The project uses the nonlinear programming formulation to define a generalized reliability index as the difference between external work and internal strain energy. The nonlinear strain energy formulations are investigated in order to introduce both linear and nonlinear material behavior. Expanded constraint sets are developed to be consistent with the more generalized mechanisms of failure associated with the nonlinear optimization objective. An alternative approach based on the static formulation is also followed, obviating the need for modal definitions. Finally, the combination of failure probabilities into system reliability is pursued in terms of the union of failure events in a stepwise search.
