Formulation and evaluation of a new four-node quadrilateral element for analysis of the shell structures
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ORIGINAL ARTICLE
Formulation and evaluation of a new four‑node quadrilateral element for analysis of the shell structures Hosein Sangtarash1 · Hamed Ghohani Arab1 · Mohammad Reza Sohrabi1 · Mohammad Reza Ghasemi1 Received: 13 January 2019 / Accepted: 25 April 2019 © Springer-Verlag London Ltd., part of Springer Nature 2019
Abstract Shell structures are lightweight constructions which are extensively used by engineering. Due to this reason presenting an appropriate shell element for analysis of these structures has become an interesting issue in recent decades. This study presents a new rectangular flat shell element called ACM-SQ4 obtained by combining bending and membrane elements. The bending element is a well-known plate bending element called ACM which is based on the classical thin-plate theory and the membrane element is an unsymmetric quadrilateral element called US-Q4θ, the test function of this element is improved by the Allman-type drilling DOFs and a rational stress field is used as the element’s trial function. Finally, some numerical benchmark problems are used to evaluate the performance of the proposed flat shell element. The obtained results show that despite its simple formulation, the proposed element has reasonable accuracy and acceptable convergence in comparison with other shell elements. Keywords Flat shell element · Shell structures · Finite element method · Membrane element · Plate bending element
1 Introduction Nowadays, shell structures (the structures that are thin in thickness and have considerable length in other two directions) are widely used in engineering, specifically in the automotive and construction industries [1]. Due to their geometrical complexity, various loading conditions and mixed boundary conditions, analytical methods cannot meet the engineer’s needs. Accordingly, numerical methods are the best solution to analyze such structures, among numerical methods finite element method is a conventional selection for engineers. Using an appropriate element which has reasonable accuracy and fast convergence is one of the serious challenges in the finite element method therefore, different kinds of elements were proposed by researchers. For instance, Carrera and Petrolo [2] presented a modified beam element for the numerical analysis of shell structures. Using a combination of the edge-based smoothed finite element (ES-FEM) and the node-based smoothed finite element (NSFEM) Nguyen et al. [3] developed a triangular shell element * Hamed Ghohani Arab [email protected] 1
Civil Engineering Department, University of Sistan and Baluchestan, Zahedan 98167‑45845, Iran
with acceptable accuracy in benchmark problems. Hernandez et al. [4] evaluated the dynamic behavior of the cylindrical shell using finite element method. A practical study was done by Yuqi et al. [5] on flange earring steel plates in deep-drawing process using the triangular shell element. In general, shell elements used in the finite element analysis of shell structures are flat shell element [6], curved shell e
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