A novel C1 continuity finite element based on Mindlin theory for doubly-curved laminated composite shells. (October 2021) - Liu, Tao; Li, Zhi-Min; Qiao, Pizhong; Jin, Sun
Abstract: As a widely used structural form, doubly-curved composite shells have been applied in aviation and other engineering fields. With a refined mechanical model, structural performances can be accurately predicted to help designers choosing best geometrical and material parameters. This work introduces a novel rectangular finite element for doubly-curved laminated composite shells based on a new set of strain-based shape functions. The governing equations are established on the Mindlin shell theory (a type of first order shear deformable shell theory), which incorporates a rectification of shear correction factor for laminates and von Kármán type nonlinearity. Based on strain approach, the shape functions for rectangular element are assumed as polynomial of 28 parameters to consider the influence of shear effect. Apart from 20 geometrical relations of four element nodes, shear force equilibrium equations are introduced to offer the additional eight equations to derive a new set of shape functions for finite element model. Using shape functions, a novel rectangular shell element is proposed for doubly curved laminated shell, which also maintains a compatibility with Kirchhoff shells. Numerical results for linear static bending, dynamic vibration and nonlinear bending cases of flat plate, cylindrical shell and doubly-curved laminated shell are compared with the available results in literatures and ABAQUS simulation for the sake of validating the present method. Highlights: A model for doubly-curved shell is derived based on Mindlin theory. Shear correction factor is rectified to consider the effect of laminates. New shape functions are proposed with strain approach which satisfies C 1 continuity. A novel element is proposed for doubly-curved laminated shell considering geometric nonlinearity.