Abstract
In this work, using new inverse trigonometric kinematic displacement function, the bending solution of simply supported isotropic and transversely isotopic thin, moderately thin and thick square plates with aspect ratio variations is given. The paper introduces a new inverse trigonometric shear deformation theory (nITSDT) for the bi-directional bending study, which is variationally compatible. The transverse shear stress can be obtained directly from the constitutive relationships on the top and bottom surfaces of the plate that satisfy the shear stress free surface conditions, so the theory does not need a factor for shear correction. The dynamic version of the virtual work principle is used to obtain the governing equations and boundary conditions of the theory. The Finite Element (FE) solution has been developed using MATLAB code based on the present theory for simply supported laminated composite plates. In order to illustrate the efficiency of the proposed theory, the results of displacements and stresses are compared with those of other refined theories and exact solution. The findings obtained from the use of the theory are found to agree well with the precise results of elasticity.
Highlights
Isotropic plates are utilised as structural elements in a variety of applications, including mechanical and civil engineering
The present work proposes a displacement-based new inverse trigonometric shear deformation theory for bi-directional bending and assessment of thick isotropic and transversely isotropic plates, which takes into account the effects of transverse shear deformation and rotating inertia
The finite element formulation for bending analysis of isotropic and transversely isotropic plate has been developed based on a new inverse trigonometric shear deformation theory
Summary
Isotropic plates are utilised as structural elements in a variety of applications, including mechanical and civil engineering. The effect of transverse-shear and normal strain on isotropic stresses in static bending has been investigated for thick plates. The influence of transversely-shear and normal deformation on thermal-mechanical analyses of FG plates was investigated, and the results were shown to be valuable as a benchmark [16]. A theory of fifth-order shear deformation considering transverse shear deformation effect as well as transverse normal strain deformation effect was proposed [17] for static flexure analysis of supported isotropic plates. The strategy utilises displacement-based potential functions for transversely isotropic plates and 3-D elasticity solutions established. The present work proposes a displacement-based new inverse trigonometric shear deformation theory (nITSDT) for bi-directional bending and assessment of thick isotropic and transversely isotropic plates, which takes into account the effects of transverse shear deformation and rotating inertia. To promote the solution and reduce the computational time [28], the symbolic words in MATLAB are implemented
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