Systematic Presentation of Ritz Variational Method for the Flexural Analysis of Simply Supported Rectangular Kirchhoff–Love Plates | Journal of Engineering Sciences

Systematic Presentation of Ritz Variational Method for the Flexural Analysis of Simply Supported Rectangular Kirchhoff–Love Plates

Author(s): Ike C. C.

Affilation(s): Enugu State University of Science and Technology, P.M.B. 01660, Enugu, Nigeria

*Corresponding Author’s Address: charles.ike@esut.edu.ng

Issue: Volume 5; Issue 2 (2018)

Dates:
Paper received: April 8, 2018
The final version of the paper received: June 10, 2018
Paper accepted online: June 12, 2018

Citation:
Ike C. C. Systematic presentation of Ritz variational method for the flexural analysis of simply supported rectangular Kirchhoff–Love plates / C. C. Ike // Journal of Engineering Sciences. – Sumy : Sumy State University, 2018. – Volume 5, Issue 2. – P. D1-D5.

DOI: 10.21272/jes.2018.5(2).d1

Research Area: MECHANICAL ENGINEERING: Dynamics and Strength of Machines

Abstract. In this work, the Ritz variational method for solving the flexural problem of Kirchhoff–Love plates under transverse distributed load has been presented systematically in matrix form. An illustrative application of the matrix presentation was done for simply supported rectangular Kirchhoff–Love plate under uniformly distributed load. The application used a one term Ritz approximating displacement (coordinate, or basis) function. A one term Ritz approximate solutions obtained for center displacement of square plates showed a difference of 1.9 % from the exact solution for displacement. Solution obtained for the bending moment at the center showed a difference of 7.9 % from the exact solution for bending moment. The one term Ritz approximation for the maximum shear force showed a difference of –10.7 % from the exact solution. The results obtained for a one term Ritz approximation of the displacement shape function was reasonably close for practical purposes.

Keywords: Ritz variational method, Kirchhoff–Love plate, shape function, total potential energy, principle of minimization.

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Scientific journal "The Journal of Engineering Sciences"
ISSN 2312-2498 (Print), ISSN 2414-9381 (Online).

Faculty of Technical Systems and Energy Efficient Technologies
Sumy State University