A MITC3+ element improved by edge-based smoothed strains for analyses of laminated composite plates using the higher-ord
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O R I G I NA L PA P E R
Thanh Chau-Dinh · Trung-Kien Nguyen · Hieu Nguyen-Van · Hoang Lan Ton-That
A MITC3+ element improved by edge-based smoothed strains for analyses of laminated composite plates using the higher-order shear deformation theory Received: 5 June 2020 / Revised: 23 July 2020 / Accepted: 23 September 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract In this paper, a new three-node triangular plate element is proposed to analyze laminated composite plates based on the higher-order shear deformation theory (HSDT). Originating from the MITC3+ shell finite elements, the displacement fields of the HSDT are interpolated by usual linear functions of the three-node triangular element and a cubic supplemented function associated with a node located at the centroid of the element. The transverse shear strain fields are separately approximated according to the MITC3+ shear-locking removal technique. The edge-based smoothed (ES) strain method is employed to improve the in-plane strain fields. Applying the divergence theorem, the surface integration of the in-plane stiffness matrices is transformed into the line integration on the boundary of the smoothing domains. The performance of the so-called ESMITC3+ plate elements is validated through several numerical examples. The numerical results of the static, frequency and buckling analyses when this new element is used converge to the exact solutions and agree well with those given in other references.
1 Introduction Laminated composite plates are fabricated of unidirectional laminae stacked together in the thickness direction. Number, type, fiber orientation and stacking sequence of the laminae are designed to afford the structural behavior in the best possible way. Laminated composite plates are widely used in many manufacturing industries such as aviation, automobile, shipbuilding, or civil engineering because of their high strength, high stiffness, low density, adaptability to the intended function of the structures and so on. Therefore, theories and models of the behavior of laminated composite plates are of great interest for research. Made up of layers stacked together, laminated composite plates can be treated using the equivalent single layer (ESL) [1], zig-zag [2], layerwise [3], or three-dimensional (3D) elasticity [4,5] theories. In the ESL theories, the properties and stacking sequence of the individual layers are characterized by equivalent properties of a single layer. The in-plane displacement fields are continuously approximated through the thickness. To perform the zig-zag distribution of the in-plane displacement fields through the thickness, the zig-zag theories modify the continuous displacement fields of the ESL theories by the piecewise continuous ones and constrain the transverse shear stresses to continue at each layer interface. In the layerwise theories, the displacement fields are independently approximated within each layer but continuous at the layer’s interfaces. The 3D-elasticity theories predict the lami
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