Document Type
Thesis
Date of Award
5-31-1984
Degree Name
Master of Science in Mechanical Engineering - (M.S.)
Department
Mechanical Engineering
First Advisor
Herbert H. Spencer
Second Advisor
Roman I. Andrushkiw
Third Advisor
James L. Martin
Abstract
This thesis is concerned with the buckling of rectangular plate-shaped elements under biaxial compressive loading with patch loading along one pair of opposite edges. The loading along the other edges is continuous but the discontinuous loading covers different patches along opposite edges. All the applied loads are uniformly distributed. The critical buckling load of this type of plate element is an important factor in the optimal design of many types of thin-walled structures. Frequently the nature of the problem prohibits an exact or even a general form of solution, thus dictating a numerical approach.
The problem has been attacked to achieve maximum possible accuracy. First the statically-indeterminant stress distribution was calculated in the various plates for the different loading cases by use of the Finite Difference method. Then these results were used to calculate the buckling loads by finding the eigenvalues of the governing equations which are partial differential equations with variable coefficients. This calculation involves numerical solutions of generalized eigenvalue problems. Finally the buckling load is found from the lowest eigenvalues.
The entire process is programmed in FORTRAN for calculation on a digital computer. The program was written so that, by inputting the parameters to describe the loading, the boundary conditions, the aspect ratio, and the desired number of plate divisions ( that determines the accuracy of the method ), the program will calculate all the stresses , eigenvalues, and ( most important ) the critical buckling coefficient and load. This is all done in one general computer program.
The problem was solved for the following two sets of support boundary conditions :
(a). Rectangular plate with all four edges simply supported,
(b). Rectangular plate with all four edges clamped.
The results of the calculations been reduced to curves suitable for design purposes. Fourteen cases are considered:
(a). Seven different load combinations for square plates;
(b). Seven different load combinations for plates with an aspect ratio varying from 1/3 to 3.
For the square plates the results are given in the form of charts, with the buckling coefficients K-cr plotted against various constants that represent the intensity of uniform loads in the direction other than direction of partial edge loads. For the rectangular plates the results are plotted in charts that show the relation between buckling coefficient and aspect ratio.
For rectangular plates the thesis presents a study of the results obtained by White and Cottingham in 1962, who investigated the buckling of plates under partial loading in only one direction while the other direction is free of loads. Their work has been corrected and improved.
Recommended Citation
Surjanhata, Herli, "Plate buckling under biaxial patch loading" (1984). Theses. 3621.
https://digitalcommons.njit.edu/theses/3621
