering is represented by color maps.…”

“…Often, membrane elements are coupled with bending discretization to be used in linear and geometrically nonlinear analysis of folded plates, box structures also assembled with other type of element, as was given in [10,11]. For this purpose, the use of drilling rotations as nodal variables is an essential feature [12][13][14][15][16].…”