Analysis of the Stability of a Flat Textiles with a Two-Parameter Deflection Curve

The issue of large deflections of textiles occurs primarily when analyzing the "drape" of curtains, tablecloths and other flat textile products. The correct drape is particularly important from an aesthetic point of view. Additionally, there is a problem with the stability of the folds created during the drape process. The analysis of this problem is difficult due to the occurrence of large deflections and non-linear properties of the material. In this article, a selected fragment of the above-mentioned issue was tested, relating only to the stability of the fold formed under given loading conditions. A typical example is a fabric resting on a flat surface and loaded with compressive forces. The presented considerations lead to obtaining the deflection curve for a given self-weight and compressive force. Additionally, the obtained shape was tested for stability. Two shape parameters used in the analysis can be applied for the simulation of different shapes of the deflection curve. The analysis has been made using the energy method relating to the total potential energy of the object. The obtained results may be used in algorithms and simulation programs for fabric folding, buckling and for another applications in the area of textile mechanics.