基于最小能量原理的机织织物理论模型与方法

以peirce模型为基础进一步提出了建立机织织物结构几何模型的数学方法.首先对被施加外部荷载的织物建立数学模型,由于相应的机织织物结构的总势能U是关于纱线形状曲线的泛函,当系统稳定时满足最小势能原理,通过求泛函极值,获得机织织物结构中纱线路径的较为真实的形状曲线,从而为描述机织织物结构几何模型和力学模型提供了相应的理论途径.

Theoretic Model of Woven Fabrics Based on the Principle of Minimal Energy

This paper proposes a new mathematic method for modeling structural geometry woven fabrics based on Peirce＇s model. First built is the model of woven fabrics subject to external load. Since U, the total potential energy of woven fabrics, is in spline function with the yam shape curve, the minimal potential energy principle is satisfied when the system is stable. Therefore, through seeking the extremum of the potential function, the relatively more accurate shape curve of yarn path in woven fabrics structure can thus be acquired. The proposed modeling approach provides a theoretic alternative for describing the geometry and dynamics of the woven fabrics structure.