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Quadrangular Grid shells have generated interest in recent years for their application in rationalizing free form geometry in the built environment. Shell structure are efficient because their form is governed by flow of internal forces. But while discretizing shells into grid shells, instead of using flow of forces, current method follows patterns and tessellation techniques. Quadrangular grids are easier to manufacture but they are not stiff inherently compared to triangulated meshed grid, which doesn’t allow them to be used as frequently. There is a scope to improve stiffness by discretization informed by flow of forces. A workflow was developed for designing quadrangular static-responsive grid shells which are structurally efficient, homogenous and has near planar cladding, including preferences of the designer. The workflow is set up in a parametric environment in grasshopper, a plugin for Rhino 3d modelling software. It uses particle spring method for form finding a shell which has membrane like load bearing behaviour. The solid shell is discretized into a grid shell by a custom stress line generator which uses principal stress vector field derived by Finite element analysis of the shell. The grid shell is homogenised and optimized for planarity by dynamic relaxation. Multiple design alternatives are generated and stored. Design space is explored by using data analytics and visualization techniques which helps user to make informed design decisions. The workflow is applied to create a grid shell over delft bus station as a case study to protect travellers from varying weather conditions. The results are quite satisfactory in terms of structural performance when compared to methods used in state of the art in practice. Stiffness of a structure can be measure by total strain energy. The grid shell for delft bus station generated using this workflow was 32% and 49% lower in terms of total strain energy(compliance) than regular quad grid shell and diagrid qua, Architecture, Urbanism and Building Sciences | Building Technology

Quadrangular Grid shells have generated interest in recent years for their application in rationalizing free form geometry in the built environment. Shell structure are efficient because their form is governed by flow of internal forces. But while discretizing shells into grid shells, instead of using flow of forces, current method follows patterns and tessellation techniques. Quadrangular grids are easier to manufacture but they are not stiff inherently compared to triangulated meshed grid, which doesn’t allow them to be used as frequently. There is a scope to improve stiffness by discretization informed by flow of forces. A workflow was developed for designing quadrangular static-responsive grid shells which are structurally efficient, homogenous and has near planar cladding, including preferences of the designer. The workflow is set up in a parametric environment in grasshopper, a plugin for Rhino 3d modelling software. It uses particle spring method for form finding a shell which has membrane like load bearing behaviour. The solid shell is discretized into a grid shell by a custom stress line generator which uses principal stress vector field derived by Finite element analysis of the shell. The grid shell is homogenised and optimized for planarity by dynamic relaxation. Multiple design alternatives are generated and stored. Design space is explored by using data analytics and visualization techniques which helps user to make informed design decisions. The workflow is applied to create a grid shell over delft bus station as a case study to protect travellers from varying weather conditions. The results are quite satisfactory in terms of structural performance when compared to methods used in state of the art in practice. Stiffness of a structure can be measure by total strain energy. The grid shell for delft bus station generated using this workflow was 32% and 49% lower in terms of total strain energy(compliance) than regular quad grid shell and diagrid qua, Architecture, Urbanism and Building Sciences | Building Technology

The theme of this paper is the modeling of focal-directorial surfaces, starting with their definition, as a locus of points, whose sum of the distances to the focus and/or directrix is constant and predefined. We presented a heuristic algorithm for modeling surfaces and their isocurves, achieved through the use of the Grasshopper visual programming editor in the RhinoCeros environment. Surfaces and their isocurves were generated in a spherical grid, because a Cartesian grid proved unsuitable for the task and the chosen approach. This paper additionally proposes a modeling algorithm of a discrete variation of focal-directorial surfaces. The proposed modeling method is a 3D convex hull implemented on a set of surface points, with the selected points close to that surface. The discrete model is realized both in a Cartesian and spherical grid. There are significant differences between the obtained results., Tema ovog rada je modelovanje fokalno-direktrisnih površi polazeći od njihove definicije, kao geometrijskog mesta tačaka čiji je zbir rastojanja do fokusa i/ili direktrisa konstantan i unapred zadat. Predložen je jedan heuristički algoritam za modelovanje površi i njihovih izolinija koji je realizovan pomoću vizuelnog grafičkog editora Grasshoper u RhinoCeros okruženju. Generisanje površi i njihovih izolinija realizovano je u sfernom gridu, pravougli grid se pokazao kao nepodesan za postavljeni zadatak i pristup. U ovom radu je, dodatno, predložen i algoritam modelovanja diskretne varijante fokalno-direktrisnih površi. Kao način modelovanja, predložen je 3D convex hull primenjen na skupu tačaka površi i izabranih tačaka bliskih toj površi. Diskretni model je realizovan u pravouglom, i u sfernom gridu. Dobijeni su rezultati koji se značajno međusobno razlikuju.

