Technique for obtaining the membrane stress ratio in a fabric arch-type shell

Purpose of research. The purpose of this work is to develop the technique for obtaining the membrane stress ratio in a fabric shell which consists of a number of arch-type sectors of given height at the center.

Methods. The iterative secant method is used for finding the membrane stress ratio. The height in the center of a sector is determined by means of the force density method at every iteration. The method includes applying a mesh on a shell surface and determining the nodal coordinates of the mesh via the solution of the set of equilibrium equations. The equations of the set are linearized by means of substitutions, which are the force to length ratios for the mesh elements.

Results. The iterative technique for obtaining the membrane stress ratio has been developed. The technique consists of the following stages: initial search range determination and discrepancy minimization between the required and calculated heights at the center of the shell sector. The quality of the algorithm is confirmed by numerical simulating of a number of sectors of an arch-type fabric roof on a rectangular plan. The discrepancy between the specified heights in the center of the sectors and the heights obtained by the specialized licensed software package does not exceed 1.0%.

Conclusion. The surface shape of fabric shells depends on the membrane stresses. The shape-finding problem is well elaborated theoretically by now. Judging by the literature survey, however, the inverse problem of finding the membrane stress ratio given the geometrical parameters of the shell has not been developed yet. The proposed technique will facilitate research and development of fabric building constructions. Further development of the technique is in the field of multi-section fabric structural analysis with supporting structure compliance considered.

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