# A Ritz's method based solution for the contact problem of a deformable rectangular plate on an elastic quarter-space

S. Guenfoud, S. V. Bosakov, Debra Laefer

Research output: Contribution to journalArticle

### Abstract

In this article, Ritz's method is used to calculate with unprecedented accuracy the displacements related to a deformable rectangular plate resting on the surface of an elastic quarter-space. To achieve this required three basic steps. The first step involved the study of Green's function describing the vertical displacements of the surface of an elastic quarter-space due to vertical force applied on its surface. For this case, an explicit formula was obtained by analytically resolving a complicated integral that did not previously have an analytical solution. The second step involved the study of the coupled system of a plate and an elastic quarter-space. This portion focused on determining reactive forces in the contact zone based on Hetenyi's solution. After determination of the reactive forces, certain features were attributed to the plate's edges. The final step involved the application of Ritz's method to determine the deflections of the plate resting on the surface of the quarter-space. Finally, an example calculation and validation of results are given. This is the first semi-analytical solution proposed for this type of contact problem.

Original language English (US) 1822-1829 8 International Journal of Solids and Structures 47 14-15 https://doi.org/10.1016/j.ijsolstr.2010.03.014 Published - Jul 2010

### Fingerprint

Ritz Method
rectangular plates
Rectangular Plate
Contact Problem
Contacts (fluid mechanics)
Analytical Solution
Vertical
Green's function
Deflection
Coupled System
deflection
Explicit Formula
Green's functions
Contact
Calculate

### Keywords

• Contact problem
• Deformable rectangular plate
• Geotechnics
• Green's function
• Multi-layered materials
• Quarter-space
• Ritz's method
• Shallow foundations

### ASJC Scopus subject areas

• Modeling and Simulation
• Materials Science(all)
• Condensed Matter Physics
• Mechanics of Materials
• Mechanical Engineering
• Applied Mathematics

### Cite this

In: International Journal of Solids and Structures, Vol. 47, No. 14-15, 07.2010, p. 1822-1829.

Research output: Contribution to journalArticle

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AU - Bosakov, S. V.

AU - Laefer, Debra

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