Analysis and prestress optimisation of membrane structures with optimal fabric alignment using modified energy minimisation

The use of light-weight tensile membrane structures (TMS) has become popular, particularly for covering vast areas. The behaviour of these structures when subjected to external actions is dependent on the initial shape, prestress and material property. The load analysis and optimisation of TMS are still challenging due to different factors including membrane wrinkling, choice of material fibre orientation and practical design considerations. This paper formulates the load analysis process by defining a modified energy functional with respect to the material fibre basis direction. The energy functional is directly minimised using a quasi-Newton solver addressing convergence issues. Improved algorithms to find the wrinkling criteria and direction are proposed. The choice of the material fibre direction and optimal seam partitioning based on the principal curvature are also developed. A practical optimisation framework for TMS is formulated based on available guidelines. The integrated methodology is successfully tested and demonstrated on a wide variety of case studies and benchmark problems. The optimal material fibre basis provides a stiffer (hence, more stable) structure and reduces the induced shear. The integrated solution along with the optimisation framework provide the end user with an effective method and tool for the design of TMS.