From Faculty of Vehicle Engineering and Mechanics
By Li Xiang, Yang Dixiong
Aircraft, buildings, bridges, etc. are sometimes subjected to random excitations such as turbulence, wind loads, and earthquakes, and the structures themselves have parameter randomness. Computational stochastic mechanics aims to solve the problems of mechanical analysis, computation and design of engineering structures and industrial equipment under the consideration of stochastic factors. Prof. Yang Dixiong’s team from Department of Engineering Mechanics/State Key Laboratory of Structural Analysis for Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, has made a breakthrough in the research of unified framework of computational stochastic mechanics and established a unified and efficient computational theory and method for stochastic structural analysis, stochastic vibration, structural reliability assessment and optimal design. The related work was recently published in Computer Methods in Applied Mechanics and Engineering and Mechanical Systems and Signal Processing. The first author of the papers is Postdoctoral Fellow Chen Guohai, and the corresponding author is Prof. Yang Dixiong.
Generally, the static and dynamic reliabilities of structures are addressed separately in the existing methods except the computationally expensive stochastic sampling-based approaches. This study establishes a unified framework of reliability analysis for static and dynamic structures based on the direct probability integral method (DPIM). Firstly, the probability density integral equations (PDIEs) of performance functions for static and dynamic structures are presented based on the principle of probability conservation. The DPIM decouples the physical mapping (i.e., performance function) of structure and PDIE, and involves the partition of probability space and the smoothing of Dirac delta function. This study proposes a new adaptive formula of smoothing parameter based on kernel density estimation. Then, the improved DPIM is utilized to obtain the probability density function (PDF) of performance functions by solving the corresponding representative values and the PDIE successively. Furthermore, the reliability of static structure is calculated by integrating the PDF of performance function within safety domain. To overcome the difficulty of evaluating first passage dynamic reliability, the two approaches, namely the DPIM-based absorbing condition (DPIM-AC) and the DPIM-based extreme value distribution (DPIM-EVD), are also proposed. Finally, several engineering examples with stochastic parameters and random excitation indicate the desired efficiency and accuracy of the established framework for unified reliability analysis. Specifically, the challenging issue of dynamic reliability assessment for nonlinear structural system is attacked based on DPIM rather than Monte Carlo simulation or other sampling-based method. The proposed method is beneficial for propagation analysis of aleatory or/and epistemic uncertainties, as well as for stochastic model updating.
The research work was supported by the National Natural Science Foundation of China, and the National Key Research and Development Program of China.
Links to the papers:
Editor: Li Xiang