Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval

An optimization method for uncertain structures is suggested based on convex model and a satisfaction degree of interval. In the investigated problem, the uncertainty only exists in constraints. Convex model is used to describe the uncertainty in which the intervals of the uncertain parameters are only needed, not necessarily to know the precise probability distributions. A satisfaction degree of interval which represents the possibility that one interval is smaller than another is employed to deal with the uncertain constraints. Based on a predetermined satisfaction degree level, the uncertain constraints are transformed to deterministic ones, and the transformed optimization problem can be solved by traditional optimization methods. For complex structural problems that the optimization model cannot be expressed in an explicit form, the interval analysis method is adopted to calculate the intervals of the constraints efficiently, and whereby eliminate the optimization nesting. Two numerical examples have been presented to demonstrate the efficiency of the suggested method.