A new homotopy-based approach for structural stochastic analysis

作者：Zhang, Heng; Huang, Bin^*

来源：Probabilistic Engineering Mechanics, 2019, 55: 42-53.

DOI：10.1016/j.probengmech.2018.09.001

• Random static problem
• Homotopy analysis method
• Taylor series
• Perturbation method
• Stochastic finite element method

This paper presents a homotopy-based method to calculate the stochastic responses of a structure under static loads involving uncertainties in materials, external loads, and structural geometries. The proposed method is based on the homotopy analysis method. In this method, the stochastic responses are represented by an infinite multivariate homotopy series of the involved random variables, and all the deterministic coefficients in the multivariate series are determined through solving a series of various order of deformation equations. This homotopy series solution obtained has a relatively large convergence domain due to the approach function compared with the Taylor series, which makes the series solution independent of random parameters with small fluctuation. Further, two dimension reduction approximations are proposed to improve the computational efficiency of the solution. Five mathematical functions and three solid-mechanics examples show that the proposed method can produce very accurate results with reduced or similar computational efforts compared with the existing methods.

• 出版日期2019-1
• 单位武汉理工大学