MODAL-ANALYSIS OF ELASTIC-PLASTIC PLATE VIBRATIONS BY INTEGRAL-EQUATIONS

A direct boundary element method for the vibration problems of thin elastic-plastic plates is presented. Dynamic fundamental solutions of a suitably shaped finite domain are used in modal form. The series Green's functions are separated into a quasistatic and a dynamic part. Often the series of the quasistatic part can be written in a faster converging form than the equivalent modal series. Analytical integration in the vicinity of the singularity is performed on the closed form fundamental solutions of the infinite domain, and only the non-singular differences from the actual Green's functions are represented in series form. This paper gives a general formulation of this method for Kirchhoff plates on an arbitrary elastic foundation. After integration, the resulting algebraic equations are arranged in a form most convenient for a time-stepping analysis of inelastic response. This rearrangement has to be performed only once, if the time step is kept constant. Constitutive equations are integrated by an implicit backward Euler scheme for plane stress. Applications are shown for impacted circular plates on several different foundations.