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

A direct boundary element method for the vibration problems of thin el astic-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. Ofte n the series of the quasistatic part can be written in a faster conver ging form than the equivalent modal series. Analytical integration in the vicinity of the singularity is performed on the closed form fundam ental solutions of the infinite domain, and only the non-singular diff erences from the actual Green's functions are represented in series fo rm. This paper gives a general formulation of this method for Kirchhof f plates on an arbitrary elastic foundation. After integration, the re sulting algebraic equations are arranged in a form most convenient for a time-stepping analysis of inelastic response. This rearrangement ha s to be performed only once, if the time step is kept constant. Consti tutive equations are integrated by an implicit backward Euler scheme f or plane stress. Applications are shown for impacted circular plates o n several different foundations.