A New Approach to the Analysis of Large Deflections of Plates

Author: Berger, Howard Martin

Year: 1954

Degree: Dissertation (Ph.D.)

Advisor: Williams, Max L.

Committee Member: Unknown, Unknown

Option: Aeronautics; Mathematics

DOI: 10.7907/FA0E-1X79

Abstract

As a result of the assumption that the strain energy due to the second invariant of the middle surface strains can be neglected when deriving the differential equations for a flat plate with large deflections, simplified equations are derived that can be solved readily. Computations using the solution of these simplified equations are carried out for the deflection of uniformly loaded circular and rectangular plates with various boundary conditions. Comparisons are made with available numerical solutions of the exact equations. The deflections found by this approach are then used to obtain the stresses, and the resulting stresses are compared with existing solutions. In all the cases where comparisons could be made, the deflections and stresses agree with the exact solutions within the accuracy required for engineering purposes.

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