Abstract
In practical engineering, uncertain loads usually cause the variations of structure stiffness to affect the security of the structure. To enhance the reliability and find the optimum structure in engineering, a topology optimization method is developed for the optimization of structural stiffness in this paper. The first-order saddle point approximation method is introduced into the topology optimization process. A multi-constrained stiffness optimization model considering uncertain loads is proposed. The corresponding sensitivity mathematical formula for stiffness is also given. The complete optimization iteration process is given. The structural stiffness optimization problems with the joint constraints of volume and displacement are solved here to illustrate the application of the proposed method. In the examples, a U-shape groove in different working situations is considered which includes the single node displacement constraint and the multi-node displacement constraint. The corresponding optimization results of different working situations are compared, and the results accord with the law of engineering.
Highlights
As the complexity of engineering increasing, the study of structural optimization has obtained more and more attentions
Bendsøe and Kikuchi propose the concept of the numerical topology optimization, which is based on the optimization methods and the homogenization theory [7]
This paper proposes a new method of topology optimization under uncertain load with the first order saddlepoint approximation
Summary
As the complexity of engineering increasing, the study of structural optimization has obtained more and more attentions. As one of the optimization strategies, the topology optimization has been widely utilized in engineering structural design [4]–[6]. The method with simplified processing leads to a lower confidence in the calculation results In engineering practice, these uncertainties could lead to the instability of the system or even have influence on safety [16]–[27]. D. Shi et al.: Structure Topology Optimization With the First-Order Saddlepoint Approximation topology optimization method under uncertain loads. This paper proposes a new method of topology optimization under uncertain load with the first order saddlepoint approximation. The stiffness optimization of multi-constrained structures under uncertain loads are mainly considers.
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