Transient Stress in an Elastic Sphere under Diametrical Concentrated Impact Loads

抄録

This paper presents an exact solution for the stress wave propagation in an elastic sphere under two equal and opposite concentrated loads varying with time as the Heaviside unit step function at the end points of a diameter. The solution is based on the stress function approach and the Laplace transform method for axisymmetric problems. The Laplace transformed solution is given by a meridional Legendre function and a radial spherical Bessel function which are derived from the method of separation of variables. Inverse transform to which is applicable the residue theorem, gives and exact solution of the transient response up to the arrival time of stress waves. The results of numerical evaluation are shown graphically for the displacement and the stress variations versus time in the elastic sphere.