Abstract
This paper analysed the flexural behaviour of SSSS thick isotropic rectangular plates under transverse load using the Ritz method. It is assumed that the line that is normal to the mid-surface of the plate before bending does not remain the same after bending and consequently a shear deformation function f (z) is introduced. A polynomial shear deformation function f (z) was derived for this research. The total potential energy which was established by combining the strain energy and external work was subjected to direct variation to determine the governing equations for the in – plane and out-plane displacement coefficients. Numerical results for the present study were obtained for the thick isotropic SSSS rectangular plates and comparison of the results of this research and previous work done in literature showed good convergence. However, It was also observed that the result obtained in this present study are significantly upper bound as compared with the results of other researchers who employed the higher order shear deformation theory (HSDT), first order shear deformation theory (FSDT) and classical plate theory (CPT) theories for the in – plane and out of plane displacements at span – depth ratio of 4. Also, at a span - depth ratio of and above, there was approximately no difference in the values obtained for the out of plane displacements and in-plane displacements between the CPT and the theory used in this study.
Highlights
A plate is said to be a flat structural component bound by two planes that are parallel to each other called faces and a cylindrical surface called an edge [1]
This research seeks to present a direct, simplified, and precise approach through the use of the Ritz energy method resulting in Polynomial Displacement Functions to solve the problems of thick rectangular isotropic plates under transverse loading
The results obtained for the deflection at the center of SSSS isotopic thick plate, the in-plane stresses, and the vertical shear stresses at the edges of the plate for different span to depth ratio corresponding to different values of b subjected to a uniformly distributed load, q are shown in Tables (1 - 4)
Summary
A plate is said to be a flat structural component bound by two planes that are parallel to each other called faces and a cylindrical surface called an edge [1]. Consequent upon the deficiency of the classical plate theory, many researchers have developed series of theories to analyze thick plates by taking into account the shear deformation. Examples of such theories include Mindlin’s first-order, Reddy’s third-order, and Reissner’s higher-order theories. Upon analysis and design of thick plates using these trigonometric displacement functions, the use of the Fourier series becomes unavoidable resulting in rigorous and complicated mathematical calculations which lead to idealizing most of these thick plates as thin plates leading to erroneous designs which are not dependable and could lead to failure. This research seeks to present a direct, simplified, and precise approach through the use of the Ritz energy method resulting in Polynomial Displacement Functions to solve the problems of thick rectangular isotropic plates under transverse loading
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