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Saudi Journal of Civil Engineering (SJCE)
Volume-4 | Issue-09 | 137-149
Original Research Article
Novel Formulas for Displacements and Stresses of Thick Anisotropic Rectangular Plate
Ibearugbulem OM, Ezeh JC, Ozioko HO, Anya UC
Published : Nov. 5, 2020
DOI : 10.36348/sjce.2020.v04i09.002
Abstract
This work concentrated on the analysis of thick anisotropic rectangular plate through exact approach using third order shear deformation theory. Refined plate theory assumptions were relied upon to formulate the total potential energy functional. Displacement field, kinematic relations, constitutive relations and stress displacement relations were also obtained from the assumptions. Kinematic relations and Stress-displacement relations were substituted into the universal strain energy equation to formulate the strain energy equation. Total potential energy functional for the analysis of thick anisotropic rectangular plate was obtained by adding the external work and strain energy equation together. The total potential energy functional was differentiated with respect to the out plane deflection (w), shear deformation rotation in x direction (_x) and shear deformation rotation in y direction (_y). This yielded the governing equation and two compatibility equations of thick anisotropic rectangular plate. Third order polynomial shear deformation function which was derived by Ibearugbulem et al. was relied upon to obtain the displacement functions. From these displacement functions, the unique displacement functions for the SSSS plate boundary condition were determined. Also the stiffness coefficients were calculated for the SSSS plate boundary condition. The formulas for calculating the coefficients of the displacements were combined with elastic equations to determine the novel formulas which were used in calculating for displacements (u, v and w) and stresses (σ_RR,σ_QQ,τ_RQ,τ_RS and τ_QS) at various angle fiber orientation (0^0, 〖15〗^0, 〖30〗^0, 〖45〗^0, 〖60〗^0, 〖75〗^0 and 〖90〗^0) and various span to thickness ratio, α (5, 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100). These formula were used to analyze typical anisotropic rectangular thick plates. The results obtained were shown on Tables 1, 2, 3, 4 and 5. These numerical results obtained showed some level of agreement with previous works by other scholars. Hence the developed method is recommended for analyzing thick rectangular anisotropic plates.
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