The Construction Of A Fabric Model Based On Topology And Its Application In Bending Stiffness

In this topic,the concept of space in the topology was used to construct fiber structure space and fiber performance space,which is the basic of researching textile problem with high dimensional abstract values.In this topic fiber can be expressed as a set of real numbers,which can express the fiber’s specific location.In the fiber space any two fibers always exists difference which can be measured with an accurate real number.In addition the fabric was interpreted as the finite fibers’ special distribution in the space,further more the fabric was expressed as matrix.In the end according to the information of fabric matrix,the bending stiffness model of arbitrary cross section of fabric was given,and the bending stiffness of fabric was interpreted as a function along with an axis.Conclusions are as follows:1.Fiber can be expressed as a set of real numbers.Because of the difference of perspective,it can be divided into fiber structure space and fiber performance space.Each of space has metric respectively which can measure the distance of any two fibers in the fiber space.Its metric can be expressed as do and do,respectively.2.The bending stiffness of arbitrary cross section of fabric is the result of synthetical performance of fibers’ bending stiffness.The concrete model is as follows:3.The bending stiffness of fabric was interpreted as a function along with an axis.Its representation form of interpolation method is as follows:...