范德华力的广义参变本构模型及其在碳纳米管计算中的应用

提出了处理非成键原子间范德华力的广义参变本构模型以及基于此进行碳纳米管结构力学行为数值模拟的数学规划算法.纳米管中原子间短程力作用采用分子结构力学模型来模拟，而作为长程力的范德华力用杆单元来模拟，这类杆单元有着特殊的非线性本构关系.对于这种非线性问题的处理，建立了广义参变本构模型与参数二次规划求解算法.与一般的数值方法相比较，本方法不需要传统的冗长的、反复的迭代，并具有非常好的收敛性，因此为碳纳米管结构力学行为的有效预测提供了保障.数值结果证明了这种方法的正确性和有效性. 关键词： 广义参变本构模型 数学规划算法 分子结构力学 有限元法

Generalized parametric constitutive law for van der Waals force simulation and its applications in computation of nanotubes

In this paper, a parametric variational principle for van der Waals force simulation between any two non-bonded atoms is established together with the corresponding improved quadratic programming method for numerical simulation of mechanical behaviours of carbon nanotubes. Carbon-carbon covalent bond interaction in carbon nanotubes is modeled and computed based on molecular structural mechanics model. Van der Waals force is simulated by the network of bars with a special nonlinear mechanical constitutive law in the finite element analysis. In comparison with conventional numerical methods, the suggested method does not depend on displacement and stress iteration, but on the base exchanges in the solution of a standard quadratic programming problem. Thus, the model and method developed exhibit very good convergence behavior in computation and provide accurate predictions of the mechanical behaviours and displacement distributions in the nanotubes. Numerical results demonstrate the validity and the efficiency of the proposed method.