Showing papers in "Journal of Applied Mechanics in 1955"

A new approach to the analysis of large deflections of plates

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.

Axially symmetric flexural vibrations of a circular disk

Abstract: At high frequencies, the flexural vibrations of a plate are described very poorly by the classical (iagrange) theory because of neglect of the influence of coupling with thickness-shear vibrations. The latter may be taken into account by inclusion of rotatory inertia and shear deformation terns in the equations. The resulting frequency spectrum is given, in this paper, for the case of axially symmetric vibrations cf a circular disk with free edges and is compared with the spectrum predicted by the classical theory.

Further Work on the General Three-Dimensional Photoelastic Problem

Abstract: Summary It is known that purely photoelastic procedures cannot solve the general three-dimensional stress problem. Photoelasticity furnishes data from which only the principal shears can be determined, but not the principal stresses. A new, general, and practical method of solution which has been described previously(1,2) is reviewed briefly, and possible variations in procedure are discussed. This method combines the photoelastic data from frozen stress patterns with a numerical integration of one of the differential equations of equilibrium in Cartesian coordinates. The actual principal stresses at each point of a homogeneous and isotropic body of arbitrary shape subjected to a general system of loads are thereby determined. The method has been applied previously to a sphere subjected to diametral compressive loads of 172 lb. The present paper contains the results from a second sphere subjected to 79.6 lb which show that the degree of reproductibility of results is high. Very good agreement is also shown to exist with a theoretical solution of the same problem by Sternberg and Rosenthal.(3) The paper also contains the solution of a short rectangular parallelepiped loaded through a small flat circular die. The investigation was conducted in the Photoelastic Laboratory of the Mechanics Department of Illinois Institute of Technology.