摘要
针对由不同特性物体所组成的多体系统,探讨了能够涵盖各种变形状态和运动形式的广义有限单元模式及其插值函数形式。对于多体接触问题,发展了能够合理描述界面特性的接触力元模型,即采用某种应力插值函数将界面上的相互作用力由接触对上的接触应力来表达,并将接触对上的接触应力当作需满足界面上屈服准则与流动法则等状态控制条件的参变量,将其作为约束条件加入系统控制方程。根据非连续变形系统的分区参变量最小势能变分原理,联立变分驻值条件与参变量的状态控制条件建立了多体系统非连续变形计算力学分析的基本控制方程,将问题最终归结为一个含有自由变量和等式约束条件的线性互补问题,对此发展了数值解法,并进行了多个算例的数值分析。计算结果表明该模型不仅能够对多体系统进行静、动力耦合分析,而且还能够模拟多体系统的变形与应力及接触界面上的接触应力和相对运动等复杂的非线性过程。
The theoretical importance and practical significance of discontinuous deformation analysis have been well recognized in geotechnical engineering. A number of attempts have been made in past studies. Nevertheless, at present there seem no methods available which can well deal with both continuous and discontinuous phenomena in the same mechanics framework. In this paper, a computational model for discontinuous deformation analysis of multi-body system is presented. In the model, various generalized finite elements with general interpolation modes which can include both rigid displacements and rotation and strain components are employed. Such generalized forms can be reduced to rigid finite elements, the displacement mode in discontinuous deformation analysis, and conventional finite elements. A contact-force element is developed for simulating the interface behavior. A certain distribution of interaction forces along the interface is pre-assumed and the behavior of the interfaces is controlled by both Mohr-Coulombs yield criterion for statics of the system and corresponding flow rule for kinematics of the system. The multi-body system comprising of rigid or/and deformable, continuous or discontinuous blocks is discretized by the generalized finite elements and the contact-force elements. On the basis of principle of virtual work, the so-called parametric variational principle for the discrete system is established in conjunction with the assumption that the contact stresses or forces at contact joints on the interfaces are taken as parametric variables which will be subjected to the constrain conditions given by both Mohr-Coulombs criterion and flow rule. According to the variational stationary conditions of the functional, the basic governing equations of the system which will be coupled with the constraint conditions of the parametric variables are formulated. The resulting issue of the problem is reduced to a linear complementary statement containing free variables and equality constraining conditions. A numerical algorithm is developed for a general multi-body system. Numerical examples for four typical problems are performed to illustrate the present method. It is shown that the proposed method can simulate complicated nonlinear behavior of interaction or contact problems of multi-body systems.
出处
《工程力学》
EI
CSCD
北大核心
2004年第4期66-74,共9页
Engineering Mechanics
基金
国家自然科学基金项目(10172022)
国家教育部跨世纪优秀人才培养计划研究基金资助项目(教技函[1999]2号)
关键词
有限元
多体系统
接触问题
变分原理/非连续变形
广义有限单元
接触力元
非线性
finite elements
multi-body system
contact problems
variational principle/discontinuous deformation
generalized finite elements
contact-force elements
nonlinearity
