Three-Dimensional Composite Multigrid Finite Shell-Type Elements
Abstract
Procedures for developing curvilinear three- dimensional composite multigrid finite elements (MFE) of a shell-like type for calculating the stress state of elastic cylindrical shells having an inhomogeneous (microinhomogeneous) structure and static loading have been proposed. MFE are developed in local Cartesian coordinate systems on the basis of small (basic) shell partitions (models). When constructing MFE (without increasing their dimensionality), arbitrarily small basic shell partitions can be used. Thus, it is possible to take into account their inhomogeneous and microinhomogeneous structure, irregular shape, complex nature of loading and fastening within the micro-approach. The stress-strain state in MFE is described by the formulas of the three-dimensional theory of elasticity (without introducing any additional simplifying hypotheses). The displacements are approximated by power and Lagrange polynomials of various orders, which take into account the displacements of the MFE as a rigid whole. Lagrangian polynomials are effectively used while developing shell-type elements. The proposed MFE yield the small dimensional discrete models (103 ÷ 106 times less than the dimensions of the reference models) and generate some approximate solutions that quickly converge to exact ones, which enable the construction of solutions with a high accuracy for a short time. A known numerical method is used to verify the MFE. Three-grid finite elements of a shell- like type have been developed and numerically studied. An example of a multilayer shell calculation using the developed three-grid finite elements and a reference model that has about 1.4 billion nodal unknowns of finite element method has been given.
DOI 10.14258/izvasu(2017)4-22
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