基于最小势能原理的快堆堆芯多组件接触非线性计算理论研究

Contact Nonlinear Computation Method for Multi-Subassemblies Interaction in Fast Reactor Core

重点研究堆芯多组件的接触非线性计算理论,证明俄罗斯学者Likhachev发展的方法的可扩展性和解决中国实验快堆(CEFR)堆芯组件变形接触计算的可行性。在Likhachev发展的组件接触非线性方法基础上,考虑组件有3个可能的接触高度,建立变形协调条件和系统势能方程,利用最小势能原理求解接触力。为了简化推导,使用正交变换和拉格朗日对偶问题变换等方法。研究结果将接触非线性计算化为带不等式约束条件的二次函数极值优化问题。结论:Likhachev方法可以由2个接触高度扩展到3个接触高度,具备一般性;多组件接触非线性转化为最优化数学理论中的常规问题,数值上可解。

The study focuses on the contact nonlinear computation method for multi-subassemblies interaction, and tries to verify the extendibility of the method proposed by Likhachev and the viability of resolving CEFR subassembly contact problem. Based on the computation method developed by Likhachev, the consistent deformation conditions and the system potential energy equations for multi-subassemblies are established at three contact levels instead of two levels. The minimum potential energy principle is utilized to acquire the contact forces. For simplicity, orthogonal transform and Lagrangian-double-problem transformation are used. Finally, the nonlinear contact analysis turns into the optimization of a quadratic function with conditional inequality constraints. Conclusions are as follows： Likhachev method can be extended for three contact levels from two, and is generally practicable; the final derived expression is a common problem in optimization theory, which could be easily solved numerically.