Optimization Cutting Pattern Analysis Of Membrane Structure By Considering The Influence Of Membrane Viscoelasticity

The membrane structure is tensioned by flexible membrane materials,which have rich surface and are favored by engineers.Different from the traditional rigid structure,the surface shape and stress state of the membrane structure has a great influence on the bearing capacity and reliability of the system.In order to make the forming surface of the actual membrane structure reach the target design state,the cutting pattern needs to be adjusted.In engineering applications,the shape of the plane cutting strips is often adjusted by a specific compensation value through material performance tests combined with engineering experience.Due to the fixed cutting compensation value in the warp and weft directions,the shape of the cutting strips will not change,and the optimum stress state of the forming surface is limited.The cutting optimization design can realize the whole optimization process of the shape and stress state of the tension-forming surface.Through the cutting optimization cutting pattern design,the shape and stress state of the actual surface can be close to the design value.In this paper,the minimum difference between the design stress and the actual membrane surface stress after construction is taken as the optimization objective,and the nodal coordinates of the cutting pattern are taken as the optimization variables to carry out the cutting analysis of the membrane structure.The elastic and viscoelastic optimization cutting methods are used to analyze the saddle-shaped surface example and the catenary surface example.The numerical analysis results of the example show that under the design prestress of2.00 k N/m,the formed surface’s warp and weft stress after construction greatly differs from the set prestress by using the fixed cutting compensation.After optimization analysis,the discrepancies between the real stress and the design stress of the membrane element is significantly reduced,and the average stress is close to the design value.The target optimization range is between 10 % and 30 %.After optimization,the stress variance of the membrane surface is close to 0,indicating that the stress distribution is more uniform,effectively avoiding wrinkles or tears on the membrane surface caused by excessive or too small stress of some elements.Due to the stress relaxation of the membrane surface,the stress of the forming surface decreases.Compared with the membrane surface stress before and after relaxation,the stress is reduced by about 30 %.The relative error of the warp and weft stress of the membrane element after viscoelastic optimization analysis is significantly reduced,and the optimization range is between 15 % and 40 %.The results obtained by the viscoelastic optimization method are more reliable.