Generative Design of Membrane Concrete Grid Shells
Architecture Urban and Landscape Design, Sub department of Structure Design
University of Kassel, Germany.
Membrane Concrete Grid Shells (MBG - Membran Beton Gitterschalentragwerke) are a new invention of the department Structural Design at the FB6 Architecture, Urban- and Landscape Design - University Kassel. It is a redeveloped construction method based on air-halls, airforms and grid shells of ultra high performance concrete (UHPC) that allows a very fast and cost effective erection of wide span concrete grid shells. Because of the very simple construction and the high compression and flexural strength of the concrete nearly every kind of concrete grid mesh on a form-giving surface is possible. Construction, dimension and shape rules could be found to generate those MBG constructions. Optimization methods to minimize and optimize the structure are simple and could easily be integrated. Thus generative design could be a strong tool respective method to generate a large variation of cost effective and architectural appealing wide span concrete grid shells.
The paper will give a short insight to the MBG invention and a theoretical description of how Membrane Concrete Grid Shells could be generatively developed with tools like the Finite Element Software ANSYS, CAD Systems, Optimization methods and simple hand based rules. It will show, that generative design could be an innovative tool for structural engineers to generate a large variation of constructions in a large solution space that would not be possible by the classical work methods of engineers.
Keywords: Membrane Concrete Grid Shell, Generative Design, structure design, finite element system, ANSYS, Topology Optimization, Soft Kill Option, air-inflated hall, shell, grid, membrane chamber, form finding, bionic.
fig. 1: Membrane Concrete Grid Shell rendering
The main idea was to combine different construction or assembly types to get a new structure and construction method. Main focus was the use of new materials and technologies to point out their technical advantages as well as the development of cost-effective construction systems. Secondarily an architectural appealing system should be the result of the new construction system.
In the last decade some new technologies in the building industry had been developed but not often used jet. New concrete types like UHPC (Ultra High Performance Concrete) that could absorb large pressure and tension forces or Membranes with new surface coatings that are more resistant against environmental influences.
The Idea of combining pneumatic moulds and concrete shell structures is not new. Innovative is the use of UHPC that includes the reinforcement in combination with inflated double-layered membrane structures, which are connected to each other directly or with membrane flaps. Those are arranged in a special way that continuous chambers are created which could be filled with UHPC or another self-hardening material. The result is a Membrane Concrete Grid Shell, particularly a thin wide spanning concrete grid shell with nearly any user-defined grid respective mesh with a curved shape.
1.1 Basic Construction Systems
The basic construction systems for MBG structures are air-halls, airforms and thin concrete shells. Inflated structures in the building industry are known since 1918. F.W. Lanchester developed a patent "An Unproved Construction for Field Hospitals, Depots, and like purposes" . Since than a lot of pneumatic structures had been build. Pioneers like Frei Otto and Walter Bird evolved a lot of forms and membrane materials. With the introduction of new technologies and computer-aided design totally new pneumatic structures and shapes are possible like the NouvelleDestination Pavilion at the EXPO.02 that was engineered by IPL (Ingenieurplanung Leichtbau GmbH - now FormTL).
The first concrete domes with the use of airforms had been built by Wallace Neff  in 1940. It was a single layer dome membrane. The reinforcement had to be fixed from outside and was covered with shotcrete. This kind of construction method is not substantially changed till today. The organisation Monolithic Dome Institute, Texas/USA is still using this method with advanced construction details. 1987 Werner Sobek developed mathematical methods to calculate inflatable structures under full fluid concrete load and form finding air supported concrete shells .
Different architects and engineers developed double-layer membrane moulds but only a few of them realized projects. Dante Bini, an Italian architect, builds the most known concrete shells with this method since 1965 [9, 2].
fig. 2: Dante Bini's shell construction 
The disadvantages of all those methods are monolithic shells that had to be opened afterwards and their simple geometrical shape.
1.2 Construction Components
Based on those known construction systems and with the use of modern technologies, materials and software the Membrane Concrete Grid Shells had been invented as described before.
