design process using mathematics-durga

DESIGN PROCESS USING MATHEMATICS

Introduction:This stage deals about the literature

study of general detail relating to modern mathematics and the design process involved in 30 St mary Axe.

And in the next stage will be dealing about the classical example of mathematics relating to angorwat and the stpeter’s basilica

Design process including the mathematicsThe main process :

The mathematics usually come into play after the shape of the design has been created. In essence, today’s CAD systems are used to support design evaluation and analysis

Literature study design process stage -II

The analysis relating to the whiril winds, acoustical properties and other details relating to orientation of the building and also the interior layouts can be analyzed through parametric modeling process


30 St Mary Axe, also known as the Gherkin and the Swiss Re Building, is a skyscraper in London's main financial district, the City of London, completed in December 2003 and opened at the end of May 2004.With 40 floors, the tower is 180 meters (591 ft) tall, and stands on the former site of the Baltic Exchange building,

Literature study 30 St Mary Axe stage -II

Design, procurement and fabrication processes were integrated through the use by the design team of three-dimensional modeling of the steel frame and a parametric approach to the design, enabling complexity to be managed with reduced risk and greater economy. The project shows the ability of structural steel to enable radical architectural ideas to be realized.


A fundamental characteristic of the Swiss Re building is the use of a consistent unifying system combined with a constantly varying geometry vertically through the building.

This type of geometry is particularly suited to a parametric design approach: many of the detailed design conditions can be investigated by setting up fixed mathematical relationships between a relatively limited number of geometric parameters defining the building shape.

This approach was used to drive optimization studies, to build up data bases of various design conditions allowing rationalization of structural components and details, and to generate 3D model geometry for analysis, co-ordination and structural design


the computer aided designs usually come into play after the shape of the design has been created.

The major research was to bring computers into the start of the creative design process, where they can augment design activity by supporting design synthesis: enhancing and highlighting options that might be open to the designer.

The vision was of a computer aided design synthesis system that can work with and manipulate designers’ sketches at the earliest stage of the design process.

Previous research in the application of shape grammars to design generation indicated that they offered a potential foundation upon which such a system could be built.


SHAPE GRAMMARS


Some ideas from

computer vision

Shape computation in

industrial designArchitecture

designDesign education

designing

Replacing people work

with software

Design Synthesis &shape

generation

SHAPE GRAMMARS


An example highlighting the basic elements of a shape grammar is given in Figure 2. Figures 2(a) and 2(b) show an initial shape (that seeds the computation) and two shape replacement rules. Figure 2(c) provides a fragment of the network of shapes that can be computed from this initial shape through the application of the shape rules.

SHAPE GRAMMARS


Parametric modeling has been around since the 1960s, but only now are architects fully exploiting its power.

PARAMETRIC DESIGN

The models allow you to play around with certain features of a building without having to re-calculate all the other features that are affected by the changes you make. This makes them extremely powerful design tools.They allow you to change a variety of geometrical features while keeping fixed those features you have decided should not change. The models function a bit like spreadsheets: changing a feature of the building is like changing an entry of the spreadsheet.


PARAMETRIC MODELLING

The shape of the toweris influenced by thephysical environment ofthe city. The smoothflow of wind around thebuilding was one of themain considerations.


The team can change geometric features of a building and see how the change affects say, aerodynamic or acoustic properties. They can explore how complex shapes that are hard to build can be broken down into simpler ones, and they can quickly calculate how much material is needed to estimate the cost.

The results are buildings that would have been impossible only a few decades ago, both because their complex shapes were next to impossible to construct and because of the degree to which they exploit science to interact optimally with their environment.


PARAMETRIC MODELLINGBut even if you're not being ruffled by

strong winds, standing next to a sky-scraper can be eery. It dwarfs you,it eclipses shorter buildings and it takes away the sunlight. Again, it's the Gherkin's distinctive shape thathelps minimize these effects. Its bulging middle and its tapered top ensure that you never see its top from


RATIONAL DESIGNThinking of a complex structure as a

collection of mathematically defined components is not just useful in the virtual world: it helps turn a model of a building into a step-by-step guide on how to actually construct it. This process of rationalization forms another important part of the SMG's work (specialist modeling group). But, as before, mathematical perfection has to make way for practicality:


RATIONAL DESIGNSurfaces that can be described by

mathematical equations such as slices of cones, tori, or spheres often form the basis of the SMG's design. This is advantageous when it comes to creating virtual models, as mathematically generated surfaces are easily represented on a computer. Rather than describing a structure by a large number of individually stored co-ordinates, you only need to store an equation. The exact shape of the surface can be controlled by varying the parameters in the equation


the building’s radical form by creating the efficient external ‘diagrid’ system (diagonally braced structure) of intersecting steel sections around the tower's perimeter.

The ‘diagrid’ comprises simple straight circular steel sections resulting in a structure which is remarkably simple to build considering the complexity of the building’s shape.

The ‘diagrid’ responds to the building's curvedshape and provides vertical support to thefloors thus allowing large internal column freeoffice space.

The central core is required onlyto act under vertical load and is free fromdiagonal bracing. In addition to being highlyefficient in resisting wind forces, the ‘diagrid’frames the communal light wells which spiralup the building enabling occupants to

Based on apparently arbitrary proportions of an "ideal man" (possibly Le Corbusier himself) combined with the golden ratio and Vitruvian Man, Le Modulor was never popularly adopted among architects, but the system's graphic of the stylised man with one upraised arm is widely recognised and powerful.

Anti-Modernists (Langhein, 2005) claim the modulor is not well suited to introduce proportion and pattern into architecture , to improve its form qualities (gestalt pragnance) and introduce shape grammar in design in building.

However, through its application in the design of some of the last century's most beautifully proportioned and harmonic buildings (Le Corbusier: Architect of the Twentieth Century, Kenneth Frampton, 2002) Le Corbusier's work strongly disputes this.

Literature study shape grammar stage -II

Introduction to shape grammar

Shape grammars in computation are a specific class of production systems that generate geometric shapes. With shape grammars, forms can be created that are not stored in the computer previously.

Shape grammars have been studied in particular in computer-aided architectural design, as they provide a formalism to create new designs. The foundation of shape grammars in architectural design have been defined in a seminal article by George Stiny and James Gips in 1971.


First introduced as paintings

A shape grammar consists of shape rules and a generation engine that selects and processes rules. A shape rule defines how an existing (part of a) shape can be transformed.

A shape rule consists of two parts separated by an arrow pointing from left to right. The part left of the arrow is termed the Left-Hand Side (LHS). It depicts a condition in terms of a shape and a marker.

The part right of the arrow is termed the Right-Hand Side (RHS). It depicts how the LHS shape should be transformed and where the marker is positioned. The marker helps to locate and orientate the new shape.Literature study shape grammar stage -II


A shape grammar minimally consists of three shape rules: a start rule, at least one transformation rule, and a termination rule.

The start rule is necessary to start the shape generation process. The termination rule is necessary to make the shape generation process stop. The simplest way to stop the process is by a shape rule that removes the marker.

A shape grammar system additionally has a working area where the created geometry is displayed. The generation engine checks the existing created geometry for conditions that match the LHS of the shape rules.

j.Christopher jones (1970)Design methodslondon

bibliography


The next stage will be dealing with the detail study of 30 stmary axe and the study about the classical example

Next stage :

design process using mathematics-durga

Documents

creative design process

design evaluation

design activity

parametric design approach

detailed design conditions

stage deals

earliest stage

st mary axe stage iidesign