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

Abstract

Summary 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). The in‐plane 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 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.

Modeling fracture in brittle materials by higher-order phase field method using C1 non-Sibsonian interpolants

“…A novel C 1 continuous finite element is developed for the analysis of laminated composites shells based on Mindlin theory in Liu et al . (2021) and for third-order shear deformation theory (TSDT) in Aurojyoti et al . (2019).…”

“…Here, the shape functions differ according to the element shapes. A novel C 1 continuous finite element is developed for the analysis of laminated composites shells based on Mindlin theory in Liu et al (2021) and for third-order shear deformation theory (TSDT) in Aurojyoti et al (2019). An eight-node 2D plane strain quad element that satisfies higher-order completeness is given in Zhang and Xiang (2020).…”

Effect of large deflection on laminated composite plates

“…Civalek studied free vibration analysis of laminated composite panels and curved plates with functionally graded materials using Love's shell theory and first-order shear deformation theory [7]. Aurojyoti et al presented a polygonal finite element for nonlinear analysis of laminated plates using Reddy's thirdorder shear deformation theory [8]. Kormanikova presented a numerical approach of mode-frequency analysis of a simply-supported laminated doubly curved shell.…”

Shape‐free arbitrary polygonal hybrid stress/displacement‐function flat shell element for linear and geometrically nonlinear analyses

“…Ho‐Nguyen‐Tan and Kim 22 developed a polygonal degenerated shell elements by assuming covariant shear strain field and employing the mixed interpolation technique. Aurojyoti et al 23 proposed an n ‐sided polygonal finite element for nonlocal nonlinear analysis of plates and laminates based on Reddy's third‐order shear deformation theory. Similar to the conventional elements, in order to obtain satisfactory results, relatively refined meshes are still needed for these new polygonal models.…”