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.
