Stress Superposition Method And Free Vibration Of Corner Tensioned Rectangular Thin Membranes

This paper proposes a new method named as the Stress Superposition Method (SSM) for accurately analyzing the pre-wrinkling stress field and the free vibration of thin tensioned membranes. Firstly, SSM is presented to illustrate the spreading manner of tension and build up the stress distribution in a rectangular membrane, which ignores the strain and specifies the edge arcs as a priori deformation. A free vibration model of the tensioned rectangular membrane is established with consideration of membrane geometric stiffness, mesh generation scheme, and air added-mass. The analytical results calculated with SSM are compared with the data from finite element analysis and published NASA experiment reports for validation. By means of SSM, illustrative examples are discussed in detail, which shows the effects from aspect ratio and edge arcs on the distributions of the maximum and the minimum principal stresses. Besides, the prediction for the location of wrinkles is conducted according to the distribution of the minimum principal stress. Finally, several characteristics regarding the fundamental frequencies and mode shapes are examined in the free vibration analysis.