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Membrane Structural Design

With the surface membrane structures established by finite element analysis theory

The design of membrane structures can be divided into three steps:

(1) To identify an initial equilibrium shape;

(2) A variety of load combinations of mechanical analysis in order to ensure safety;

(3) Cutting. Developed countries, starting from the sixties made a variety of calculation methods. So far in the finite element method for the most advanced and most widely used method. The unit type are triangular constant strain plane element, the method is rigid shell from the large deformation theory transplant.

From the following analysis, we can see that only the tensile membrane structure as the soft shell was not suitable for such a plane unit, as for the rigid shell, this flat-panel units can be regarded as plane stress element and plate bending element The combination, with the unit matrix can be just the two units have just array merging. The membrane structure as soft-shell is not bending, and can only rely on the curvature changes in thin-film surface; causing membrane surface in the redistribution of internal force to resist the external load is perpendicular to the surface. If you still use this only a plane stress plate element, then the strain will not be reflected in the linear part of the z-plane direction of the impact of displacement, which leads to cell does not contain z-node counter-force, in respect of each unit for the static force is unbalanced. Fortunately, the strain of the non-linear part of the consideration of the impact of z displacement, making the total of all units combined through constant iteration of the equilibrium equations can approximate balance, disadvantage is the need excessive displacement of the plane to meet the balance of requirements, but the reality is that only a certain plane and the plane displacement and curvature change on it.

Given all of these, our membrane structure and technical designers tries at the international level the first time music mask unit, part of the introduction of the linear response to the displacement z and the unit of curvature and torsion, non-linear part of the retained to the displacement of z items. No matter that each unit or each unit of the combined balance equation can be easily satisfied, significantly reduced the number of iterations, while the deformation results more in line with the actual situation. And because all the points of stress within the cell are not the same, to judge whether there would be more precise folds. Finally each unit sought by the rate of curvature and torsion to determine initial form-finding for the positive errors and the pros and cons, as well as cutting can provide a lot of very useful information.

With the surface membrane structure established by finite element and stress calculation of form-finding minimal surface has a very perfect surface shape and stress state, is the ideal membrane structure the most reasonable initial state. The so-called minimal surface is defined as the area under the given boundary conditions, the smallest surface. On this surface stress at any point are equal. Developed countries, starting from the sixties on the membrane structure proposed by a variety of form-finding method, such as the physical model method, force-density method, dynamic relaxation method and so on, so far as to the finite element method for the most advanced, the most common method used . Not only domestic and abroad to date calculations are based on theory as a flat mask cell membrane structure calculation model. This method is from the rigid plate and shell theory of large deformation transplant. Tensile membrane structure as only the soft shell was not suitable for such a plane unit, the drawback is too much plane displacement of the need to meet the balance requirement, but the reality is that only a certain plane and the plane The displacement and curvature change on it. The consequence is that internal forces to be carried out later in the calculation, substituting into the real material constants, due to be in front of a very small form-finding and the actual surface membrane structures that may exist in the shape of the gap may not be visual, but the calculations are can not be ignored, so the calculation is easy to fold divergence or there. This is a common drawback in front of other methods, they tend to the continuous process divided into the idealized form-finding and the actual checking in two phases, also can not guarantee to find the shape of the membrane can be built with real stress such as extreme a small surface.

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