基于离散零空间法的机织物降维多体模型

摘要

In the light of that in the model of rigid bodies with Cardan angular coordinates for plain-weave fabrics (CMRBF) the dimensionality is high and poor of the efficiency, the discrete null space method is applied to reduce the dimensionality of the equations of motion for multibody systems. Applying the implicit Runge-Kutta method(IRK) to directly discretize the equations and combining with discrete null space equivalent transformation , the Lagrange multipliers are eliminated, and the nodal reparametrisation is carryied out, thus twice dimensionality reduction of system is realized. Hence, the dimension reduction multibody model of rigid bodies for woven fabrics based on discrete null space method (DR-CMRBF) is proposed. Through the Kawabata Evaluation System for Fabrics(KES) uniaxial tensile experimens and simulations, the correctness and validity of the proposed model are tested and verified. Furthermore, by comparing the index of computational complexity and computational efficiency of two models, the superiority of dimensionality reduction and high efficiency is reflected. The proposed model is especially suitable for large-scale fabric simulation.%针对机织物卡尔丹角多体模型维数较高、计算效率较低的问题，采用离散零空间法降低多体动力学方程维数。通过隐式龙格库塔法对方程直接离散，结合离散零空间等效变换，消去拉格朗日乘子项和结点参数化实现两次系统降维，提出基于离散零空间法的机织物降维多体模型；通过KES单轴拉伸试验与仿真，验证了模型的正确性和有效性；并通过两种模型计算复杂度及计算效率的特征指标对比，证实了本文模型在降维和计算高效方面的优势，尤适于大型织物仿真。