Keywords: membrane structures, non-linear analysis, finite element method, object-oriented methods, form finding, cutting patterns, textile materials.

The design and calculation of pre-stressed membrane structures is a complex procedure in the field of civil engineering. Membrane structures are built from patterns of foil or woven fabric and pre-stressed mechanically or by internal pressure in the assembled state. The anisotropic material behaviour as well as the deformation dependent shear stiffness strongly influences the equilibrium form and the stress distribution of the resulting structure. During the design process the equilibrium form of the pre-stressed structure and the material properties have to be taken into account properly to avoid wrinkling or local stress peaks, which can lead to failure of the membrane.

Within the design and calculation process four main tasks can be identified: Firstly during the form finding process the desired form of the structure and the corresponding stress distribution is computed. The calculation of cutting patterns divides the membrane into various material strips; the main problem is here how to transform the generally double curved geometry into plane material patterns. The process of cutting pattern assembly connects the calculated plane patterns and applies the desired pre-stress state to the membrane. Finally, with the static analysis task the structure is calculated under the desired external loads. Currently available membrane calculation programs decouple the static analysis from the cutting pattern generation completely. Static analysis is done on the desired ideal geometry of the membrane structure in the pre-stressed state, while the cutting pattern generation is performed as a geometrical process neglecting the influence of the material properties and the pre-stress. The real structure resulting from the assembly of the calculated patterns will not even be compared to the desired ideal geometry. The error between the real and the calculated stresses is often significantly high and inhibits a realistic prediction of the behaviour of the membrane structure.

In this paper a new holistic approach for the calculation process of membrane structures and its implementation into the SCOOP framework [1] is described. The relevant calculation tasks as form finding, cutting pattern generation, cutting pattern assembly and static analysis of the resulting pre-stressed structure are combined in a generalized calculation procedure.

Taking into account that the whole calculation process can only be done numerically efficient when it is performed on the discretised structure, it can be seen - from an abstract point of view - that the four main tasks have a certain similarity. All program modules read some input data (geometry, topology, material, internal and external loads etc.), perform some operations on the discretised membrane structure and finally write some output data, which generally is of the same kind as the input data.

Regarding for example the governing equations of the form finding task, either formulated by force densities or by the Updated Reference Strategy (URS) [2], it is obvious that the main work to be done by the form finding module is to solve an equation system directly or iteratively which is composed from certain contributions of the discrete elements of the structure - the same procedure as in the static analysis. The output consists of modified geometry data and the pre-stress field, which is some kind of internal load data.

The SCOOP program (Structural Computation using Object-Oriented Programming in Engineering) is a modular framework developed by FEMSCOPE for the analysis of complex structures, mainly using the Finite Element Method (FEM). The kernel of SCOOP consists of an ANSI-standardized, platform-portable calculation framework, which is written in C++ using modern software engineering methods and advanced programming tools. Not only the SCOOP modules but also the analysis data (input, output and intermediate data) are managed by a database module. The hierarchical concept of the framework and the high level of abstraction of the structural analysis solution process could easily be extended to solve the different tasks of the membrane design process mentioned above.

By consequent abstraction the similarities in the different tasks of the design process for membrane structures could be identified. The new holistic approach led to new SCOOP modules, which allow a fast and comfortable calculation of all relevant steps of the analysis of membrane structures under the same calculation environment. The framework SCOOP-RD (Research & Development) has provided a fast and easy way to create the necessary new objects, data structures and procedures, as well as a powerful and safe environment to test the new modules. First tests with the new program system gave quite satisfactory results.

1

Reimann, K., Gil, L., Jentsch, M., Sánchez, M.: "SCOPE, a Framework of Objects to Develop Structural Analysis Programs in C++", Proceedings of Computational Structures Technology Civil-Comp Press, Edinburgh, UK, 2000. doi:10.4203/ccp.68.7.2

2

Bletzinger, K., Ramm, E.: "A general finite element approach to the form finding of tensile structures by the updated reference strategy", Int. J. of Space Structures, 14:131-145, 1999. doi:10.1260/0266351991494759

3

Blum, R.: "Beitrag zur nichtlinearen Membrantheorie", Mitteilungen / SFB 64 Weitgespannte Flächentragwerke, Universität Stuttgart 73, 1985.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £125 +P&P)