Abstract: Because of the continuum structural with uncertainty is common, the research of reliability-based topology optimization is of great significance. Techniques from the fourth prime matrix and the finite element method are employed to present the practical and effective method for the reliability-based topology optimization for continuum structural with abnormal distribution parameters in the case of given the first-forth moments of basic random variables. The topology optimization is described as pattern recognition to element and the K nearest neighbor method is extracted from the technique of pattern recognition to seek the optimized result with the element stress as variable and Euclidean distance of stress as recognition standard. Several numerical examples given to compare with optimized results with deterministic indicate that the approach proposed is a convenient and practical method.

Key words: Continuum, Fourth prime matrix, K nearest neighbor, Reliability, Topology optimization