Graduate Thesis Or Dissertation
 

Deflections of simply supported plywood plate under uniform loading by finite-difference equations

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  • This paper offers a practical solution of the complicated equations for the deflections of nonorthotropic plates; in this discussion plywood plates made of Douglas fir are considered. The intricate partial differential equations are expressed in terms of finite differences. The simultaneous algebraic linear equations thus obtained are easily solved. The theory of obtaining the required elastic constants for the plywood plates is discussed in the introduction. The theory is expanded in Appendix IV by developing the general expression for the deflection of a thin plate. This expression is used in the experimental methods for obtaining the elastic constants. Part I explains the tests performed on the plywood plates to derive the elastic constants. The plates were cut with the face grain making angles of 0, 22 1/2, 45, 67 1/2, and 90 degrees with the coordinate axes. Bending and torsion tests were conducted on each plate. Three means of supporting the plates in the bending tests were investigated in order to determine the method which would give the most reliable values for the elastic constants. The nonorthotropic plate equation is expressed in terms of finite-difference equations for uniformly loaded and simply supported plates in Part II. These equations are simplified considerably by the considerations of the symmetry that is possessed by the plywood plates. The complete derivation of the nonorthtropic plate equation is given in Appendix III. The theory for the deflections of plywood plates is verified in Part III byconducting experiments on uniformly loaded and simply supported plates. The theoretical and the experimental values of the deflections are compared in a tabulated form; the discrepancy, which varies from 23 to 38 percent, is also indicated. Sample calculations for the elastic constants are included in Appendix I. The generalized Hooke's law is discussed in Appendix II. Also, the stress and strain equations applied to plywood plates are included.
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