# ANALYTICAL BENDING SOLUTION OF ALL CLAMPED ISOTROPIC RECTANGULAR PLATE ON WINKLERâ€™S FOUNDATION USING CHARACTERISTIC ORTHOGONAL POLYNOMIAL

• EI Ogunjiofor DEPT. OF CIVIL ENGINEERING, CHUKWUEMEKA ODUMEGWU OJUKWU UNIVERSITY, ULI, ANAMBRA STATE, NIGERIA.
• CU Nwoji DEPARTMENT OF CIVIL ENGINEERING, UNIVERSITY OF NIGERIA, NSUKKA, ENUGU STATE, NIGERIA.
Keywords: Analytical solution, Winkler foundation, Isotropic rectangular plate, Characteristic Orthogonal Polynomials, works method.

### Abstract

The analytical bending solution of all clamped rectangular plate on Winkler foundation using characteristic orthogonal polynomials (COPs) was studied. This was achieved by partially integrating the governing differential equation of rectangular plate on elastic foundation four times with respect to its independents x and y axis. The foundation was assumed to be homogeneous, elastic and isotropic. The governing differential equation was non-dimensionalised to make it consistent. The deflection polynomials functions were formulated. Thereafter, the Galerkinâ€™s works method was applied to the governing differential equation of the plate on Winkler foundation to obtain the deflection coefficient, . Numerical example was presented at the end to compare the results obtained by this method and those from earlier studies. The percentage difference obtained for central deflection of all clamped rectangular plate loaded with UDL using the method and earlier research worksÂ  for K = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 are: 0.000042, 0.000052, 0.000043, -0.000011, -0.000068, 0.000001, 0.000001, 0.000001, -0.000001, 0.000000, 0.000001. 0.000033, 0.000035, 0.000033, -0.000018, -0.000072, -0.000003, -0.000003, -0.000003, 0.000002, -0.000002, -0.000001. The result showed that an easy to use and understandable model was developed for determination of deflections of all clamped rectangular plates on Winklerâ€™s elastic foundation using principle of COPs.

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Published
2017-06-30
Issue
Section
Building, Civil & Geotechical Engineering

## Journal Identifiers

eISSN: 2467-8821
print ISSN: 0331-8443