Abstract:
Total potential energy was formed based on the traditional refined plate theory assumptions. Displacement field, kinematic relations, constitutive relations, stress displacement relations were derived from the deformed section of a thick anisotropic plate respectively. Strain energy was formed by substituting the kinematic relations and stress-displacement relations into the universal strain energy equation. By the addition of the external work to the strain energy equation, total potential energy functional for analysis of thick anisotropic rectangular plate was obtained. The total potential energy functional were minimized by differentiating it with respect to the deflection, shear deformation rotation in x direction and shear deformation rotation in y direction respectively. This yielded the governing equation and two compatibility equations of thick anisotropic rectangular plate. A third order polynomial shear deformation function was derived from shear stress across the thickness of a rectangular plate section. The third order polynomial shear deformation function was employed to the governing equation and compatibility equation to obtain the displacement function (deflection, shear deformation rotation in x direction and shear deformation rotation in y direction). The general displacement functions obtained were used to satisfy the specified boundary conditions which gave the unique displacement functions for the various plate, (ssss), (cccc), (ccss), (cscs), (cccs), (csss), (ssfs), (ccfc), (csfs), (scfs), (scfc), (ccfs) respectivelyssss. Stiffness coefficients for various plate with their unique displacement functions were calculated. Minimizing total potential energy functional with respect to the coefficients of the displacement functions gave the formula for calculating the coefficients of the displacements and other formulas to calculate the displacements and stresses of the anisotropic thick plate. These formula derived herein were used to analyze typical anisotropic rectangular thick plates. The numerical results obtained for displacements (w) were in good agreement with previous work by other scholars.
Keywords:
Total potential energy