Concrete in a large variety is obtainable. Relating to MBG structures, concrete with integrated reinforcement should be used. The reduction of weight respective concrete load during the assembly of the MBG inflated system and the minimization of concrete for structural, architectural and design aspects are the main idea. For this, the UHPC (Ultra High Performance Concrete), which is developed and adapted for the MBG structures by a research cooperation of the University Kassel, is the best choice. UHPC is a self-compressing concrete with a high Young's module and a high permissible strength. Among other things, the integrated steel fibres achieve this property. The compressive strength of UHPC could be between 200N/mm² and 400N/mm². The Young's module is about 55000 N/mm². Splitting tensile strength is up to 17 N/mm² and bending stiffness 39 N/mm² [1, 8]. Further values are W/b=0.2 and w/z=0.28. These are approximately given specifications that could be changed for the needs of MBG structures. The material could be pumped with a piston pump, thus allows a simple handling.
Material for air-halls or airforms could be PTFE Foils, PTFE coated fibre fabrics and PVC coated Polyester fabrics or ETFE Foils. For large inflatable structures with high loads PVC coated Polyester fabrics are the common membrane types. Five classes, from TYP I with low permissible stress (3000 N/5cm) up to TYP V with high permissible stress (9800 N/5cm) are available . Regarding to MBG structures, the internal pressure, the concrete load and the resulting tensile stress is very low. Depending on the size of the structure it is possible to use membranes TYPE II or TYPE III. The connection respective membrane details are very simple and easy to manufacture. High frequency weldings or steel clamping plates are very simple and cost-effective. In combination with hook and loop fasteners or other zip connections the membrane could be manufactured removable.
Steel, wood or bamboo is often used to build grid shell structures. Concrete is an exception, finally not of the material itself, but because of the complex formwork. The cost of a concrete grid shell is out of all proportion to the structure.
So there is nearly no experience with monolithic concrete grid shells. A lot of questions are open and interesting research topics could be defined. An important question is the stability of such a concrete grid shell under dynamic loads during assembly like dynamic wind loads and the stability after completion through e.g. earth quakes. Especially because of the atypical shape and mesh of architectural designed concrete grid shells that could be found with special optimization algorithms as there are structure optimization, CAO (computer aided optimization), SKO (Soft Kill Option), evolutionary design or generative design which is the topic of this paper.
Focused on generative design it is necessary to analyse the construction and its components to understand the functioning of the structure and to find rules, properties and parameters for the concrete grid shell.
2.1 Moulds & Membrane Chamber System
fig. 3: Example for a membrane concrete chamber system
The airform or mould exists out of two layers membrane, connected via direct welding or flap (fig. 3). Space between those weldings will act as concrete chambers. The mesh could vary on the surface and generate different patterns. Those patterns are arbitrary. Depending on the curvature of the surface, the mesh could be adapted. With this simple concept it is possible to generate concrete grid shells within a large solution space. The final geometry of the concrete chambers respective membrane moulds must be recognized for the patterning of the airform. Wrinkles could weaken the concrete profile extremely. To produce that complex double-layered membrane moulds demands a high technical understanding and production facilities are required. Generally it is possible to build almost every pneumatic supported form.
2.2 Construction Assembly
The Figure (fig. 4) shows the assembling of the MBG system on side. The double-layered membrane is outspread on the ground and the edges fixed at the circumferential foundation. The System will be erected by inflating the airform. After the inner maximum pressure is achieved, the second membrane chamber system could be inflated. This will simplify the handling and reduces deformations through wind. Concreting sections from the foundations to the top or pole will be defined and filled with UHPC in a special order and given time steps. The dimensions on these concreting sections are depending on the size of the whole MBG construction and the imperfections.
