This paper discusses two aspects of the finite element analysis of membrane structures; (i) the efficient finite deformation finite element analysis of membrane structures that have been inflated and are subsequently externally loaded under the condition that the enclosed mass of gas (usually air) remains constant, and (ii) the minimization of element distortion that can lead to a poor representation of the minimum surface during form-finding. The first problem is addressed by augmenting the total potential energy expression with a term representing the potential energy of the enclosed gas and relating enclosed pressure to volume using Boyle's law. The formulation develops the correct tangent matrix term relating to the constant gas mass constraint thereby maintaining quadratic convergence of the nonlinear solution. The second, formfinding, problem is incorporated into the general membrane formulation by introducing a pseudo strain energy function involving the surface area to be minimised together with distortional strain energy function employed to eliminate locally inplane mechanisms and minimise the element distortion. Alternatively the mesh distortion problem is solved by the popular dynamic relaxation procedure with the addition of 'viscous truss members'. Finally examples are presented which demonstrate the application of the techniques discussed.

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