Masters Theses


"Many engineering structures use thin rectangular plates as members. These plates may be loaded and supported in numerous ways. The edges may be freely supported, rigidly supported, or supported by elastic members. The load may be applied normal to the plane of the plate, in which case the problem becomes essentially one of bending. If the load is applied in the plane of the plate, placing it in compression, the problem becomes one of stability.

This investigation is concerned with the stability of plates rigidly supported on all edges and having a compressive load applied to two opposite edges of the plate. The smallest load that causes the plate to buckle is the only one of interest. In a problem of this type, the exact solution involves solving a fourth order differential equation from which difficult transcendental equations result. To make these equations easier to handle curves may be plotted. Solutions do not exist for all possible edge restraints and boundary conditions. This investigation has two objectives, namely, to investigate and verify an approximate solution to these problems based on the assumption of an equation for the buckled plate or rather the shape of the buckled plate, and to apply the approximate method to solve a problem having no known solution.

The first objective is attained by applying the energy method to problems with known solutions. Subsequent use of the approximate method, on these same problems, yields results which can be compared to those found by the energy method.

The specific problems used in this verification are a column simply supported at both ends, a column built-in at both ends, a plate simply supported at all edges and a plate simply supported at two edges and built-in at two edges.

After the verification of the approximate method, the problem concerning a plate built-in at all edges was solved"--Introduction, pages 1-2.


Miles, Aaron J.

Committee Member(s)

Rankin, Rolfe M., 1892-1974
Schaefer, Rodney A., 1926-2002
Remington, Charles R., 1924-2013


Mechanical and Aerospace Engineering

Degree Name

M.S. in Mechanical Engineering


Missouri School of Mines and Metallurgy

Publication Date



vi, 33 pages

Note about bibliography

Includes bibliographical references (page 32).


© 1959 James Arthur Jones, All rights reserved.

Document Type

Thesis - Open Access

File Type




Subject Headings

Plates (Engineering) -- Stability -- Mathematical models
Buckling (Mechanics)
Structural analysis (Engineering) -- Approximation methods

Thesis Number

T 1233

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