TABLE OF CONTENTS In this chapter we derive equations for the deflection of a thin elastic plate. The bulk of the chapter is devoted to the solution of the problem of axisymmetric bending of solid and annular circular plates. Symbolic manipulation packages are used extensively to obtain solutions for various combinations of the boundary conditions as well as for various loads, with an emphasis on Green's functions. The method of Fourier series is applied to analyze the deflection of a simply supported rectangular plate, a plate on an elastic foundation, and a rectangular membrane. Approximate methods (finite differences and Rayleigh Ritz method) are discussed in some detail, and worked-out examples provide a comparison with exact results. Interactive Fortran programs are accessible on a diskette.
A thin plate is a three-dimensional structure bounded by two parallel planes, such that the distance between them is small compared to the other two dimensions (Fig. 10-1). This geometric assumption allows for an important simplifying hypothesis. Let us call the plane halving the distance between the two bounding planes the middle surface of the plate, and define this to be the z = 0 plane. The following assumptions are made.
The normal to the middle surface remains normal after deformation. This is analogous to the hypothesis of the simple beam theory, which states that a plane, normal to the neutral axis, remains normal after deformation. The consequences of both assumptions are also similar: linear distribution of stress across the thickness of the beam or of...
