Abstract
In this paper, the stress superposition method (SSM) is proposed to solve the stress distribution of regular polygon membranes. The stress-solving coefficient and the calculation formula of arbitrary point stress of regular polygon membrane are derived. The accuracy of the SSM for calculating stresses in regular polygonal membranes is verified by comparing the calculation results of the SSM with the finite element simulation results. This article is the first to propose a method to investigate the response of the arch height of the membrane curved edge to the membrane’s mechanical properties while keeping the effective area constant. It is found that the equivalent stress and the second principal stress at the midpoint of the membrane curved edge are effectively increased with the increase of the arch height of the curved edge. The second principal stress at the edge region of the membrane is relatively small, leading to the occurrence of wrinkles. When the stress at the midpoint of the curved edge is equal to that at the center of the membrane, the membrane plane attains the maximum stiffness and reduces the possibility of wrinkling at the edge.
Highlights
The accuracy of the superposition method (SSM) in the calculation of ortho-hexagonal membranes is verified by comparing the stresses at sampling points of ortho-hexagonal and ortho-heptagonal membranes with the results of finite element simulation
The curved edge of corner point tensioned regular polygonal membranes is more sensitive to stress
It is proposed for the first time to optimize the arc edge of the membrane in order to improve the maximum stiffness of the membrane while keeping the effective area of the membrane unchanged
Summary
When an object is subjected to an external force, it produces a small deformation. According to the article [31], a two-ended rope subject to tension F is equivalent to the superposition of two ropes, each of which has one end under tension and the other end fixed. Materials 2022, 15, 192 two opposite points This method is unable to solve regular polygonal membranes with odd tension points, such as regular triangles and regular pentagons. The direction of the tension is in the connection line from the center of the shape to the corner point. This method decouples the stress distribution of the regular polygon structure in the multi-point tension state into the superposition of the single-point tension state, so that the analytical solution of the stress field of the regular polygon membrane under the corner tension can be obtained. The corner pull direction is on the line connecting the center of the regular polygonal membrane to the corner points
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