Showing papers in "Acta Mechanica Sinica in 1960"

Rectangular plates with free edges on elastic foundations

Abstract: This paper is a generalization of H Hapel's paper "Ueber das Gleichgewicht von' elastischen Plaiten unter einer Einzellast" (Mathematische Zeitschrift, 6, 1920) It differs from Hapel's paper in four respects:(1) Both symmetrical and unsymmetrical loadings are discussed in detail(2) Origin ,of coordinates are placed at the corner of the plate instead of at the center In this way the functions U, V and its integrals are considerably simplified(3) Both isotropic and ofthotropic plates are treated(4) Both Ritz's and Galerkin's methods of variation are used to solve the problem In the paper the variation equations are tabulated in a standard form and the values of the func-tions U, V and its second derivatives at 11 × 11 points are also listed Once the dimensions a,b and the rigidity D of the plate, the modulus k of the foundation and the concentrated loads P are known, the reader may calculate the deflections of, and the moments in the plate by directly applying these equations