Improved response surface method and its application to stiffened plate reliability analysis

An improved response surface method is proposed and applied to the reliability analysis of a stiffened plate structure. The response surface function is formed in a cumulative manner in order to account properly for the second order effects in the response surface with acceptable computational effort involved in the evaluation of the state function. First, a linear response surface is formed by searching for the design point by the first order reliability method. The vector projection technique is used to allocate the sampling points close to the response surface. Then, the linear response surface is improved by adding square terms, and the second order reliability method is employed to search for the design point. All the available sampling points except those generated in the very initial stage are used to obtain a well-conditioned system matrix for regression. Lastly, the response surface obtained is checked for the selected sampling points. If the response surface function is not satisfactory, it is improved adaptively by adding cross terms and removing some of the second order terms. In this way an appropriate incomplete second order response surface can be obtained and used for reliability analysis. A stiffened plate under combined load effects is analysed. The load components, plate thicknesses, and Youngʹs modulus are treated as random variables. Structural imperfection in the form of critical buckling mode is also treated as a random variable. Sensitivity analyses are performed with respect to these random variables.