The Shape Optimization of Plane Truss Structures with Constraints based on the Failure Probability of Member

부재(部材)의 파괴확률(破壞確率)을 고려(考慮)한 트러스 구조물(構造物)의 형장최적화(形狀最適化)

The algorithm proposed utilizes the tow-levels technique. In the first level which consists of teeatment only the applied load and design stress as the random variables whose parent distribution has the normal distribution, the cross-sectional areas of the truss members such that the their probabilities of failure have the preseribed failure probabilites are optimized by transforming the nonlinear problem into SUMT, and solving it utilizing modified Newton-Raphson method. In the second level, the geometric shape of truss structure is optimized by utilizing the unidirectional search technique of Powell method which makes it possible to minimize only the objective function. The algorithm proposed is numerically tested for the several truss structures with various shapes and loading conditions. The numerical analysis shows that the rate of decreasing the weight of truss structures is dependent on the prescribed failure probability of the each member of truss structure and the covariance of the applied load and design stress.

본(本) 연구(硏究)에서는 전최적화(全最適化) 과정(過程)을 two-Levels로 나누었다. Level-1에서는 작용하중(作用荷重) 및 설계응력(設計應力)을 정규분포(正規分布)로 하는 확률변수(確率變數)로 하여 각부재(各部材)가 허용파괴확률(許容破壞確率)을 초과(超過)하지 않도록 단면(斷面) 최적화(最適化)하고 Level-2에서는 트러스의 절점좌표(節點座標)를 변수(變數)로 하여 형상(形狀) 최적화(最適化)한 것이다. Level-1에서는 유도(誘導)된 비선형계획문제(非線型計劃問題)를 SUMT문제(問題)로 교환(交換)시켜 Modified Newton-Raphson Method에 의한 SUMT법(法)을 채택(採擇)하고 Level-2에서는 Powell Method의 일방향(一方向) 조사법(調査法)에 의해 목적함수(目的函數)만이 최소(最小)가 되도록 하는 기법(技法)을 도입(導入)하여 형상(形狀) 최적화(最適化)를 하였다.