基于对偶神经网络的固体火箭发动机药柱非线性粘弹性力学分析方法

Nonlinear viscoelastic mechanics analysis method of solid rocket motor grain based on dual neural network

针对固体火箭发动机药柱非线性理论及有效数值方法研究中大量亟待解决的问题,通过粘弹性对应原理,将非线性粘弹性力学问题对应为弹性力学问题进行求解。给出对偶神经网络对弹性力学问题的求解方法,计算得到非线性粘弹性本构关系中的瞬时应力分量,准确构造粘弹性本构关系。为得到泊松比拟合模型中的未知参数,引入自定义神经网络拟合方法对其进行拟合。运用对偶神经网络积分法对粘弹性本构关系中的积分问题进行求解,得到材料的现时应变分量,从而实现一类非线性粘弹性力学问题的精确求解。数值算例表明,该方法是一种可用于求解固体火箭发动机药柱非线性粘弹性问题的高效、高精度计算方法。

Aiming at a large number of problems to be solved in the study of the nonlinear theory and effective numerical meth⁃ods of solid rocket motor grain,the nonlinear viscoelastic mechanics problem was corresponded to the elastic mechanics problem by the viscoelastic correspondence principle.The method of solving the elastic mechanics problem with dual neural network was given.The instantaneous stress component of the nonlinear viscoelastic constitutive relation was calculated and the viscoelastic constitutive relation was constructed accurately.For obtaining unknown parameters in the relaxation modulus fitting model,a custom neural net⁃work fitting method was introduced to fit this modulus.The integral problem in the viscoelastic constitutive relation was solved by the dual neural network integration method,and the current strain component of the material was obtained,so that a class of nonlinear viscoelastic mechanical problems can be solved accurately.Numerical results show that the proposed method is an efficient and high⁃precision method for solving nonlinear viscoelastic problems of solid rocket motor grain.