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在膜结构找形中,力密度法引入了“力密度”的概念,使问题简化。但力密度法需要多次试算后才能确定合适的力密度取值,这给找形过程带来困难。该课题组对力密度法的找形过程进行改进,避开其中“力密度”的概念,使找形计算过程简洁高效。该文即对这种“改进力密度”法进行了试验研究,以验证该方法的正确性。试验模型为一平面尺寸为4m×4m柔性索边界、四点支承的马鞍形张拉膜结构。张拉过程采用应力和位移同时控制,量测模型零状态、中间状态和张拉成形后状态边索和膜面的应变值及膜面监测点的空间坐标。通过试验值与理论值在膜面应变、索应变及膜面空间坐标的比较及与ANSYS法、解析法的比较,说明改进力密度法是正确的,可用于实际工程的膜结构找形分析。另外,通过本次实验,我们对膜面应变的量测也得到了一些经验教训。
In the film structure finding shape, the force density method introduced the concept of “force density”, so that the problem is simplified. However, the force density method requires several trial calculations to determine the appropriate value of the density of forces, which is difficult to find the shape-finding process. The research group improved the method of finding the shape of the force density method and avoided the concept of “density of force”, which made the calculation of shape finding concise and efficient. In this paper, this “improved density” method was tested to verify the correctness of the method. The test model is a saddle-shaped tensioned membrane structure with a 4m × 4m flexible cord boundary and four support points. The tensioning process uses both stress and displacement control simultaneously to measure the strain value of the tributary and membrane surface in the zero state, the intermediate state and the tension state after tensioning and the spatial coordinates of the membrane surface monitoring point. The comparison between the experimental values and the theoretical values on the film surface strain, the cable strain and the space coordinates of the film surface and the comparison with the ANSYS method and the analytic method shows that the improved force density method is correct and can be used to find the shape of the membrane structure in practice. In addition, through this experiment, we also obtained some experiences and lessons on the measurement of strain on the membrane surface.