Bending Analysis of Thick Anisotropic Rectangular Plate using Modified First Shear Deformation Theory


Authors : K.O. Njoku; O.M. Ibearugbulem; L.O Ettu; U.C. Anya

Volume/Issue : Volume 8 - 2023, Issue 10 - October

Google Scholar : https://tinyurl.com/p2zmd2hn

Scribd : https://tinyurl.com/3jsshfb5

DOI : https://doi.org/10.5281/zenodo.10046850

Abstract : In this work, displacement functions obtained by direct integration of governing equation were used to analyse anisotropic rectangular plates that are simply supported on its four edges (SSSS) and clamped on two adjacent edges and simply supported on the other two (CCSS). A modified first order shear deformation theory was used to develop the kinematic and constitutive relations of the plate. The total potential energy functional was formulated from which the governing and two compatibility equations were developed and solved to generate the polynomial displacement functions. By satisfying the boundary conditions of the plates, their peculiar displacement functions were determined. With these functions the anisotropic stiffness coefficients were obtained. By differentiating the total potential energy functional with respect to the displacement coefficients, the formulae for the coefficients were obtained. For each boundary condition analysis in this study, the displacement parameter values, in-plane stresses parameter values and out-of-plane stresses parameter values at various span to depth ratios (7.142857, 10 and 20), aspect ratios (0.5 to 2) and angle of fibre orientation of 00 were calculated. The solutions of this work were compared with those from various researchers and their results were close.

Keywords : Polynomial Displacement Function; Total Potential Energy Functional; Thick Plate; Anisotropic; Displacement; Stress, Governing Equation.

In this work, displacement functions obtained by direct integration of governing equation were used to analyse anisotropic rectangular plates that are simply supported on its four edges (SSSS) and clamped on two adjacent edges and simply supported on the other two (CCSS). A modified first order shear deformation theory was used to develop the kinematic and constitutive relations of the plate. The total potential energy functional was formulated from which the governing and two compatibility equations were developed and solved to generate the polynomial displacement functions. By satisfying the boundary conditions of the plates, their peculiar displacement functions were determined. With these functions the anisotropic stiffness coefficients were obtained. By differentiating the total potential energy functional with respect to the displacement coefficients, the formulae for the coefficients were obtained. For each boundary condition analysis in this study, the displacement parameter values, in-plane stresses parameter values and out-of-plane stresses parameter values at various span to depth ratios (7.142857, 10 and 20), aspect ratios (0.5 to 2) and angle of fibre orientation of 00 were calculated. The solutions of this work were compared with those from various researchers and their results were close.

Keywords : Polynomial Displacement Function; Total Potential Energy Functional; Thick Plate; Anisotropic; Displacement; Stress, Governing Equation.

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