9312640 Lin The research is directed at evaluating the reliability (1 probability of failure) of strongly nonlinear dynamical systems under severe earthquake excitations. Two types of nonlinear systems are considered: (l) highly hysteretic structures, exhibiting large deformations, and (2) non structural systems, which respond to seismic excitations in the form of rocking, sliding, or combined rocking and sliding, essentially as rigid bodies. Failure of hysteretic structures is conceived to be an accumulation of damage to a critical magnitude, which is measured by both the largest deformation and the total dissipated hysteresis energy. Failure of rigid body type systems occurs due to topping, colliding, or pounding against each other. When a failure state is reachable, it provides an absorbing boundary for the sample space in which the sample functions are distributed. A sample function is removed from the population, once it reaches the absorbing boundary. Therefore, the total probability cannot be conserved within the sample space. Such an absorbing boundary must be taken into account; otherwise, the reliability estimate is unconservative. Moreover, while failure of a hysteretic structure is manifested primarily in a predominant failure mode, a random excitation consisting of a wide band of frequencies has the tendency to push the system slightly from the dominant mode from time to time, thereby permitting some energy to be consumed by other non dominant modes. These facts will be considered in this research to obtain an accurate probabilistic characterization of the response of these highly nonlinear systems. ***
