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

• Published in: International journal for numerical methods in engineering Vol. 76; no. 13; pp. 2117 - 2136
• Main Authors: Zhang, Hexin, Kuang, J. S.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 24.12.2008; Wiley
• Subjects: Applied sciences; Buildings; Buildings. Public works; Computational techniques; drilling degrees of freedom; eight-node element; Exact sciences and technology; External envelopes; Floor. Ceiling; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; membrane element; Physics; shell element; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; tall buildings; thick plate; transfer plates; Floor; Quadrilateral finite element; tall buildings; transfer plates; shell element; Thick plate; drilling degrees of freedom; Modeling; Exact solution; Finite element method; eight-node element; membrane element; Pile cap; Membrane; High rise building; Numerical convergence; Civil engineering
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2395

The 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. Copyright © 2008 John Wiley & Sons, Ltd.