Static homotopy response analysis of structure with random variables of arbitrary distributions by minimizing stochastic residual error

Innovation and Contributions

Associate Professor Heng Zhang of Yangtze University, together with corresponding author Professor Bin Huang and their collaborators, advanced the determination of homotopy parameters in the homotopy stochastic finite element method from a sample-point approach to a stochastic residual approach. This work advances the development of the homotopy stochastic finite element method.

Abstract

Modelling uncertainties in real engineering structures often involves a variety of probability distributions, creating a need for broadly applicable stochastic analysis methods. This paper proposes a new stochastic homotopy method for evaluating the static response of structures with random variables of arbitrary distributions. A homotopy series expansion approximates the stochastic static response, and its optimal form is determined by minimizing the residual of the stochastic static equilibrium equation, irrespective of the distributions of the random variables. Numerical results for a logarithmic function and a thin plate demonstrate improved accuracy and stability relative to the homotopy stochastic finite element method, whose performance depends on sample selection. At comparable accuracy, the proposed method is more computationally efficient than the arbitrary polynomial chaos (aPC) method. For non-Gaussian random variables with large fluctuations, it also exhibits better convergence than the aPC and perturbation stochastic finite element methods as the expansion order increases. A cable-stayed bridge example further demonstrates its application to a large-scale structure.

Keywords: Stochastic static response; Homotopy; Arbitrary distribution; Karhunen–Loève expansion; Stochastic residual error; Stochastic finite element method

Selected Figures

Citation

DOI: 10.1016/j.compstruc.2023.107153