New higher order shear deformation theories for free vibration and buckling analysis of laminated and braided composite plates

In this work, two new shear deformation theories namely Trigonometric Deformation Theory (TDT) and Trigonometric-Hyperbolic Deformation Theory (THDT) are developed and implemented for the analysis of laminated and three dimensional braided composite plate. Both models are based upon shear strain shape function which yields non-linear distribution of transverse shear stresses and these models also satisfy the traction free boundary conditions on top and bottom surfaces of the plate. Virtual work principle is used to obtain the governing differential equations and boundary conditions. Both the proposed theories are formulated and validated for the free vibration and buckling of laminated and Three Dimensional (3D) braided composite plate. From the obtained results, the proposed theories are more accurate in predicting the response for free vibration and buckling 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 conditions, fiber volume fraction and braiding angle have significant effect on the free vibration and buckling response of the 3D 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. (C) 2017 Elsevier Ltd. All rights reserved.