This remark represents the simple idea behind the construction. But in the next paragraph you will see the complexity of the interdependencies for assembly, airform, details, concrete grid shell and the complete structure.
fig. 4: Scheme of MBG construction assembly
Several physical states of the construction will appear. Particularly the UHPC will change his properties during time extremely, from a very fluent to a high compressed material. These Properties must be considered for designing airforms and concrete grid structures. Also the airform itself demands a special geometry and construction to work as concrete mould. The grid shell must fulfil several static functions to be stable, which depends on the geometry of the grid mesh and the airform. So every construction part or detail is associated with other parts or functions as roughly shown in fig. 5 and described in the following paragraphs.
airform The shape of the airform itself is given by the patterns of the membrane and the inner pressure. The deformation of the airform ("pre"shape) is a result of the local concrete dead load in the chamber system. Reshaping counteracts the deformation of the final concrete grid shell ("final"shape).
chamber-system The geometry of the chamber system respective the mesh depends on different possible parameters or usages. The mesh could be shaped for architectural, design or statical interests and is totally free in its geometry. Only two boundary condition must be fulfilled a) the chamber system must be continuous to get a grid shell structure b) the complete concrete grid shell must be stable.
grid-shell In this case a concrete grid shell could be defined as a monolithic concrete shell with holes in its surface. Their size respective the "mesh" geometry is arbitrary. The thickness off the shell respective grid could vary and depends on the minimal statical requirements for the stability of the grid shell. These properties are directly linked to the shape of the whole grid shell.
concrete UHPC (Ultra High Performance Concrete) is an almost new material. It is self-compacting and could take very high pressure, tension and bending loads. The composition of the material could be adapted to the statical requirements of the grid shell. The thickness of the grid depends on the material composition.
imperfections During concreting in sections the dead load of the concrete deforms the airform. With this comes the deformation of the final concrete grid shell. Changing the inner pressure of the airform counteracts the imperfections but with this comes another "pre"shape of the airform to get the "final"shape of the concrete grid shell.
fig. 5: Excerpt of MBG construction interdependencies
At first the sense of generative design with respect to membrane concrete grid shell structures must be defined. The simplest definition could be:
Generative Art refers to any art practice where the artist uses a system, such as a set of natural language rules, a computer program, a machine, or other procedural invention, which is set into motion with some degree of autonomy contributing to or in a completed work of art. Philip Galanter 
C.Soddu gives a more complex description of generative art or design in relation to architecture. The idea could be seen as artificial DNA with a set of transformation rules that must be setup for the clients needs. Thru this it becomes a dynamic auto-organizing system with an increasing complexity because of cycling results. The result will be the generation of endless scenarios that allows the client to select and choose among different proportions. With the feedback of the client the DNA could be adapted and the process could restart .
The design process is always an interactive process of creating samples, comparing, modifying, making incremental improvements and so on. It is a kind of evolutionary process with genetic variation and natural selection, done manually. Through computer technology it is possible to automate parts of this process with genetically inspired algorithms. But the variation of the solutions related to structures is often very restricted because of strict boundary conditions .
Generally generative design, in this case, should be seen as additional design tool that independently determines good solutions for the structural and architectural design of MBG shells and as decision facility for architects or designers with the result of possible new and maybe unpredictable solutions. This is possible because of the clear structural problem and the direct mathematical results calculated by finite element systems. These structural properties and the thereby essential shape of the structure could be seen as fitness function that allows to deselect senseless constructions out of a large variation of solutions. On the other hand the costs of buildings and structures are very important for the building industry and could be an indicator for a further fitness function.
To define the generative design process, the aim of the whole procedure must be clear and analysed. As shown in the previous paragraphs there are many parameters, boundary conditions, fitness and objective functions.
3.1 Objective Function
In architecture and structural design the main aim are cost effective constructions. Normally those constructions or structures are very simple and don’t fit to the architecture of the building in geometry and design. The engineering and designing of vary of structures for one building is very expensive because it is done manually. The engineers, architects or designers themselves are having ideas in mind; so they will not change their concept or design intensely and thereby generate a small vary of similar solutions. They will just find a local good solution for their problem.
Generative design systems are able to generate arbitrary good solutions for a problem by combining, solving, analysing and resolving a problem autonomous. But therefore all parameters, boundary conditions, fitness functions and objective functions must be defined and implemented in the system by the designer.
