Posts Tagged ‘structure’

final deformable skin

The following post has to be seen as a continuation and completion of the overall process and especially of the last post. Its content doesn’t represent the intire project but has to bee seen in the context of the previous ones.

At the port of Piraeus this tower rises on a very prominent site with a vital surrounding. To resolve the problem of the sleeping giant, this project proposal suggests a deformable skin which creates interactions on different levels between the Piraeus Tower and its context.
Taking the current structure as starting point, surrounding urban hotspots attract parts of the façade to reconfigure. These occurring deformations provoke synergies with the surrounding which allow new happenings and revaluate the whole area.
At one side the skin stretches to provide a roof for the market and its lively atmosphere penetrates the ground floor. On another side the skin allows building a pedestrian bridge across the busy road and creates a stronger relation to the waterfront and the port.
On the plinth the structure covers an open space and grows then upward approximately following the existing structure until it detaches again from the existing to end the tower at its top.
The new stairway climbs up and changes the skin as well. The parametrical creation of the structure which follows the form of the deformable skin undertakes several steps of adaption and optimisation to suit its structural and programmatical needs.
The deformable skin starts its life as a new appearance at the port of Piraeus whose tubular steel structure interacts with its surrounding. The facets are empty or faced with aluminum frames holding different infill panels which will changed over time. The so called “sleeping giant” gets lively and looses its name when people start to occupy the empty space. As the stairway will serve all the stories from the beginning on, the occupants can choose their level as they wish.


REPRESENTATION in drawings and renderings

visualisation of the market penetrating the Piraeus Tower

visualisation of an interior conected to the staircase

visualisation of the tower in the urban cotext

the following drawing shows the different materialities and how they’re connected with each other

During the final week I was building a model at a 1:5 scale which shows the different aspects of my project. the new structure is attached to the existing and is attracted to the outside to cover and hold the new staircase. The tubular structure and its joints are shown in an abstraction using wooden components.

GH-file creating the structure in lines
GH-file translating the lines into tubes and adding joints
PDF of the presentation

deformable skin

Considering the project state from the last crit as form finding process, the aim for this crit was to optimize its structure. Several analysis show the strucutre’s weaknesses and strengths. One issue was the maximum span of my structural members and another one consists in the curvature analysis of the deformed surface.

To deal with this optimization idea I first did a quick research in general optimization strategies. Taking them rather as general inputs then as actual algorithms, I came up with my own strategy. The point grid from the form finding process generates several more or less horizontal curves which I first subdivide into segments with the same lenght, which gives a polyline as output. The length can be chosen and in addition there is an option to change the resolution of the polyline following the curve. When the curve’s curvature is higher than a certain value the structural length at that point is only equal the half of the other lengths. The subdivision starts at a given point which consists in the curve’s closest point to the stair attractor and ends by keeping a cerain cap to the starting point.
After the creation of these “horizontal” polylines the neighbours are linked at each point with the two minimal distances. These new “vertical” structural members sometimes have a way too long span to be taken as valuable output. For that reason another subdivision process runs through all of them and subdivides each element taking in account the input value as maximal length. These subdivision points are again linked between each other and sometimes supported by columns standing on the plinth.
Another process at the end consists in bringing the forces down to the ground at certain points.


To be sure about the homogeneity of the lengths I ran again an analysis of the structural length.
Image showing the length analysis before the “vertical” analysis:

And after all the optimization processes all is green:

Finally there are a few special moments in the structure. The first consists in the stair leading up to the dissolving top where the structure gives bigger openings at certain points and looks more dynamic.

The pedestrian bridge is suspended from the structure and crosses the road which today separats the port from the tower.

The columns which support the structure above the plinth create a possibility for a public space or restaurant’s outdoor space covered by steel tubes.

As the Piraeus Tower has quite big dimensions, there are many structural joints which hold up the new deformable skin and fix it to the existing concrete structure. But not all joints connect the same number of tubes and all of them come in with a different angle. To deal with this changes and having one system for all the tower the joints have to be adaptive and able to react to each situation. The following joint allows up to seven tubes coming in and each of them can be adapted with two rotation axis. Two steel plates hold the members together and have to be squeezed together. Where the structure is attached to the existing concrete the squeezing is done by the consoles, otherwise a simple screw can fix the joint.

Overview of the structure in elevations and plan:

strucural optimisation

Taking my research on structural optimisation as a base for the further development of my project for the Piraeus Tower I’d like to show here my intentions. As I researched, there are plenty of different ways of optimising. Some of them are way to advanced and some others go in another direction, but taking them as inspiration and resources I’ve come up with two directions I’d like go. It doesn’t have to be one OR the other but the goal consists in combining them. Taking the point grid from the deformable skin as starting point, I run a first optimisation which uniforms the distribution of points. The aim is to get a point grid where each point is the location of a structural joint and the points are always within a min and max distance to their neighbours.
After the uniforming process the curvature of the skin is analysed in both horizontal and vertical section. When a high curvature occures (which means location where a lot of forces act) the number of points is increased to get a denser structure.

