Extreme events come with extreme loads, which force structural systems to their limit states. These states are often manifested through large inelastic displacements and rotations that utterly defy linear predictions. Numerically accurate and computationally efficient assessment of responses in materially and geometrically nonlinear regimes is thus indispensable, especially in cases where statistical estimation and stochastic control are the ultimate objectives. This research is involved in the study and development of computational approaches, broadly pertaining to constitutive modeling of materials with coupled plasticity and damage considerations, Bouc-Wen phenomenological hysteretic simulators, and structural element formulations based on hybridized variational principles. In this direction, a major objective of this research is to advance the joint platforms of computational structural mechanics and optimization, as these relate to how nonlinear programming concepts can be integrated with the analysis process to tame sources of computational complexity, and, reversely, to how highly nonlinear simulators can be integrated with optimization algorithms to drive dynamic design and structural intervention decisions.