The aim for the design of Membrane Concrete Grid Shells should be finding cost effective and architectural appealing solutions by a large vary of shapes and meshes. To lose not all sense of perspective the illustration of the complete problem will be strongly simplified for this proceeding. The variation of shapes is a mathematical and related to airforms complex problem that will be unnoticed in the further descriptions. So the objective function (1) will only have one parameter.
Now the definition of cost effective must be analysed to find the required parameters. Minimizing the costs means minimizing the concrete structure that means minimizing the internal forces, bending moments and maximizing the stability of the structure by performing the architectural appealing. This could be done by optimizing the mesh resp. concrete grid, optimizing the concrete chamber resp. moulds, optimizing the thickness of the grid shell and or optimizing the composition of the Ultra High Performance Concrete. Also the re-shaping or adapting the shell geometry of the given structure could perform the stability and reduction of structure. So cost effectiveness (2) is a function of four parameters.
These four parameters are related to each other and could be used reverse. So maximizing the stability could be defined as function of internal forces and the grid shape. The internal forces could be seen as function of the material composition and loads. One direct solution is not possible and in the case of generating generative structures not desired. This causes a very large solution space with any kind of solution that could not be controlled. Because of these relations it is necessary to find fitness functions respective design rules for finding good solutions. Or in other words: a pre-selection of good solutions.
3.3 Fitness Functions
Minimizing the structure by reducing internal forces is a perfect fitness function. Two tools could be used for this a) Topology Optimization and the b) Soft Kill Option.
"Topology Optimization is an shape or layout optimisation with the goal of finding the best use of material for a structure, body or surface such that the objective (fitness) function takes on a maximum or minimum value to given constrains such as volume reduction... Standard formulation for Topology Optimisation is the problem of minimising the structural compliance while satisfying a constraint on the volume V() of the structure. Then minimising compliance (Young's modulus) means maximising the global stiffness of the structure."  See fig. 6 for a simple topology optimized shell.
fig. 6: Simple topology optimized Shell with an hole at the front. The bright areas could be defined as primary structure. A secondary structure must be defined in further optimization shapes.
With the Soft Kill Option all lazy finite elements could be killed or deactivated. "If the procedure is functioning well, the good elements are becoming stronger and stronger while the bad elements are getting weaker and weaker. At the end, the bad elements will not take any loads because of their very low Young's modulus."  Those elements could be deactivated. The pure statical structure will be left.
3.4 Design Rules
Another method for minimizing the structure could be re-shaping the already given surface by adding folds and buckles to stabilise the structure. For Example, a single curved surface will be much more stable if the edges are bend in a way that the single curved surface will be modified into a double curved surface (see fig. 7).
fig. 7: Folding and bending to increase structure stiffness
In this case there are several design rules, distinguishable into different geometrical and structural respective material parametric dependencies. An excerpt is shown in fig. 8. The shape of the MBG structure could be changed directly thru bending, folding, buckling or displacing. Changing the Young’s modulus, the thickness or section of profiles and the mesh respective grid is influencing the "hardware" accordingly the structure and is interacting with the shape. These characteristics concerning interdependencies are already mentioned in paragraph 2.3.
fig. 8: Excerpt of design rules
Using the design rules is another challenging research assignment because the order of applying those rules could change the results of the generation according the structure. For example changing the thickness of a shell would cause lower forces in the structure but would maybe prevent the autonomous folding of the structure. Folding the structure at first will reduce the forces in the structure and prevents maybe the autonomous thickening of the structure. So the start policy of geometry and structure as well as the order of using the rules is important and could contribute the good or bad results. Parameters and rules for the generative design process must be defined.
3.5 Generative Design Process
Aforementioned the order of using design rules for structures could be very important for the quality and the amount of the results. Depending on the generative design approach, the fitness and objective functions it must be proofed whether the design rules must be used in a serial order or could be used simultaneous.
