The surface (F= sin (β)+ cos (μ)) is restrained on the ground and a vector force of 10 000 N in Z direction is applied to the peak point of the geometry. The maximum equivalent stress varies from 78373 PA to 83404 PA for different panelization methods by the use of steel as material.
Computational Fluid Dynamics (CFD) is operated on the surface (F= sin (β)+ cos (μ)). The graphical display represents contours of static pressure, velocity vectors and path lines in given the boundary conditions. The wind flow is aligned with the velocity vectors.
Different panelization options are generated via the code for the geometry with the assigned curve function: F= sin (v)+cos (u). The script* performed at RhinoScript platform. Because planar quadrilateral panels obtain advantage of having a lower node complexity and are feasible for manufacturing, planar quadrilateral panels are operated for the geometry. The code enables that the architectural designer can identify if the geometry contains any holes. If yes, then the shapes of them needs to be defined. The algorithm runs with the following procedural steps which the user needs to identify during the execution of the code:
- Selecting the NURBS surface.
- Defining the U and V values of the surface.
- Specifying types of holes if exists any.
- Introducing the shapes of the holes.
- Defining the percentage of the holes within overall panels.
- Deciding if the hole sizes vary or not.
*Special thanks to Fabio Mantuano.
Advanced computer aided design (CAD) techniques liberated architectural form, by enabling architectural designer to generate complex forms, such as freeform surfaces. In today’s common architectural practices, computational tools, associated with performance analysis and evaluation, are undertaken during a later stage of the design process, following the form generation. ParaMaterial aims to discuss how material can be integrated into a system in which architectural geometry, material and structural performance are interdependent to increase efficiency by identifying critical procedures towards manufacturing of complex forms in architecture. Mathematically driven surfaces are explored of which geometrical attributes can be altered parametrically. Because buildings are designed to withstand various complex loading conditions, simulations are undertaken for surfaces via Finite Element Method (FEM) and Computational Fluid Dynamics (CFD) analysis tools to investigate how material informs architectural geometry in respond to the static and dynamic loading conditions.
The use of mathematics in computational design process enables from simple to highly complex geometries with control parameters. Numerous different types of mathematically driven surfaces such as sphere, torus, cylinder, catalan, moebius strip, klein surface, catenoid helicoids, henneberg, elliptic paraboloid, enneper and many more can be structured in parametric systems by assigning their respective mathematical curve functions.
Finite Element Method analysis is undertaken for: (a) Equivalent stress (b) Total deformation (c) Directional deformation (d) Shear stress
The video of total deformations can be watched in the following link: https://www.facebook.com/pages/ParaMaterial/161745380551435#!/photo.php?v=10151103382082060
Mechanical properties of the structural steel.
(a) A vector force of –10.000 N is applied (b) By imposing the boundary conditions, it is critical to indicate the surfaces where the geometry sits on the ground, besides assigning the architectural material, structural steel.
(a) Surface curvature analyses are undertaken to identify problem areas by running gaussian and mean tools. (b) The double-curved surface is subdivided into components where quadrilateral panels are assigned to the points on divisions of the x and y directions (U-V curves).
Different stiffness values (S= 125 to 4000) for the springs are tested. Following the selection of the solution with S=1000, the geometry is adjusted by shifting one corner to break the symmetry and generate large spans.
Although some studies investigate physics based dynamic systems to generate structurally efficient forms and incorporate forms with fabrication constraints and performance requirements, there is a gap in the current research questioning of how to link structurally efficient architectural geometry with material.
The proposed methodology consists of form-finding, analysis, evaluation and optimization. It offers a dynamic system for form-finding via catenary model generated in parametric design medium, Grasshopper plug-in Kangaroo add-on. Various stiffness values for the material (spring) are used to test different structural options. The feasible geometry is investigated further via surface analyses and panelization tools.
By imposing the loads and boundary conditions and by assigning the architectural material (structural steel), Finite Element Method (FEM) analysis is operated to assess the structural performance of the geometry. In the last stage, input and output parameters are defined for optimization where mechanical properties of the material and thickness of the geometry are interlinked to the equivalent stress and the total deformations.