UC San Diego

The geometric, mechanical, material and loading parameters used to define the mechanics-based finite element (FE) models of structural systems as well as their seismic input are characterized by significant uncertainties. The rational treatment of uncertainties in computational mechanics has been the object of increasing attention in recent years. Modern design codes indirectly account for parameter and model uncertainties in order to ensure satisfactory designs. Thus, in addition to accurate deterministic models, methods are needed to propagate uncertainties from the parameters defining the FE model of a structure to the engineering demand parameters. FE response sensitivities (RSs) to both model and loading parameters represent an essential ingredient in studying this complex uncertainty propagation. New RS algorithms based on the Direct Differentiation Method (DDM) are derived and implemented in general-purpose nonlinear structural analysis frameworks. The use of the DDM is extended to (1) force-based frame elements, (2) steel- concrete composite structures, and (3) three-field mixed FEs. In addition, the effects on RS continuity of using smooth versus non-smooth material constitutive models are thoroughly examined. An efficient simulation technique for an existing fully non-stationary stochastic earthquake ground motion model is developed. The definition of non- geometric spectral characteristics is extended to general complex-valued non-stationary stochastic processes. Closed -form approximate solutions of the first-passage problem are developed for single- and multi-degree-of-freedom linear elastic systems. First-order second-moment approximations of the first- and second-order statistics of the response of linear/nonlinear structural systems with random/uncertain parameters and subjected to quasi- static and/or dynamic load(s) are computed efficiently using DDM-based FE RSs. The probability of a structural response quantity exceeding a specified threshold level is obtained by using the First-Order Reliability Method in conjunction with the DDM-based FE RSs in the search for the Design Point(s) (DP). A new method, referred to as Multidimensional Visualization in the Principal Planes, is developed to explore the geometry of limit-state surfaces near the DP(s) in reduced-spaces defined by planes of major principal curvatures at the DP. A new hybrid reliability analysis method (DP search - Response Surface - Importance Sampling) is developed and tested. Based on pushover and time history analyses, examples of both time- invariant and time-variant reliability analysis of structural systems are presented to illustrate the probabilistic methods developed