KANTOROVICH-EULER LAGRANGE-GALERKIN’S METHOD FOR BENDING ANALYSIS OF THIN PLATES

Authors

  • CC Ike DEPT. OF CIVIL ENGINEERING, ENUGU STATE UNIVERSITY OF SCIENCE & TECHNOLOGY, ENUGU. ENUGU STATE. NIGERIA

DOI:

https://doi.org/10.4314/njt.362.1281

Keywords:

Kantorovich-Galerkin, thin plate, potential energy functional, Euler-Lagrange differential equation.

Abstract

In this work, the Kantorovich method is applied to solve the bending problem of thin rectangular plates with three simply supported edges and one fixed edge subject to uniformly distributed load over the entire plate surface. In the method, the plate bending problem is presented using variational calculus. The total potential energy functional is found in terms of a displacement function constructed using the Kantorovich procedure, as the product of an unknown function of x (f(x)) and a coordinate basis function in the y direction that satisfies the displacement end conditions at y = 0, y = b. The Euler-Lagrange differential equation is determined for this functional. The Galerkin method is then used to obtain the unknown function f(x). Bending moment curvature relations are used to find the bending moments and their extreme values. The results obtained agree remarkably well with literature. The effectiveness of the method is demonstrated by the marginal relative error obtained for one term displacement solutions.

http://dx.doi.org/10.4314/njt.v36i2.5

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Published

2017-03-31

Issue

Section

Building, Civil & Geotechnical Engineering

How to Cite

KANTOROVICH-EULER LAGRANGE-GALERKIN’S METHOD FOR BENDING ANALYSIS OF THIN PLATES. (2017). Nigerian Journal of Technology, 36(2), 351-360. https://doi.org/10.4314/njt.362.1281