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Analysis of Cable-Membrane Structures

               
(a)       (b)
Figure 1  Cable-membrane structures: (a) typical beach shelter (b) Foshan Stadium, China


Cable-membrane structures are lightweight structures that can span large distances and assume aesthetically pleasing shapes. They are widely used for roofs and canopies of modern structures (see Figure 1 above) and in the aerospace industry for large on-board antenna reflectors that are to be deployed in space.

Every part of the cable-membrane structure must be in tension as the structure cannot resist compressive or bending stresses. Analyzing these structures requires advanced techniques since there are strongly nonlinear (geometrically and materially) effects. The material response must include deformation mechanisms such as crimp interchange, yarn extension and crushing, and fabric wrinkling.

When designing tensile cable-membrane structures, engineers must determine the:

  1. Shape Finding Loads: These are the cable loads required to pre-tension the membrane into the desired shape without wrinkling or tearing the fabric.

  2. Dynamic Characteristics of the Structure: The cable-membrane structure can vibrate vigorously under earthquake loading. The structure must not collapse under the dynamic loads.

  3. Structural Response to Wind Loads: A major concern is wind loads. Powerful gusts can cause high stresses, breaking cables or tearing the membrane.

In this Brief, we demonstrate how engineers used ADINA to design a landmark cable-membrane structure in China. The Brief illustrates the analysis steps taken using a simplified geometry, but these steps can of course be applied to any geometric shape.

The first analysis step is the shape-finding phase. Figure 2(a) shows a saddle-type cable-membrane structure prior to shape-finding, and Figure 2(b) shows the structure after shape-finding.

The membrane is modeled using ADINA 3D plane stress (membrane) elements with the ADINA fabric material model that includes wrinkling effects. Anisotropic fiberglass material properties are used. During the shape-finding phase, ADINA alignment elements are used to pull the membrane into position as shown in the movie below. The alignment elements are extremely useful for such analyses.





Figure 2  Shape-finding phase: (a) original (stress-free) shape, (b) final shape after shape-finding




Shape-finding using alignment elements



After the shape-finding step, the dynamic characteristics of the cable-membrane structure are investigated using modal analysis. With these modes, a frequency domain response spectrum analysis is performed to determine the excitation of the structure under earthquake ground motion.

In the final analysis step, the cable-membrane response to gust loads is considered. Since the structure is very flexible, the structural deformations strongly affect the response of the fluid, and vice versa. Therefore a fully-coupled FSI analysis was performed using ADINA FSI to study the effect of gust loads.

To validate the ADINA FSI model, the ADINA FSI results are compared to wind tunnel test results. Figure 3 shows the wind tunnel test setup and the FSI fluid mesh. The movie below shows the calculated velocity field.





Figure 3  Verification model: (a) wind tunnel test setup, (b) ADINA FSI fluid mesh;
the membrane is embedded in the fluid mesh as shown in the movie below




Velocity field shown over three connected cutting planes


The actual membrane deflections, measured using lasers, are compared to the ADINA FSI results in Table 1, and we see that that the ADINA results match closely with experiment.


Table 1  Membrane displacement at the center point for a wind speed of 16m/s
and a membrane pre-tension of 2.24kN/m

  Experiment (mm) ADINA FSI (mm)
Average displacement 11.0 11.2
Standard deviation 0.86 0.81


The engineers performed a detailed analysis of the actual cable-membrane structure to arrive at a final design that was safe, functional, and aesthetically pleasing.

This Tech Brief demonstrates how the reliable and comprehensive structural and FSI analysis capabilities offered in ADINA makes ADINA the ideal analysis tool to design complex structures under a wide range of loading conditions.



Reference

  • Q. Zhang, Y. Yan and H. Li, "Theoretical and experimental studies on wind-induced vibration of tension structures", Journal of Southeast University (Natural Science Edition), Vol. 43, No. 5, Sep. 2013.



Keywords:
Cable-membrane structure, shape finding, alignment element, gust loads, wind loads, modal analysis, response spectrum analysis, dynamic loading, fluid-structure interaction, FSI


Courtesy of Radux Industry Technologies, Inc., Beijing, China

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