Description of the research
Elastic gridshells are usually transformed from a flat configuration to their final three dimensional form. In their final form, the stresses in the bars could be very high due to the curvature of the bars. In this research project different strategies were used to optimise the mesh in order to minimise the stresses in the final form of the gridshell. Another problem is to predict if a form can be meshed by a Tchebychev net without singularities.
(Bouhaya 2009) proposed a method by dropping numerically the mesh on a rigid surface and allowing the mesh to slide on the surface. (Bouhaya 2011) and (Bouhaya 2014) proposed to minimise the curvature of the bars with the of genetic algorithms on an imposed surface. (Lafuente Hernández 2013) proposed to start with an irregular mesh to give a final configuration with a lower level of stresses.
It has been demonstrated that a sphere cannot be meshed by a Tchebychev net without singularities. A Tchebychev net can only cover certain surface, the ongoing research tries to predict which surface can be covered and with which type of singularities.
- Architectural Geometry
- Steel Structures
- Active Bending
A re-parameterization approach for the construction of domes with planar facets – R. Mesnil (2018)
The aim of this article is to propose parameterization with planar facets of dome structures. The technique
introduced in this paper starts from an input parameterization and creates a dual pattern with planar quadrilateral facets. The derivation of the analytical solution allows to link the method with the creation of meshes with planar hexagonal facets and of circle packing on spheres. The method can be used in various contexts and allows designers to design with two superimposed parameterizations, which allows for a potential decoupling between structure and envelope.
Non-standard patterns for gridshell structures: Fabrication and Structural Optimization – R. Mesnil et al. (2017)
R. Mesnil, C. Douthe, O. Baverel
The design of gridshells is subject to strong mechanical and fabrication constraints, which remain largely
unexplored for non-regular patterns. The main technological constraints for glazed gridshells are related to the planarity of facets and the existence of torsion-free offsets. The authors propose indicators to evaluate a priori the quality of design space of gridshells covered with different patterns for these fabrication constraints. By comparing these metrics, the kagome grid pattern is identified as a pattern with a complexity similar to the ubiquitous quadrilateral pattern. Finally, the authors propose to generate gridshells with planar facets with the marionette technique and to explore the resulting design space by the means of multi-objective optimization. The results of the study show that our framework for shape modeling has similar performances as more usual frameworks, like NURBS modeling, while maintaining the facet planarity.
Optimization of gridshell bar orientation using a simplified genetic approach – L. Bouhaya et al. (2014)
L. Bouhaya, O. Baverel, J.-F. Caron
Gridshells are defined as structures that have the shape and rigidity of a double curvature shell but consist of a grid instead of a continuous surface. This study concerns those obtained by elastic deformation of an initially flat two-way grid. This paper presents a novel approach to generate gridshells on an imposed shape under imposed boundary conditions. A numerical tool based on a geometrical method, the compass method, is developed. It is coupled with genetic algorithms to optimize the orientation of gridshell bars in order to minimize the stresses and therefore to avoid bar breakage during the construction phase. Examples of application are shown.
On the design and construction of elastic gridshells with irregular meshes – E. Lafuente Hernández (2013)
E. Lafuente Hernández, O. Baverel, C. Gengnagel
Despite the time and cost advantages by the manufacture, transport and assembling of elastic gridshells, high material stresses are induced on the structures during their shaping process. An optimisation of the grid arrangement in order to reduce the curvature of the grid profiles and with it the initial bending stresses is therefore crucial when considering the stress reserves under subsequent external loading.To be able to deploy and bend the structure as a whole grid and thereby accelerate their construction process, elastic gridshells usually exhibit constant mesh size (regular gridshells). However, this condition makes the optimisation of regular gridshells only possible until a certain level. In this paper, several double-curved gridshells have been optimised allowing variation on the mesh size (irregular gridshells), so that a further reduction of the profiles' curvature and lower concentration of stresses could be obtained.By the construction of irregular gridshells, the grid profiles are normally independently bent in an incremental process, generally more time-consuming than by regular gridshells. Nevertheless, if the bending stiffness of the grid profiles is low enough, large deformations can be induced on the irregular meshes and the structures can be built by bending the whole grid. The stresses generated during the construction process must be previously controlled, e.g. using numerical simulation. For this paper, the erection process of an elastic hemisphere with irregular mesh and 10m diameter has been analysed by means of finite element modelling and tested on a 1:1-prototype. The comparison of the resulting geometry and load-bearing behaviour between the modelled and real structures are presented.
Mapping two-way continuous elastic grid on an imposed surface: Application to grid shells – L. Bouhaya et al. (2009)
L. Bouhaya, O. Baverel, J.-F. Caron
This paper presents a method to generate a grid shell on an imposed shape and imposed boundary conditions. The proposed method is done by mapping a two-way continuous elastic grid on an imposed surface using an explicit dynamic finite element method. An initially flat two-way grid, with free boundary conditions, is set up over a fixed surface that has the desired shape. Then, the grid is dropped on the fixed surface. Moreover, different strategies of formfinding are presented and a comparison with other methods is done. Finally, many examples are shown to illustrate the proposed method.