Abstract: In this paper, we show that Backlund transformation derived by Leibbrandt et al. for the Liouville’s equation in three spatial dimensions, ▽²a=expa, ▽²=-∂_x²+∂_y²+∂_z² can be decomposed into several Backlund transformations for the same equation in two spatial dimensions, moreover, the superposition formula which is derived from this transformation is actually invalid, thus the discussions based on that formula is incorrect as well. We also considered some results about the Liouville’s equation in N spatial dimensions.

Key words: engineering structure, dynamic response, dynamic sensitivity, reliability constraint, optimal design