Surfaces with planar curvature lines: Discretization, generation and application to the rationalization of curved architectural envelopes

Tellier, Xavier; Douthe, Cyril; Hauswirth, Laurent; Baverel, Olivier

doi:10.1016/j.autcon.2019.102880

Cited by 16 publications

(13 citation statements)

References 27 publications

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“…Due to the robustness of this method, in recent years, many advances have been made in the development and variety of methods based on this approach. [8][9][10] Second method: Optimal discretization of free-form surfaces (the top-down approach). Geodesic domes can be considered as one of the first notable examples of optimal discretization of spherical surfaces.…”

Section: The Optimization Methods For Connection Anglesmentioning

confidence: 99%

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Optimized orientation of jointing system in free-form lattice space structures

Esmailnejad

Chenaghlou

Abedi

2023

International Journal of Space Structures

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The recent decades have witnessed the development of a new generation of space structures called free-form space structures. In this new family of space structures, due to the geometric nature of the structure, the orientation of the members varies substantially within the joints, meaning that the members need to be connected to the joints at different angles. The wide distribution of these angles throughout the structure will significantly affect the cost of fabrication. Therefore, accurate and automatic calculation of connection angles and their optimizations have always been of interest to researchers and manufacturers. This article has the following two main objectives. The first objective is to provide geometric calculations and obtain the connection angles of single-layer lattice space structures. The second, and more important objective is to review the existing methods and to develop a geometrical method for their optimization, referred to as the “node orientation optimization” method throughout this article. Using the mentioned method, a series of optimizations are carried out in a number of free-form lattice space structures and the results are studied.

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Section: The Optimization Methods For Connection Anglesmentioning

confidence: 99%

“…Due to the robustness of this method, in recent years, many advances have been made in the development and variety of methods based on this approach. 8–10…”

Section: The Connection Angles and Existing Strategies For Their Opti...mentioning

confidence: 99%

Optimized orientation of jointing system in free-form lattice space structures

Esmailnejad

Chenaghlou

Abedi

2023

International Journal of Space Structures

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“…The analysis from the previous section is necessary to help us in determination of the initial curves for the process of generation. The idea to start from two curves and try to generate a PQ mesh system is drawn from the research of Tellier [21], where the authors deal only with planar curves as defined edges of the both starting and other discretized curves of the mesh system, which is not the case in this research. Although in showed case study only the starting curves are planar it is possible to use other.…”

Section: Determination Of the Initial Curves For Generationmentioning

confidence: 99%

Design and Optimization of Free-Form Surfaces for Modular Concrete 3D Printing

Tošić¹,

Eichenauer²,

Ivaniuk³

et al. 2022

Preprint

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Shell-like, double curved and thus above-average performance structures, are usually produced monolithically on site. For industrial advancement, however, they must be divided into transportable modules which can be assembled on the construction site (design for assembly). Models are lattice shells made of steel and glass, in which predominantly flat sub-surfaces (modules) are used. Therefore, the main question is: Which modularizations are suitable for flow production with mineral building materials? In this paper designed free-form surface is going to be discretized as PQ circular mesh system, suitable modules for 3D concrete printing. Moreover, the multi-criteria optimization is done with Response Surface Methodology (RSM) in order to get optimal final shape. The goal is to start from the arbitrary shape, that can be generated from two curves, with possible two-way division into modules and compare it with the resulted discretized PQ circular mesh system, realized with new algorithm. The comparison can be defined through two main criteria: geometrical and structural.

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“…Extracting the geometric information from the surface depends on the parametrization that is using as a coordinate system on the surface. Using geodesic or line of curvature coordinates are suitable for many tasks not only in differential geometry but involves other areas of applications, such as integrable systems [4], surfaces motions [5,6], and architectural shape design [7,8].…”

Section: Introductionmentioning

confidence: 99%

Construction of Developable Surface with Geodesic or Line of Curvature Coordinates

Althibany

2021

Journal of New Theory

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In this paper, a developable surface with geodesic or line of curvature coordinates is constructed in the Euclidean 3-space. A developable surface is coordinated by two families of parametric curves, base curves (directrices) and lines (rulings). Since any part of a straight line on a developable surface is geodesic and line of curvature, we only need to show that the directrices curves are geodesics or lines of curvature to ensure that the developable surface is parameterized by geodesic or line of curvature coordinates. The necessary and sufficient conditions for the directrices curves to be geodesics or lines of curvature are studied. The main results of this paper show that the developable surface with geodesic coordinates is a generalized cylinder, and the developable surface with line of curvature coordinates is a tangent surface.

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Surfaces with planar curvature lines: Discretization, generation and application to the rationalization of curved architectural envelopes

Cited by 16 publications

References 27 publications

Optimized orientation of jointing system in free-form lattice space structures

Optimized orientation of jointing system in free-form lattice space structures

Design and Optimization of Free-Form Surfaces for Modular Concrete 3D Printing

Construction of Developable Surface with Geodesic or Line of Curvature Coordinates

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