Abstract Summary
Incremental dynamic analysis (IDA) constitutes one of the most commonly employed methodologies for estimating the functional relationship between the Intensity Measures (IMs) and the selected Engineering Demand Parameters (EDPs). Subsequently, the information provided via this functional relationship is utilized in conjunction with appropriately defined limit states for quantifying system fragilities [1]. For an EDP-based criterion the twisting patterns of IDA curves can point multiple limit-state points, requiring the handling of this ambiguity on an ad hoc basis. Clearly, the mathematical entity of an IDA curve is interwoven with scaling as well as timing ambiguity. This peculiarity brings to the fore the need for studying the problem of the limit state exceedance (i.e. the onset of stiffness and strength degradation which signals the entrance of a structure into a limit/damage state) through the lens of the first-passage excursion time. A novel stochastic incremental dynamics (SIDA) methodology is developed for nonlinear structural systems exposed to a seismic excitation vector consistently aligned with contemporary aseismic codes provisions. Rendering to the concept of non-stationary stochastic processes, the vector of the imposed seismic excitations is characterized by evolutionary power spectra compatible in a stochastic sense with elastic response acceleration spectra of specified modal damping ratio and scaled ground acceleration [2]. The proposed technique can be construed as a two-stage approach. Firstly, relying on a statistical linearization treatment [3], the equivalent time-dependent natural frequencies (t) and modal damping ratios (t) are determined. Secondly, utilizing the time-dependent equivalent elements in conjunction with a combination of deterministic and stochastic averaging treatment [4,5], the system first-passage limit state exceedance probability density functions (PDFs) are determined for various limit states in an efficient and rigorous manner. The proposed SIDA technique has a number of noteworthy attributes such as (i) accounting for nonlinear/hysteretic system behavior; (ii) modeling the seismic excitation in the form of a vector of stochastic processes endowed with non-stationary characteristics; (iii) proposing a novel EDP that of the first-passage limit state exceedance which is naturally coupled with limit-state requirements; and (iv) providing reliably higher order statistics (PDF) of the selected EDP in a computationally efficient manner, by avoiding demanding nonlinear response time-history analyses in a Monte Carlo-based context. References: [1] Vamvatsikos D., Cornell C. A. Incremental dynamic analysis, Earthquake Engineering and Structural Dynamics 2002; 31:491-514. [2] Cacciola P., 2010. A stochastic approach for generating spectrum compatible fully nonstationary earthquakes, Computers & Structures 88, 889–901. [3] Roberts JB, Spanos PD. Random vibration and statistical linearization. New York: Dover Publications; 2003 [4] Mitseas, I.P., Kougioumtzoglou, I.A., Spanos P.D., Beer, M. Nonlinear MDOF system Survival Probability Determination Subject to Evolutionary Stochastic Excitation. Journal of Mechanical Engineering; 62 7-8, 440-451, 2016. [5] Kougioumtzoglou I. A., Ni P., Mitseas I. P., Fragkoulis V. C., Beer M., 2022. An approximate stochastic dynamics approach for design spectrum based response analysis of nonlinear structural systems with fractional derivative elements, International Journal of Non-Linear Mechanics 146, 104178, doi: 10.1016/j.ijnon linmec.2022.104178
