Form Finding, Patterning Of Membrane Structures And Study Of Membrane Tension Measurement By Ultrasonic

As a newly developed structure, membrane structures are widely used in gymnasiums and public facilities, owing to the excellent characteristic. Behaviors of membrane structures are depended to properties of membrane materials, which is flexible, non-linear and anisotropic. Stiffness of membrane structures is provided by surface curve and pre-stresses, therefore form-finding is the first and foremost step in design of membrane structures. In order to obtaining space surfaces from plane membrane materials, patterning is a peculiarly procedure for membrane structure design. Since proper pre-stress ensures the erection and safety under loads, measurement of membrane tension is a necessity for quality control.According to the aforementioned points, main contents of this dissertation are as follows:1. History and application of membrane structures were reviewed , and main steps for design of membrane structures and the state of the art were summarized.2. A kind of PVDF membrane material was experimentally studied. Sample strips parallel to the warp, or fill direction, as well as those through 45°angle direction were tailored and tested. Also a kind of crossed sample was tested by a self-made biaxial test equipment. Mono-axis tests give strip strengths and stress-strain curves of the material, while biaxial tests yields elastic module and Poisson's ratio. These experiments made materials'properties clear and laid foundations for the following analysis.3. A conclusion was induced from equilibrium equations of shells as follows: stress distribution in membrane structures can be either homogeneous and isotropic, resulting in a minimum surface or inhomogeneous and anisotropic, resulting in a equilibrium surface.4. Form finding of membrane structures was carried out by dynamic relaxation. As one of the most frequently used form finding method for membrane structures, dynamic relaxation features the facility of no need to assemble and solve structure stiffness equations, while the cost is the relatively numerous iterations. In this paper dynamic relaxation was modified to accelerate the convergence. During the form finding procedure the calculating parameters were continuously adjusted according to changes of the structure, and the iteration steps to convergence were greatly reduced comparing with those without parameter adjusting. The excessive distortion of elements, which may occur due to omitting of the in-plane shear stiffness can be overcame by sequential designation of node coordinates.5. Two simulating procedures for discrete membrane structures were introduced. By piecewise interpolating of the discrete surface resulted from form finding procedures, continuous smooth curved surfaces were obtained. Samples showed that though both of the simulating processes led to satisfying presentation of curved membrane surfaces, discrepancies of the simulated surfaces from the standard coordinates to the C1 surfaces were much less than that to the C0 surfaces. Discrepancies decreased with the reduce of the grid/span ratio, while as the ratio was less than 1/8 , the discrepancies gradually diminished.6. Geodesic of surfaces is similar to straight lines in planes, and thus makes geodesics the mostly frequently used dividing lines in patterning of membranes. It is proved that geodesics can be produced by stretch elastic strings along a smooth surface. Equilibrium of stretched strings were found by dynamic relaxation, thus gave tracks of geodesics.7. Adopting geodesics as dividing lines, space surfaces were developed by minimal extremum method. Firstly, curved surfaces were discretized into triangles, and a plane mesh was supposed to be the developed surface, then nodes in the plane mesh were adjusted to minimize distance differences between plane and space surface. The aforementioned procedures were summarized into a non-boundary extremum problem, and the non-linear equations were solved by Monte Carlo iterations. Examples were given to illustrate the stated procedures, and patterning of a rhombic saddle was provided.