Assessment and Accuracy of New Nonpolynomial Shear Deformation Theories for Static Analysis of Laminated and Braided Composite Plates

Abstract

In the present study, two new shear deformation theories, trigonometric deformation theory (TDT) and trigonometric-hyperbolic deformation theory (THDT), are proposed. These theories are examined in detail for their effectiveness in static response of laminated and three-dimensional (3D) braided composite plates. Both models are based upon a shear strain shape function that yields nonlinear distribution of transverse shear stresses and also satisfies the traction-free boundary conditions on top and bottom surfaces of the plate. Thus, requirement of shear correction factor vanishes. Virtual work principle is used to obtain the governing differential equations and boundary conditions. These models are formulated and validated for the static responses of laminated and braided composite plates. A variety of numerical examples are analyzed. Comparison of various higher order theories with the proposed theories are performed. It is observed that both proposed theories are efficient and accurate for the static analysis of laminated and 3D braided composite plates. Intensive numerical studies of 3D braided composite are performed in detail. It is further observed that the geometric parameter (aspect ratio), boundary condition, fiber volume fraction, and braiding angle have a significant effect on the static response of the braided composite plates. In the framework of finite element analysis, both proposed theories anticipate exemplary results for the laminated and braided composite plates compared to existing theories.