Three-Dimensional Analysis of Anisotropic Rectangular Plate Using the Alternative II Refined Plate Theory

Abstract:

In this work, the total potential energy of an anisotropic plate subjected to uniformly distributed lateral forces was developed using a complete three-dimensional constitutive relation. The kinematics equations were developed based on the Alternative II Refined plate theory. Variation of the total potential energy with respect to displacement and rotations gave the governing equation and compatibility equations respectively. By solving the governing and compatibility equations, a polynomial displacement function was obtained which by satisfying the boundary conditions gave the peculiar displacement function for any specific case. The stiffness coefficients for an anisotropic plate were then obtained using the displacement function. Thereafter, using the stiffness coefficients and the displacement functions, the equations for the in-plane normal and shear stresses as well as the transverse normal and shear stresses were determined. Also, the equations for the lateral displacement and the in-plane displacements were determined. The numerical values of the in-plane and out-of-plane stresses parameters as well as the displacement parameters were determined for a square plate for span to thickness ratios of 5, 10, 20 and 100 at angle of fiber orientations of 08, 308, 458, 608 and 908. It was observed that the variations in the stresses and displacements are only significant for span to thickness ratio of 20 and less. This signifies that the theory which considers shear deformation is suitable for thick plate analysis. The results from this work are compared with the works of previous researchers using simple percentage difference and the values are reasonable as the maximum percentage difference is 19.49%.

• Periodical: International Journal of Engineering Research in Africa (Volume 73)
• Pages: 97-115
• DOI: https://doi.org/10.4028/p-EM5iEh
• Online since: May 2025
• Authors: Duke I. Bertram*, David O. Onwuka, Owus M. Ibearugbulem, Chinenye Okere
• Keywords: Alternative II Theory, Anisotropic, Rectangular Plate, Three-Dimensional Analysis, Total Potential Energy

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