Simulation of composite shells based on the generating finite elements

Abstract

In the present paper, a method of generating finite elements (FE) to construct complex-shaped three-dimensional composite multi-grid finite elements (MgFE) of two types is proposed. When constructed m-grid finite element (mgFE), m nested grids are used. The fine grid is generated by the base partitioning of mgFE, taking into account its heterogeneous structure and shape. The displacement functions and stress state in the MgFE described by the equations of the three-dimensional elasticity problems (without introducing any additional simplifying hypotheses), are represented in local rectangular coordinates. When constructed MgFE (without increasing their dimension), arbitrarily small basic partitions can be used arbitrarily closely taking into account the complex inhomogeneous structure and shape of the MgFE, and arbitrarily closely describing the three-dimensional stress state in the MgFE. The 1st type MgFE region is obtained by turning a given flat generating single-grid FE (complex shape) about a given axis by a given angle, the 2nd type MgFE region is obtained by parallel moving the generating FE in a given direction by a specified distance. The 1st type MgFE is applied to calculate some composite rotational shells; the 2nd type is for composite cylindrical shells. The advantages of the proposed MgFE make it possible to account for the inhomogeneous structure of the shells, thus giving rise to small-dimensional discrete models and accurate solutions