Due to the deficiency of the classical Monte Carlo method and many stochastic finite element (SFE) methods [1,2,3] and even the poor accuracy of obtaining qualitative information in stochastic systems, a much more elaborate but accurate approach covering the probability distributions of structural responses is employed in the present study [4,5,6].

A considerable simplified numerical procedure is also adopted in this paper to implement a successful stochastic simulation of a short-pier shear wall specimen, which is mainly composed of a deterministic nonlinear analysis procedure, choice of sampling points with a number-theoretical method and the stochastic analysis based on probability density evolution.

By using a novel elasto-plastic damage constitutive model for concrete, the load-displacement curves between experimental result and analytical prediction are firstly compared to validate the deterministic nonlinear analysis of short-pier shear wall specimen with twin coupling beams.

By means of the number-theoretical method, 217 combinations of Young's modulus and the compressive strength are selected as the final sampling points. A series of structural loads, tensile damage and shear damage curves with regard to the free-end displacement are first extracted from the short-pier shear wall model using 217 combinations of the Young's modulus and the compressive strength and then converted into the corresponding equidistant stochastic processes.

By using density evolution theory, the characteristics of means, standard deviations and coefficients of variation of the structural load, tensile and shear damage at the root of the compression side are calculated respectively; moreover, the probability density functions of above-mentioned structural response at typical levels of displacement together with their corresponding contours of equal probability at the ultimate state are also obtained, which clearly illustrated the fact that the diversity and complexity of the stochastic damage evolutions are covered by the deterministic representation of the macro structural response. Although the stochasticity of the damage evolutions is remarkably greater than that of macro mechanical response, abundant stochastic fluctuations might lead to stable and uniform structural behaviours in the end.

1

S. Nakagiri and T. Hisada, "Stochastic finite element method applied to structural analysis with uncertain parameters", Proceedings of the International Conference on Finite Element Methods, Aechen, Germany, 1982, 206-211.

2

I. Elishakoff, Y.J. Ren and M. Shinozuka, "Improved finite element method for stochastic structures", Chaos, Solitons & Fractals, 5 (5), 833-846, 1995. doi:10.1016/0960-0779(94)00157-L

3

G. Muscolino, G. Ricciardi and N. Impollonia, "Improved dynamic analysis of structures with mechanical uncertainties under deterministic input", Prob. Engrg. Mech., 15 (2), 199-212, 2000. doi:10.1016/S0266-8920(99)00021-1

4

J. Li and J.B. Chen, "Probability Density Evolution Method for Dynamic Response Analysis of Structures with Uncertain Parameters", Computational Mechanics, 34, 400-409, 2004. doi:10.1007/s00466-004-0583-8

5

J.B. Chen and J. Li, "Dynamic Response and Reliability Analysis of Nonlinear Stochastic Structures", Probabilistic Engineering Mechanics, 20(1), 33-44, 2005. doi:10.1016/j.probengmech.2004.05.006

6

J. Li and J.B. Chen, "Dynamic Response and Reliability Analysis of Structures with Uncertain Parameters", International Journal of Numerical Methods in Engineering, 62, 289-315, 2005. doi:10.1002/nme.1204

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