Analysis of thick anisotropic plate through exact approach using third order shear deformation theory
Date
2021-09
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Publisher
Federal University of Technology, Owerri
Abstract
This work presents the Analysis of Thick Anisotropic Plate through Exact Approach using Third Order Shear Deformation Theory. Total potential energy was formed based on the refined plate theory assumptions. Displacement field, kinematic relations, constitutive relations and stress displacement relations were derived from the deformed section of a thick rectangular anisotropic plate. 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 the analysis of thick anisotropic rectangular plate was obtained. The total potential energy functional was minimized by differentiating it with respect to the changes in out-plane deflection, δw, shear deformation rotation in x direction, δ ௫ , and shear deformation rotation in y direction, δ௬ . This yielded the governing equation and two compatibility equations of thick anisotropic rectangular plate. A third order polynomial shear deformation was employed in the governing and compatibility equations to obtain the displacement functions (deflection, w, shear deformation rotation in x direction, ௫ , and shear deformation rotation in y direction, ௬ ). These displacement functions (w, ௫ , ௬) obtained satisfied the specified boundary conditions and it gave the unique displacement functions for each of the twelve plate boundary conditions SSSS, CCCC, CSSS, CCSS, CSCS, CCCS, SSFS, CCFC, SCFS, CCFS and SCFC solved. The stiffness coefficients (ܭଵ, ܭଶ, ܭଷ, ܭସ, ܭହ, ܭ, ܭ, ܭ଼ (were calculated for each of the twelve plate boundary conditions. The formulas for calculating the coefficients of the displacements were combined with elastic equations to determine the formulas which were used in calculating for displacements (u, v and w) and non-dimensional stresses (σୖୖ, σ୕୕, τୖ୕, τୖୗ ܽ݊݀ τ୕ୗ) at various angle fiber orientation (0 , 15 , 30, 45 , 60 , 75 and 90 ) and various span to thickness ratio, α(5, 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100) and for all the twelve boundary conditions. These formulas were used to analyze some typical anisotropic rectangular thick plates by the help of a functional excel worksheet program. The numerical results obtained for displacement (w) and stresses (σതത୶୶തത and σതതത୷୷തത) at aspect ratio of 1.0 and span to thickness ratio of, 20.0, 10.0, and 7.14286, in this study, when compared with the results of Shimpi and Patel showed percentage difference of 0.59, 1.47, 2.70; 0.62, 1.20, 1.91 and 1.31, 0.97, 3.91% which is in good agreement. Hence the developed method is recommended for analyzing thick rectangular anisotropic plates.
Description
This thesis is for the award of Doctor of Philosophy (PhD.) in Civil Engineering (Structures)
Keywords
Potential energy, anisotropic, displacement, stress and governing equation, Department of Civil Engineering, thick plate
Citation
Ozioko, H. O. (2021). Analysis of thick anisotropic plate through exact approach using third order shear deformation theory [Unpublished Doctoral Thesis]. Federal University of Technology, Owerri, Nigeria