三维粘弹性大变形动力响应分析

AN ANALYSIS ON DYNAMIC RESPONSE IN THREE DIMENSIONAL VISCOELASTIC LARGE DEFORMATION

关键词:  粘弹性  应力－应变关系  应力计算  有限元法  动态响应  固体推进剂

Key words:  Viscoelasticity  Stress-Strain relationship  Stress computation  Finite element method  Dynamic response  Solid propellant

摘要:

将大变形增量问题的ＴｏｔａｌＬａｇｒａｎｇｉａｎ法应用于粘弹性结构的动力响应分析。利用Ｐｒｏｎｙ级数导出以Ｋｉｒｃｈｈｏｆｆ应力和Ｇｒｅｅｎ应变表示的粘弹性积分型增量本构方程及其递推公式，从而给出一种计算三维粘弹性大变形动力响应的有限元增量迭加方法。经算例验证，所述方法及其相应程度具有机器内存少、计算量小和效率高的优点。

Abstract:

The Total-Lagrangian approach of large deformation increment is used in dynamic response analysis of viscoelastic structures. The viscoelastic integral constitutive relation and a recurrence formula denoted by the Kirchhoff stress-Green strain are derivid from Prony series on incremental form. A finite element incremental superposition method for dynamic response of three dimensional viscoelastic large deformation is given. It is proved by examples that the approach given in this paper has some advantages in decreasing computer storage and calculation amount, and increasing calculation efficiency.