A THEORETICAL SOLUTION FOR AXIALLY SYMMETRIC PROBLEMS IN ELASTODYNAMICS

This paper presents a theoretical solution for the basic equation of axisymmetric problems inelastodynamics.The solution is composed of a quasi-static solution which satisfies inhomogeneous boundaryconditions and a dynamic solution which satisfies homogeneous boundary conditions.After the quasi-static so-lution has been obtained an inhomogeneous equation for dynamic solution is found from the basic equation.By making use of eigenvalue problem of a corresponding homogeneous equation,a finite Hankel transform isdefined.A dynamic solution satisfying homogeneous boundary conditions is obtained by means of the finiteHankel transform and Laplace transform.Thus,an exact solution is obtained.Through an example of hollowcylinders under dynamic load,it is seen that the method,and the process of computing are simple,effectiveand accurate.