Calculation of composite cylindrical shells using multigrid elements

Calculating the three-dimensional elastic composite cylindrical shells with different coefficients of fullness that is reduced to the construction of discrete models consisting of complex curvilinear multi-grid finite elements has been proposed. The basis of such elements construction is curvilinear double-grid finite elements. Double-grid and complex multi-grid elements are designed based on the basic finite element models of composite shells which take into account their heterogeneous structure and have high dimension. Constructing the curvilinear double-grid and complex multi-grid elements in the local Cartesian reference systems has been shown. Displacement fields are interpolated by known degree polynomials of various orders, the stress state is described by the three-dimensional elasticity problem (without introduction of the simplifying hypotheses on the nature of the displacement fields, strain and stress distribution). Approximating polynomials and the equations of three-dimensional elasticity problem are recorded in the local Cartesian reference systems. Advantages of the proposed elements are that they describe the three-dimensional stress state in composite shells, take into account their heterogeneous structures, complex fixing and generate multi-grid discrete models with a small number of nodal unknowns. The dimensions of multi-grid discrete shell models are by several orders less than the dimensions of the basic ones. Time spending of the finite element method (FEM) realization on a computer for discrete models of multi-grid composite shells is significantly less than for the basic models. A complex multi-grid element of the 3rd order to calculate the composite cylindrical shells is proposed. The FEM calculation example of cantilever sandwich shell using complex multi-grid elements of the 3rd order has been given. Shell calculation results show the high efficiency of the proposed complex elements.