The theme of this paper is the modeling of focal-directorial surfaces, starting with their definition, as a locus of points whose sum of the distances to the focus and/or directrix is constant and predefined. We presented a heuristic algorithm for modeling surfaces and their isocurves, achieved through the use of the Grasshopper visual programming editor in the RhinoCeros environment. Surfaces and their isocurves were generated in a spherical grid, because a Cartesian grid proved unsuitable for the task and the chosen approach. This paper additionally proposes a modeling algorithm of a discrete variation of focal-directorial surfaces. The proposed modeling method is a 3D convex hull implemented on a set of surface points, with the selected points close to that surface. The discrete model is realized both in a Cartesian and spherical grid. There are significant differences between the obtained results.

p. 966-876, The new geometrical developments open new perspectives for free-form design, making it possible to escape from planar triangular or quadrilateral discretizations. Recent advances in theory algorithms allow for the discretization of any surface using only single curvature panels thus allowing the realisation of smooth double curvature glazed envelops of any form. Grid shell structures usually present a nearly in plane uniform behaviour, but previous realisations have shown that grid shells can be designed also according to an anisotropic inplane arrangement. The control of principal direction and the fine tuning of the stiffness of the different structural elements (arcs, cables etc.) is a tool for adjusting the form-finding thus controlling the resulting geometry. Moreover, the form-finding can also be performed without researching a constant stress (self weight); in this case an even wider range of forms become possible. These new geometrical and structural approaches have been coupled together and tested in re-designing, as a case study, the glazed roof of the Neumunster Abbey in Luxembourg. Such approach allowed for the conception of an efficient structure supporting a smooth double curvature glass skin, made out of only single curvature panels, perfectly coherent with the perimeter of the courtyard i.e. matching all the edges without any gaps.

p. 966-876, The new geometrical developments open new perspectives for free-form design, making it possible to escape from planar triangular or quadrilateral discretizations. Recent advances in theory algorithms allow for the discretization of any surface using only single curvature panels thus allowing the realisation of smooth double curvature glazed envelops of any form. Grid shell structures usually present a nearly in plane uniform behaviour, but previous realisations have shown that grid shells can be designed also according to an anisotropic inplane arrangement. The control of principal direction and the fine tuning of the stiffness of the different structural elements (arcs, cables etc.) is a tool for adjusting the form-finding thus controlling the resulting geometry. Moreover, the form-finding can also be performed without researching a constant stress (self weight); in this case an even wider range of forms become possible. These new geometrical and structural approaches have been coupled together and tested in re-designing, as a case study, the glazed roof of the Neumunster Abbey in Luxembourg. Such approach allowed for the conception of an efficient structure supporting a smooth double curvature glass skin, made out of only single curvature panels, perfectly coherent with the perimeter of the courtyard i.e. matching all the edges without any gaps.

p. 966-876, The new geometrical developments open new perspectives for free-form design, making it possible to escape from planar triangular or quadrilateral discretizations. Recent advances in theory algorithms allow for the discretization of any surface using only single curvature panels thus allowing the realisation of smooth double curvature glazed envelops of any form. Grid shell structures usually present a nearly in plane uniform behaviour, but previous realisations have shown that grid shells can be designed also according to an anisotropic inplane arrangement. The control of principal direction and the fine tuning of the stiffness of the different structural elements (arcs, cables etc.) is a tool for adjusting the form-finding thus controlling the resulting geometry. Moreover, the form-finding can also be performed without researching a constant stress (self weight); in this case an even wider range of forms become possible. These new geometrical and structural approaches have been coupled together and tested in re-designing, as a case study, the glazed roof of the Neumunster Abbey in Luxembourg. Such approach allowed for the conception of an efficient structure supporting a smooth double curvature glass skin, made out of only single curvature panels, perfectly coherent with the perimeter of the courtyard i.e. matching all the edges without any gaps.