New laminate constitutive equations for analysing the mechanical behavior of anisotropic plates and shells

Two novel laminate constitutive equations (LCE) for the static analysis of anisotropic shells are presented and implemented in this work. The LCE, developed for both two-dimensional (2D) and three-dimensional (3D) analysis, are more general than those obtained using the Kirchhoff-Love (K-L) equations, Reissner-Minddlin (R-M) type models, refined 2D/3D models, and some general anisotropic doubly-curved shell theories. Our study presents a 2D LCE model that accounts for classical mechanical couplings based on previous models plus additional couplings including extensional-twisting-shearing, extensional-twisting, Gauss bending-twisting-shearing, and Gauss bending-shearing mechanical couplings related to the third fundamental, or Gauss tensor. Moreover, the developed 3D LCE model accounts for all 2D mechanical couplings cited above plus additional mechanical couplings due to the section warping tensor, which arises from the stretching-through-the-thickness variable. These mechanical couplings are pertinent to the optimal design of a composite and are often disregarded in various static and dynamic analysis studies. Neglecting these new mechanical couplings in the design and analysis of laminated composite shells (LCS) can result in significant errors, from both physical and mechanical viewpoint. As such, we recommend employing new complete constitutive relations that integrate these pertinent mechanical couplings for the aforementioned study. Based on our analysis of the impact of additional couplings, we have developed several mathematical formulations that address several challenges encountered in laminated shell theory. As we increase the shell's thickness ratio, our research examines the effects of these couplings on mechanical behavior, buckling shape, critical buckling pressure, and failure analysis through computational modelling and various tests. The examination of the thickness ratio of composite shells illustrates the contrast between our newly developed LCE and some existing LCE as the shells increase in thickness.