Contents lists available at ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct A new triangular shell element for composites accounting for shear deformation Imam Jauhari Maknun a , Irwan Katili a, ⁎ , Adnan Ibrahimbegovic b , Andi Makarim Katili a a Universitas Indonesia, Civil Engineering Department, Depok 16424, Indonesia b Université de Technologie de Compiègne, Sorbonne Universities, CNRS FRE 2012 Roberval, 60203 Compiègne, France ARTICLEINFO Keywords: Composite structures DKMT18 Naghdi-Reissner-Mindlin shell theory ABSTRACT In this paper, we propose an efcient 3-node shell element with 6 DOFs per node based on Naghdi-Reissner- Mindlin theory. This new composite shell element, further denoted as DKMT18, takes into account shear de- formation and coupled bending-membrane energy. DKMT18 element passes membrane, bending, and shear patch tests with no spurious mode. It also performs successfully in standard tests for thick and thin shells pro- blems without membrane or shear locking. The proposed shell element is capable of dealing with composite laminated shell structures. The computed results by the DKMT18 element converge more rapidly towards the reference solution compared to any state of-the-art shell element. 1. Introduction The two basic approaches used to formulate general shell elements are: plate bending and membrane superimposed that leaves two efects uncoupled versus formulations based on three-dimensional continuum mechanics that can take such coupling into account. The frst approach of superimposing plate bending and membrane is very simple and can be efective for some applications. For this reason, we rely here on a general continuum mechanics based approach for the shell theory of Naghdi-Reissner-Mindlin [1–7]. The fnite element based on such formulation could converge to the exact solution, irrespective of the shell geometry, and adequately ac- counts for membrane, bending, coupled membrane-bending, and shear efects. For modeling of complex engineering structures, triangular f- nite elements are frequently used. The triangular shell elements can also more successfully deal with major difculty in the development of shell fnite elements, related to the locking phenomenon for bending dominated shells [8–11]. Locking cure for membrane and shear has been an interesting topic of research. Many diferent techniques have been proposed. The re- duced and selective integration techniques [12–22] are the most straightforward cure that can successfully reduce the numerical locking. However, reduced and selective integration can also result in rank defciency due to spurious modes. An alternative treatment for locking is the Assumed Natural Strains (ANS) [23–25] method that exhibits better accuracy and robustness. One of the simplest and efective transverse shear formulation is proposed by Hughes and Taylor [26] for a 3-node plate bending element. The more refned ANS is frst used for 4-node shell element, referred to as MITC4 (Mixed In- terpolation of Tensorial Components), that has been widely used in engineering practice [27]. Lee and Bathe [28] also proposed a 3-node MITC3 shell element, but this element is not free of shear locking. When exact integration is performed, the MITC3 element locks. If one point is used for the eva- luation of the shear energy, locking is avoided, but the element has one spurious mode. More recently, the MITC3+ [29] as a new 3-node tri- angular shell fnite element was developed (Lee et al., 2014) to improve the performance of MITC3. Here a cubic bubble function is used for the interpolation of the rotations to enrich the bending displacement felds. Similarly, a new MITC4+ shell element was developed [30] to provide a signifcantly improved performance in distorted meshes compared to the MITC4 shell element [27]. Our previous work on the subject builds on top of the development of 3-node DKT [31] and 4-node DKQ [32] elements for thin plate using Discrete Shear and Assumed Natural Strains (ANS) methods to elim- inate shear strains [10]. DKT and DKQ elements rely on the Reissner- Mindlin plate model and only impose discrete Kirchhof constraint to eliminate shear efects. The frst attempts to include the shear strain with a triangular element, called DST (Discrete Shear Triangular) [33], and with quadrilateral element, called DSQ (Discrete Shear Quad- rilateral) [34]. Unfortunately, in the thick plate problem, neither of these pass the patch test. DST-BK was proposed by Batoz and Katili [35] https://doi.org/10.1016/j.compstruct.2020.112214 Received 9 November 2019; Received in revised form 11 March 2020; Accepted 12 March 2020 ⁎ Corresponding author. E-mail address: irwan.katili@eng.ui.ac.id (I. Katili). Composite Structures 243 (2020) 112214 Available online 22 March 2020 0263-8223/ © 2020 Elsevier Ltd. All rights reserved. T