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

•A novel stochastic homotopy method is proposed to solve static problems involving arbitrarily distributed random variables.•The optimal homotopy series expansion is obtained by minimizing the stochastic residual error.•The proposed method shows better convergency and efficiency than the aPC method in the case of non-Gaussian random field.•This method is successfully applied to the stochastic static analysis of the large-scale engineering structure.