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Shear correction factors for layered plates and shells. (English) Zbl 1398.74054

Summary: In this paper layered composite shells subjected to static loading are considered. The theory is based on a multi-field functional, where the associated Euler-Lagrange equations include besides the global shell equations formulated in stress resultants, the local in-plane equilibrium in terms of stresses and a constraint which enforces the correct shape of warping through the thickness. Within representative volume elements warping displacements are interpolated with layerwise cubic functions in thickness direction and constant shape throughout the reference surface. Elimination of warping and Lagrange parameters by static condensation leads to a material matrix for the stress resultants and to shear correction factors for layered plates and shells. For linear elasticity the computation can be done once in advance. The condensed material matrix is used in displacement based elements along with the enhanced strain method or in mixed hybrid elements with the usual 5 or 6 nodal degrees of freedom. This allows standard geometrical boundary conditions and the elements are applicable also to shell intersection problems. The interlaminar shear stresses are evaluated via the constitutive law by back substitution of the eliminated parameters. The computed transverse shear stresses are automatically continuous at the layer boundaries and zero at the outer surfaces. Furthermore, the integrals of the shear stresses coincide exactly with the shear forces without introduction of further constraints.

MSC:

74E30 Composite and mixture properties
74S05 Finite element methods applied to problems in solid mechanics
74K25 Shells
74K20 Plates
74K15 Membranes

Software:

PARDISO
PDFBibTeX XMLCite
Full Text: DOI

References:

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