Abstract: A new type of viscoelastic incremental FEM suitable for incompressible materials was developed. Based on this, viscoelastic stochastic FEM under random Poisson’s ratio was investigated. The local averaging method was used to discretize the random field. Second-order perturbation FEM equations were given. Numerical results reveal that the proposed approaches are accurate and effective for structural analysis of solid propellant grain with random Poisson’s ratio.

Key words: Propellant grain;Viscoelasticity;Incompressibility;Finite element method;Poisson ratio;Structural analysis

摘要： 为了研究泊松比的分布对固体推进剂药柱结构分析的影响 ,发展了一种适用于不可压缩材料的粘弹增量有限元方法 ,进行了泊松比随机粘弹性有限元的研究 ,采用局部平均方法对随机场进行离散 ,给出了二阶摄动有限元变异方程。算例表明 ,对药柱进行随机模拟 ,计算效率和精度较高。

关键词: 推进剂药柱;粘弹性;不可压缩性;有限元法;泊松比;结构分析