The following flow chart summarises my intention for the whole optimisation process:

As alrady introduced, the first step will be an uniforming process. The aim is to have a recursive optimisation after the point grid is created. The reason for doing that is the standardisation of the structural members. So far some steel tubes were way too long, so that the structure would simply be impossible. While uniforming the point grid I hope to be able to keep the input shape of the point grid and get as an output a more realistic structure with elements of only a small range of lengths.

A first sketch of how I’d like to realize this:

The input will be a tree structured point collection (as I used it so far). Each branch containing the same amount of points with more or less the same Z-coordinate. To allow a recursive function I’ll try to use a VB-component within GH which runs several times. Always analysing the most recent point collection until all the structural member lengths are in a given range.
The main challange will be to be able to access the right points with its neighbours while keep the point organization over the optimasing process. Then to check the neighbouring distances and decide what to do: nothing, moving a neighbour or adding a point when moving would be not effective enough.

The output of the uniforming process will be a very uniform point grid. Given that the shape of the deformable skin won’t be that uniform a structural adaption will be necessery. With adaption I mean a differenciation of structural density depending on the skin’s curfature. The idea is, to take the point grid from the structural optimisation and add points where a high curvature occures.

A first sketch of how I’d like to realize this:

I think the “easiest” way of doing this, will be again a recursive function which compares points, with again more or less the same Z-coordinate, with the curve’s curvature on which they are located. when the curvature at a certain location is higher than a given value the engine adds a point between two neighbours.
As this will only solve structural issues on a more or less horizontal level, it would be good to do the same in the vertical section. For this I’d have to reorganise the point collection tree, to get the curvatures in the section and then run the script from the horizontal adaptive subdivision again for the vertical part.

Of course the best way would be to take directly the surface’s curvature instead the one of some random curves. But I’ve no idea how I could achieve that… Another concern is the structural advantage of this step. It’s my intention, that the highest forces on the skin occure where the curvature is high. I’ll try to check this with an civil engineer and then revise this point.

So I guess now I shoud start writing some scripts…

research in structure optimisation

So far my project was more about the deformation process of the initial Piraeus Tower’s skin. Even though – while looking at the project’s representation – the structure seems to be a very important part, I somehow neglected it so far. This led to a rather weak structural solution which rises a lot of problems and questions.

As a next step I’ll try to find a more sophisticated engine driven solution for the tower’s structure. For that reason, I was researching in different structural optimisation processes. I haven’t yet chosen something for my project but it informs me what possibilities there are and what potential solutions I’d be able to create in the further development.
The following flowchart shows which way I’d like my project to go.

There are two main optimisation processes, which are the adaptive subdivision and the surface relaxation. The following extracts are only a small selection of what exists, but for me they seem to be quite illustrative and interesting:


Adaptive subdivision of mesh models
United States Patent 6356263

A computer-based system and method for refining of mesh model of a three-dimensional (3D) object or surface through adaptive subdivision that results in a smooth interpolation of the mesh surface. In one example, the system operates upon a triangulated mesh model and analyzes each edge of the triangle in question to determine whether that particular edge should be subdivided based on a predetermined subdivision criteria. After an analysis of each of the edges of that triangle (using the adaptive subdivision criteria) the system and method may make one of several different types of subdivisions – e.g. dividing the mesh triangle into two, three or four smaller triangles.

images taken from this PDF

There are also several analogies to the adaptive subdivision in many fields such as biology, chemistry, physics and art as well. The latter one seems very interesting to me because it could have paralellel ideas to my project as I could use gradients for instance to create subdivision depending on colours.


Dynamic Relaxation

Dynamic relaxation is a numerical method, which, among other things, can be used do “form-finding” for cable and fabric structures. The aim is to find a geometry where all forces are in equilibrium. In the past this was done by direct modelling, using hanging chains and weights (see Gaudi), or by using soap films, which have the property of adjusting to find a “minimal surface”.

The dynamic relaxation method is based on discretizing the continuum under consideration by lumping the mass at nodes and defining the relationship between nodes in terms of stiffness (see also the finite element method). The system oscillates about the equilibrium position under the influence of loads. An iterative process is followed by simulating a pseudo-dynamic process in time, with each iteration based on an update of the geometry.

