Abstract
A new displacement based higher order element has been formulated that is ideally suitable for shear deformable composite and sandwich plates. Suitable functions for displacements and rotations for each node have been selected so that the element shows rapid convergence, an excellent response against transverse shear loading and requires no shear correction factors. It is completely lock-free and behaves extremely well for thin to thick plates. To make the element rapidly convergent and to capture warping effects for composites, higher order displacement terms in the displacement kinematics have been considered for each node. The element has eleven degrees of freedom per node. Shear deformation has also been considered in the formulation by taking into account shear strains ( rxz and ryz) as nodal unknowns. The element is very simple to formulate and could be coded up in research software. A small Fortran code has been developed to implement the element and various examples of isotropic and composite plates have been analyzed to show the effectiveness of the element.
Highlights
Development of plate bending elements dates long back in the history of finite element method itself
A small Fortran code has been developed to implement the element and various examples of isotropic and composite plates have been analyzed to show the effectiveness of the element
The first developments were based on thin plate theory (Kirchhoff’s plate theory), which neglects the effects of transverse shear deformation on bending
Summary
Development of plate bending elements dates long back in the history of finite element method itself. A lot of research works have been directed to the development of elements based on Reissner-Mindlin plate theory [1,2] The advantage of this approach is the independence of transverse deformation and rotations and only C0 continuity is required at the nodes. Attempts have been made to develop elements with shear deformation for composite plates [15,16,17,18,19,20] It is shown in some works [15,16,18,20,21] that the numerical computation using isoparametric elements has its limitations, that might lock in thin plate situations. Results have been provided for various isotropic and composite plates in thick and thin situations
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