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A New Approach to the Analysis of Large Deflections of Plates


Berger, Howard Martin (1954) A New Approach to the Analysis of Large Deflections of Plates. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/FA0E-1X79.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Aeronautics and Mathematics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Minor Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Williams, Max L.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1954
Record Number:CaltechETD:etd-12042003-163054
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4772
Deposited By: Imported from ETD-db
Deposited On:11 Dec 2003
Last Modified:07 Jun 2023 22:59

Thesis Files

PDF (Berger_hm_1954.pdf) - Final Version
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