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.
The mode-I interlaminar fracture toughness (IFT) property of room temperature (RT) cured glass-epoxy (LY556/HY95 1) composites was studied using a double cantilever beam (DCB) test specimen with unidirectional fibre orientations of 0°, +450/-450, +600/-600 and 900 in the neighborhood of the crack zone. Three IFT data reduction techniques, viz.: (1) Modified Beam Theory (MBT), (2) Compliance Calibration Theory (CC) and (3) Modified Compliance Calibration Theory (MCC) were verified for the DCB data generated for 0° fibre oriented specimens. The fracture toughness property estimates were noted to be approximately the same for all three techniques. Only the MBT reduction procedure (as per ASTM) was used for other orientations. It was observed that the IFT increased as the fibre orientation was changed from 0° to 900 with reference to the direction of crack propagation.
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