A hierarchic structure will be the mapping of using rules in serial order. This makes it easy to find chain structures for the generative design process, which will benefit the solution. But only those 8 design rules (fig. 8) will cause possible 40320 combinations in one process cycle that must be proofed. According to the complexity of MBG structures one process cycle is not sufficient. Approximately ten process cycles must be calculated to get good intelligent results. Projected to ten cycles there will be 7.16E118 combinations with the trial and error method. This is not practicable particularly if one FEM calculation of a larger structure needs up to 10 minutes. So it is essential to evaluate a strategy for the order of design rules to reduce the amount of possible combinations.
fig. 9: Generative Design process
The usage of several design rules at the same time will improve the solution speed but should only be utilized if dependencies are not relevant and the system very easy. So different design rules could be combined and used parallel to get results but this could be seen as a trial-and-error process. Drawing conclusions after some process cycles according to an intelligent design strategy is not possible.
Regarding the previous mentioned background the MBG structures should be generated with the serial usage of design rules. As reflected from small test series the most effective way is to change geometry and finally the thickness or material of a structure. With this knowledge the possible amount of design rule combinations could be reduced dramatically. So fig. 9 shows the simplified generative design process for MBG structures.
As described before the process of generating and optimizing a structure regarding all boundary conditions, fitness and object functions as well as architecture and design is very complex. To fulfil all conditions requires an ambitious work, if an engineer does it manually. The output is then hardly reduced to one or two solutions and will take a lot of time.
Using Generative Design during the structure design process could be a very effective method to get a lot of good results in a large solution-space, and solutions that maybe could be beyond any inconceivability and will give the engineer, architect or designer new inspirations. Spin-off is not only the large amount of solutions but also the economy of time.
Generative Design, applied to Membrane Concrete Grid Shells points up these effects. By defining the boundary conditions, design rules, fitness and objective functions the structure and the aim of the design concept will be clear. Implementing this knowledge into software is a large expense but will be worthwhile thru the large amount of solutions and the economy of time. Once the generative design process for an application is implemented it is possible to repeat or start new structure designs anytime. So far the method described in this paper is almost theoretical. The implementation into ANSYS occurs stepwise. First positive results and exemplary generative designed MBG structures are created. But the greatest challenge is the interaction between 3D graphic software and the finite element software that is often not able to cope with parametric geometrical properties. So at the moment some of the above mentioned design rules and intermediate steps must be done manually. This is creating needs on open software interfaces.
At least the MBG structures are only one field of application for generative design on structure design. There are much more defiance’s like frameworks, space frames, shells...
 Bornemann, Schmidt, Fehling and Middendorf, Ultra-Hochleistungsbeton UHPC , Beton- und Stahlbetonbau, 2001 , 96 , 458-467
 Dante Bini; BiniSystems, http://www.binisystems.com , 7/2004
 FormTl, NouvelleDestination, www.formtl.de, 3/2002
 Philip Galanter; What is Generative Art? Complexity Theory as a Context for Art Theory , In GA2003, Proceedings of the 6th international conference GENERATIVE ART 2003
 Lanchaster; Improvements in the construction and Improvements in the construction and roofings of buildings for Exhibitions and like Purposes, Patent, GB000000145193A, 1919
 Jörg Minte; Das mechanische Verhalten von Verbindungen beschichteter Chemiefasergewebe, Fakultät für Maschinenwesen, PhD Thesis, Fakultät für Maschinenwesen,TH Aachen, Germany, 1981
 Wallace Neff; Improved method of erecting shellform concrete structures , Patent, US000002892239A, 1952
 M. Schmidt; Ultra-Hochfester Beton - Planung und Bau der ersten Brücke mit UHPC in Europa; Tagungsbeiträge zu den 3. Kasseler Baustoff- und Massivbautagen, university press, Kassel, 2003 , 5-20
 Werner Sobek; Auf pneumatisch gestützten Schalungen hergestellte Betonschalen, Ursula Sobek Verlag, Stuttgart, 1987
 Celestino Soddu; Visionary Aesthetics and Architecture Variations, In GA2003, Proceedings of the 6th international conference GENERATIVE ART, 2003
 G. Zimmermann; Structure Optimization, BOD.DE, 2005 (Feb.)
 Results of an internal FEM test series with several simple two-dimensional beam structures. Regarding and assigned to MBG structures - a rough estimation.