Gaudi’s form-finding by hanging chains:

Soap film surfaces are examples of “minimal surfaces”, or surfaces with zero mean curvature. The surface that spans a given boundary set is the one that minimizes the surface area. That is, among all possible surfaces that could span the wire frame, the one that appears is the one with minimal surface area. This is due to the surface tension in the film.

Structural Relaxation

The object of a structural relaxation is to obtain the groundstate relaxed geometry of the system under consideration. This may include the equilibrium lattice constants. For a given ionic configuration, a self-consistent single-point calculation is carried out, and from this, the forces obtained. If these forces are greater than some minimum tolerance, then the ions are moved in the direction of the forces. This procedure is repeated until an equilibrium structure, with vanishing forces (within the numerical tolerance) is obtained. The lattice constants may also be varied by determining the stresses acting, and obtaining an equilibrium structure with vanishing stresses.

Surface Relaxation

This GH-forum entry has some quite interesting answers to the question “What is surface relaxation?” as for instance the following:
- a method of balancing forces in a dynamic manner
- dynamic relaxation should find surfaces of stable equilibrium

The two following projects are quite interesting and could give a better understanding of the structural optimisation process.

Santa Maria Del Pianto Station, Naples, Italy

The project brings up interesting question such as how to optimize a complex arrangement? The given answer shows an image and sais “Evolution of species: survival of the fittest”. It also shows very well that the optimisation is using an evolutionary algorithm to get to the final solution. A lot of infromation – included the present ones – can be found on a PDF on their site.

The British Museum Great Court Roof, London, England

The position of the nodes of the steelwork grid upon this surface was determined by a relaxation process applied to a ‘numerical grid’.The coarser structural grid is obtained by joining diagonal nodes of the numerical grid. The relaxation process involved moving each of the nodes on the numerical grid until it was the weighted average of the surrounding nodes. This process was repeated for the whole grid a large number of times, until the grid stopped moving. The weighting functions varied with position, mainly to try and limit the maximum size of glass panel. Figure 30 shows the grid before relaxation and figure 31 after relaxation.

As the structure has to be analysed to be improved there are several kinds to represent this. These stress analysis can give all information needed for a response as discribed with the flowchart in the beginning of this post. They could ask for a densification at certain parts using an adaptive subdivision or show the curvature analysis which can be used for a surface reflexation

from the book called Advances in Structural Optimisation published by Kluwer Academic Publishers

Some flow charts which show optimisation procedures:

So far, all these information are only research. They influence my thinking and further work might be using one or more of their ideas.

response_growing parasite structure

In response to the mid-term crit on the 15th of April 2010 and as continuation of my very first esquisse, I take the following conclusion:
The deformable skin doesn’t cover the whole tower anymore, but rather uses it at certain points as a host. This parasite structure covers the existing structure only where public interaction or attraction would take place. This aims as well to push the idea of phasing the tower’s life and let it change over time. Starting with taking in account the immediate context, interacting wiht it, providing an enclosed safty staircase and a lookout point on the top, the Piraeus Tower will be covered more and more as its value rises and the indoor space gets occupied.

For clarifing reasons the attraction maths and creation of the structure, used in the GH definition, will be reworked and demonstrated in diagrams.

deformable skin


At the port of Piraeus this tower rises on a very prominent site with a vital surrounding. To resolve the problem of the sleeping giant, this project proposal suggests a deformable skin which creates interactions on different levels between the Piraeus Tower and its context.
Taking the current structure as starting point, surrounding urban hotspots attract parts of the façade to reconfigure. These occurring deformations provoke synergies with the surrounding which allow new happenings and revaluate the whole area.
At Dimosthenous and Lykourgou Street the skin stretches to provide a roof for the market and its lively atmosphere penetrates the ground floor of the new Piraeus Tower. On the other side at Akti Poseidoneos Street the skin allows building a pedestrian bridge across the busy road and creates a stronger relation to the waterfront and the port.
Above the plinth the skin grows upward approximately following the existing structure. Only where the new stairway climbs up, the skin deforms itself to enclose and hold it. At the top the deformation detaches again from the existing structure, pointing on one side towards the Acropolis to focus a dramatic view, while on the other side it provides a panorama across the port. These two deformations can be seen from outside as pointing towards the Acropolis and on the other as a welcoming gesture towards the sea. These deformations at the top interact on a bigger and more visual scale than the lower ones and enhance the tower’s status in a larger city context.
The duality of interior and exterior value underlines the fact, that the building is alive with and without occupied indoor space and interacts on several levels with its context.
The overall project is designed and drawn in a parametric way to allow changes very easily. Attractions can be changed or even added and the written design engine updates the project dynamically.

