Exact geometry four-node solid-shell element for stress analysis of functionally graded shell structures via advanced SaS formulation

The exact geometry four-node solid-shell element formulation using the sampling surfaces (SaS) method is developed. The SaS formulation is based on choosing inside the shell N not equally spaced SaS parallel to the middle surface in order to introduce the displacements of these surfaces as basic she...

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Bibliographic Details
Published in:Mechanics of advanced materials and structures 2020-06, Vol.27 (12), p.948-964
Main Authors: Kulikov, G. M., Plotnikova, S. V.
Format: Article
Language:English
Subjects:
3D stress analysis
Chebyshev approximation
Exact geometry solid-shell element
Functionally gradient materials
hybrid-mixed method
Interpolation
Locking
Material properties
Mixed methods research
Nodes
Polynomials
sampling surfaces method
Shells
Shells (structural forms)
Stress analysis
True strain
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Summary:The exact geometry four-node solid-shell element formulation using the sampling surfaces (SaS) method is developed. The SaS formulation is based on choosing inside the shell N not equally spaced SaS parallel to the middle surface in order to introduce the displacements of these surfaces as basic shell unknowns. Such choice of unknowns with the use of Lagrange basis polynomials of degree N − 1 in the through-thickness interpolations of displacements, strains, stresses and material properties leads to a very compact form of the SaS shell formulation. The SaS are located at Chebyshev polynomial nodes that make possible to minimize uniformly the error due to Lagrange interpolation. To implement efficient 3D analytical integration, the extended assumed natural strain method is employed. As a result, the proposed hybrid-mixed solid-shell element exhibits a superior performance in the case of coarse meshes. To circumvent shear and membrane locking, the assumed stress and strain approximations are utilized in the framework of the mixed Hu-Washizu variational formulation. It can be recommended for the 3D stress analysis of thick and thin doubly-curved functionally graded shells because the SaS formulation with only Chebyshev polynomial nodes allows the obtaining of numerical solutions, which asymptotically approach the 3D solutions of elasticity as the number of SaS tends to infinity.
ISSN:1537-6494
1537-6532
DOI:10.1080/15376494.2018.1502380