拉压刚度不同桁架的动力参变量变分原理和保辛算法  

Dynamic parametric variational principle and symplectic algorithm for trusses with different tensional and compressional stiffnesses

作　　者：高强[1] 张洪武[1] 张亮[1] 钟万勰[1] 

机构地区：[1]大连理工大学工程力学系,工业装备结构分析国家重点实验室,大连116024

出　　处：《振动与冲击》2013年第4期179-184,共6页Journal of Vibration and Shock

基　　金：自然科学基金(11272076,11232003);973项目(2011CB711105)

摘　　要：对于一些展开结构,为达到其设计性能,必须采用特殊的索、膜结构,这些索、膜部件表现出不同的拉压性质。具有拉、压不同性质的材料或结构的力学分析,体现出较强的非线性特征,需要针对这类问题发展有效的求解算法。建立了由拉压刚度不同杆单元组成的桁架结构的动力学参变量变分原理,将拉压刚度不同桁架问题的非线性动力分析转换为线性互补问题求解。结合时间有限元方法构造了求解此问题的保辛数值积分方法,此方法不需要迭代和刚度矩阵更新,避免了迭代求解方法的收敛问题,计算过程稳定、高效。For deployable structures, some special structures, such as, cables and membranes are used to achieve their design performance. These cable and membrane components show different tensile and compressive properties. The differences in tension and compression bring strong nonlinear behaviors and effective numerical methods are needed. Dynamic parametric variational principle for trusses with different stiffnesses in tension and compression was established and the nonlinear dynamic analysis of these trusses could be transformed into a complementary problem. Based on the time finite element method, a symplectic method for solving this problem was established. It was shown that the proposed numerical method is stable and efficient, and it does not need iterations and update of stiffness matrix.

关 键 词：拉压刚度不同 非线性 参变量 辛 

分 类 号：TU323[建筑科学—结构工程]