version PDF


The skeletal structure consists of a triangulation of the skin which is realized in circular steel tubes and assembled with spherical joints, each of which connects six tubes. The spherical geometry of the joints allows the assembly of different angles in which the tubes meet each other.
The structure is connected to the existing concrete whenever no deformation occurs. Cantilevered parts are self-supporting and limited by their structural properties.
The deformable skin starts its life as a new appearance at the port of Piraeus whose tubular steel structure interacts with its surrounding. The facets are empty or faced with aluminum frames holding different infill panels which can also be changed over time.
Starting with DuPont’s ETFE membranes, while the tower is still unoccupied, they can cover or mark certain parts of the tower. This includes for instance providing natural light and protection to the stairs and the passage to the port or backlit elements which can light the surrounding during the night. Solar panels will be installed to profit from the enormous available surface and produce cheap and clean energy for a green future.
As Piraeus Tower’s value increases and it starts to be occupied more and more the façade continues to change. Office and administrative spaces will need more light, restaurants and lookout points desire to have nice views from the top and the infill panels will change to glazing in DuPont SentryGlas Interlayer to provide the best performance for the tenants.

the GH definitions are split in two parts, because in one it wouldn’t be possible to work in. The first definition allows to deforme the the existing structure of the Piraeus Tower.

GH canvas for creating the deformable skin

rhino screen shot of the deformable skin

The second definition applies a tubular structure to the deformable skin from the first GH definition.

GH canvas for the tubular structure

rhino screen shot of the structure

An overview of all the files can be found in the following gallery:

research on attractor geometry and possible forms

Seeking for solutions for my project I tried to look for different possibilities for several aspects of my current state.

  • different attractor geometries using a GH definition -> what happens if the attractor would be a line, curve or even a surface and not only a point as it has been so far?
  • different sizes of the facetting -> larger triangles would need another (smaller) structure for filling up the surfaces, but smaller facetting might need a supporting structure. Both possibilities would be possible, but they need different kinds of detailing and would give a different appereance of the tower
  • analyzing some possible forms I can produce, using the current GH definition

In general I’m inclined to go for the smaller facetting because it gives a smoother appereance and consists in only one structure all over the facade instead of having a main structure and then a kind of filling structure. To avoid a supporting structure for the small facettes, I’ll try to “touch” the existing structure as often as required.
The different attractor geometries – I analysed in a seperate GH file – have to be developed to be used within my project. Concerning the final overall form of the facade, I think I leave this at this point for a while and come back to it, when I know more precisely what I want and for which reasons.

Origami tower – structure

The skin of the tower derives from the idea of a folded plane. The facets of the skin vary in size and orientation.

The grid applied to each facet depends on the spatial orientation of the longest edges. Therefore, when the angle between the two edges is small, the visual connections to the outside is limited, whereas bigger openings are get by a large angle.

The structure can be seen as an independant element in 3 dimensions, composed of the triangulation of the edges : each of the sides converge to one point which is linked to the slabs. The system is made rigid by both the addition of vertical elements by using the support of the existing pillars and by the steel grid that supports the glass.

At the end, the structure acts as a whole  by creating more complexe stresses where each 3d unit is supporting itself as well as the whole system.

Some external elements would then influence the skin :

- The Skin would react to the sun by the application of a sun factor depending on both the orientation of the tower and the angle of incidence which derives from the inclination of the facets. Where sun protections are needed, an expanded aluminium mesh will be added according to the sun factor that would be evaluated.

- The views would be generated by a random factor in order to get a multiple orientation. Some bigger openings would be created, as well as perforated ones to provide some space for terraces.

As a result, the skin pattern would react on both the facets and the site.

DLA: pattern becomes structure

I modified the 3D DLA VB component in order to get a list of lines between each new point and it’s neighbour. The starting poins lies on the xy-plane. Every new point is positionned one level higher in z-direction than his neighbouring point, once it has found one. That means every branch is growing upwards.

Animation of the growth

GH definition
VB component

Hexaraeus Process

source for the reference images:

Why am I interested in cable-membrane tensile structure/skin?

1) Structural: The structure of Piraeus tower has not been protected for the 30 last years. Maybe we can’t afford adding a heavy façade. The “cable-membrane tensile structure/skin” is very light.

2) Economical: Economical situation in Greece is not at the best. Are the materials of a “cable-membrane tensile structure/skin” cheap? To be verified.. But it is possible to create large formal variations with the exact same pieces.

3) Formal: The membrane is capable of taking “complex” shapes with a very simple process

4) Comfort/Ecology: Looking at the interior photographies of the tower, they seemed pretty dark: it seems that the sunlight is not so strong. But still we know that in summer, the sun in athens is very hot, and a glass façade could result in overheating. These translucent membranes don’t block light, but offers a protection to sun rays.