HYBRID PERTURBATION-GALERKIN METHOD FOR GEOMETRICAL NONLINEAR ANALYSIS OF TRUSS STRUCTURES WITH RANDOM PARAMETERS

The hybrid perturbation-Galerkin stochastic finite element method is used to solve the geometrical nonlinear truss structures with random parameters. The power polynomial expansions are adopted to express the random secant elastic modulus and random responses with respect to displacement terms, respectively. Using the high-order perturbation method, the coefficients of the power polynomial expansions can be obtained, so that the expression of the geometrical nonlinear displacement can be determined. The coefficients terms of the power polynomial expansions obtained are used as the Galerkin trial functions, and the Galerkin projection technique is employed to determine the coefficients of these trial functions. Since the trial functions come from the linear combination of the perturbation solutions, the trial functions selected are self-adaptive to the nonlinear problem. The numerical example about multi random variables with different probability distributions show that since no probability conversion is required for the proposed method so that the conversion errors in the calculation process are avoidable, which results in that the accuracy of the proposed method is higher than that of generalized polynomial chaos method (GPC method). Meanwhile, when the results are equally accurate, the nonlinear algebraic equations about the coefficients of the trial functions obtained by the proposed method is more easy to be solved than that by the GPC method, and the calculation cost of the suggested method is less than that of the GPC method. When the fluctuation of the random variable becomes large, the statistical moments of the structural response calculated by the hybrid perturbation-Galerkin method are closer to the results of the Monte Carlo simulation method than that of the high-order perturbation method, which illustrates that the hybrid perturbation-Galerkin method is effective in solving the stochastic geometric nonlinear problems.