engleski

Two-layered Plates with assumed Shear Strain Fields

We present a finite element model for a two-layered moderately thick plates based on the Mindlin plate theory. Starting from the pure displacement-based approach and the general expressions for the shear strains, selective constraints for the shear are assumed and a new layered plate element is introduced based on the mixed formulation. In the bending part of the formulation the starting transverse displacement interpolation has a cubic order and the rotation interpolations are quadratic while they are linked in both fields following the problem-dependent linked interpolation expressions. In the membrane part the displacement interpolations are quadratic and also linked with the drilling nodal rotations by the constraints on constant stresses within the patch test. The element passes the general constant-bending patch test and has 36 degrees of freedom after the internal bubble parameters are statically condensed in the element stiffness matrix. The layers can have different material characteristics, but these are assumed to be linear for each layer. The element is tested on a set of benchmark problems and compared with the results produced by the displacement-based layered elements without reduction in shear and which stiffness matrix is calculated by the reduced integration technique. The element is also compared with the other elements from the literature.

layered plate structures, assumed shear strain method, Mindlin plate theory, finite elements

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