An n ‐sided polygonal finite element for nonlocal nonlinear analysis of plates and laminates

Aurojyoti, P and Raghu, P and Rajagopal, Amirtham and Reddy, J N (2019) An n ‐sided polygonal finite element for nonlocal nonlinear analysis of plates and laminates. International Journal for Numerical Methods in Engineering. ISSN 0029-5981

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Abstract

In this study, a locking‐free n‐sided C1 polygonal finite element is presented for nonlinear analysis of laminated plates. The plate kinematics is based on Reddy's third‐order shear deformation theory (TSDT) [1, 2]. The inplane displacements are approximated using barycentric form of Lagrange shape functions. The weak‐form Galerkin formulation based on the kinematics of TSDT requires the C1 approximation of the transverse displacement over the polygonal element. This is achieved by embedding the C0 Lagrange interpolants over a cubic Bernstein–Bezier patch defined over the n‐sided polygonal element. Such an approach ensures the continuity of the derivative field at the inter‐element edges. In addition, Eringen's stress‐gradient nonlocal [3]. constitutive equations are used in the present formulation to account for nonlocality. The effect of geometric nonlinearity is taken by considering the von Kármán' geometric nonlinearity. Examples are presented to show the effect of nonlocality, geometric nonlinearity, and the lamination scheme on the bending behavior of laminated composite plates. The results are compared with analytical solutions, conventional FEM results and with those available in the literature. Shear locking is addressed considering reduced integration and consistent interpolation techniques. The patch test is used to check the convergence of the element developed.

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