A Study On Reliability-based Structural Optimization

This dissertation presents a study on the theories and algorithmics of reliability based structural optimization. Efficient algorithmics are proposed for failure probability and reliability based structural optimization considering failure probability.The creative work presented in this dissertation is in the following three aspects:(1) In order to enhance the accurracy of the polynomial response surface function, the current response surface method usually employed a higher order response surface function in the field of structural reliability analysis, which inevitably brought greater computation and its result was far from ideal. A new strategy utilizing a mixed variable based response surface function is proposed for the failure probability calculation, which combines with the success theory of the intermediate variable method.(2) It is almost impossible to get a reliable estimation of structural reliability using reliability index and the computational cost is often too high to calculate accurate failure probability. An alternative formation with approximate failure probability is proposed for the reliability based structural optimization, and problems with the reliability index based optimization formulation are discussed.(3) An efficient algorithm is proposed for sensitivety analysis of failure probability based on the relationship between reliability index and failure probability, and a new algorithmic is proposed utilizing a sequential linear programming algorithm based on failure probability.Four main conclusions of this dissertation are as follows:(1) The mixed variable based response surface reliability analysis method proposed is very efficient and accurate compared with the current response surface method.(2) The current response surface method is very sensitivity to the variation coefficient of random variable, the allowable displacement, and the magnitude of the failure probability, accuracy of the proposed method is not affected by these factors.(3) It is showed that the mathematical model based on the approximate failure probability is more reasonable than the model based on reliability index as the structure can be optimiged with its reliability properly considered.(4) The sequential linear programming algorithm proposed in this dissertation is very effective for the optimization of truss structures with reliability constraints.