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2023
Journal article
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Deployable strip structures
Liu D, Pellis D, Chiang Yc, Rist F, Wallner J, Pottmann H
We introduce the new concept of C-mesh to capture kinetic structures that can be deployed from a collapsed state. Quadrilateral C-meshes enjoy rich geometry and surprising relations with differential geometry: A structure that collapses onto a flat and straight strip corresponds to a Chebyshev net of curves on a surface of constant Gaussian curvature, while structures collapsing onto a circular strip follow surfaces which enjoy the linear-Weingarten property. Interestingly, allowing more general collapses actually leads to a smaller class of shapes. Hexagonal C-meshes have more degrees of freedom, but a local analysis suggests that there is no such direct relation to smooth surfaces. Besides theory, this paper provides tools for exploring the shape space of C-meshes and for their design. We also present an application for freeform architectural skins, namely paneling with spherical panels of constant radius, which is an important fabrication-related constraint.Source: ACM TRANSACTIONS ON GRAPHICS, vol. 42 (issue 4), pp. 1-16
DOI: 10.1145/3592393
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Liu D, Pellis D, Chiang Yc, Rist F, Wallner J, Pottmann H
We introduce the new concept of C-mesh to capture kinetic structures that can be deployed from a collapsed state. Quadrilateral C-meshes enjoy rich geometry and surprising relations with differential geometry: A structure that collapses onto a flat and straight strip corresponds to a Chebyshev net of curves on a surface of constant Gaussian curvature, while structures collapsing onto a circular strip follow surfaces which enjoy the linear-Weingarten property. Interestingly, allowing more general collapses actually leads to a smaller class of shapes. Hexagonal C-meshes have more degrees of freedom, but a local analysis suggests that there is no such direct relation to smooth surfaces. Besides theory, this paper provides tools for exploring the shape space of C-meshes and for their design. We also present an application for freeform architectural skins, namely paneling with spherical panels of constant radius, which is an important fabrication-related constraint.Source: ACM TRANSACTIONS ON GRAPHICS, vol. 42 (issue 4), pp. 1-16
DOI: 10.1145/3592393
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dl.acm.org 
| ACM Transactions on Graphics | CNR IRIS | CNR IRIS
2023
Conference article
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Principal symmetric structures
Pellis D, Pottmann H
We introduce a new class of quadrilateral gridshell structures in axial force equilibrium where beams run symmetrically to the principal stress directions of their limit membrane shell. This kind of structures have the property that, at each node, the axial forces in the four connected beams are approximately equal. This allows for a more homogeneous distribution of forces in the structure, particularly in shapes where stresses are significantly anisotropic, in which case a conventional gridshell typically results in numerous beams remaining nearly unloaded. In this work, we first discuss the properties of principal symmetric structures and evaluate their advantages relative to other types of gridshells. We introduce then a computational pipeline for the design of such structures based on a quadrilateral remeshing and a subsequent optimization, and show some results.Source: LECTURE NOTES IN CIVIL ENGINEERING, vol. 437, pp. 359-368. Turin, Italy, 26-28/06/2023
DOI: 10.1007/978-3-031-44328-2_37
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Pellis D, Pottmann H
We introduce a new class of quadrilateral gridshell structures in axial force equilibrium where beams run symmetrically to the principal stress directions of their limit membrane shell. This kind of structures have the property that, at each node, the axial forces in the four connected beams are approximately equal. This allows for a more homogeneous distribution of forces in the structure, particularly in shapes where stresses are significantly anisotropic, in which case a conventional gridshell typically results in numerous beams remaining nearly unloaded. In this work, we first discuss the properties of principal symmetric structures and evaluate their advantages relative to other types of gridshells. We introduce then a computational pipeline for the design of such structures based on a quadrilateral remeshing and a subsequent optimization, and show some results.Source: LECTURE NOTES IN CIVIL ENGINEERING, vol. 437, pp. 359-368. Turin, Italy, 26-28/06/2023
DOI: 10.1007/978-3-031-44328-2_37
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2023
Journal article
Open Access
C-Shells: deployable gridshells with curved beams
Becker Q, Suzuki S, Ren Y, Pellis D, Panetta J, Pauly M
We introduce a computational pipeline for simulating and designing C-shells, a new class of planar-to-spatial deployable linkage structures. A C-shell is composed of curved flexible beams connected at rotational joints that can be assembled in a stress-free planar configuration. When actuated, the elastic beams deform and the assembly deploys towards the target 3D shape.We propose two alternative computational design approaches for C-shells: (i) Forward exploration simulates the deployed shape from a planar beam layout provided by the user. Once a satisfactory overall shape is found, a subsequent design optimization adapts the beam geometry to reduce the elastic energy of the linkage while preserving the target shape. (ii) Inverse design is facilitated by a new geometric flattening method that takes a design surface as input and computes an initial layout of piecewise straight linkage beams. Our design optimization algorithm then calculates the smooth curved beams to best reproduce the target shape at minimal elastic energy.We find that C-shells offer a rich space for design and show several studies that highlight new shape topologies that cannot be achieved with existing deployable linkage structures.Source: ACM TRANSACTIONS ON GRAPHICS (ONLINE), vol. 42 (issue 6)
DOI: 10.1145/3618366
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Becker Q, Suzuki S, Ren Y, Pellis D, Panetta J, Pauly M
We introduce a computational pipeline for simulating and designing C-shells, a new class of planar-to-spatial deployable linkage structures. A C-shell is composed of curved flexible beams connected at rotational joints that can be assembled in a stress-free planar configuration. When actuated, the elastic beams deform and the assembly deploys towards the target 3D shape.We propose two alternative computational design approaches for C-shells: (i) Forward exploration simulates the deployed shape from a planar beam layout provided by the user. Once a satisfactory overall shape is found, a subsequent design optimization adapts the beam geometry to reduce the elastic energy of the linkage while preserving the target shape. (ii) Inverse design is facilitated by a new geometric flattening method that takes a design surface as input and computes an initial layout of piecewise straight linkage beams. Our design optimization algorithm then calculates the smooth curved beams to best reproduce the target shape at minimal elastic energy.We find that C-shells offer a rich space for design and show several studies that highlight new shape topologies that cannot be achieved with existing deployable linkage structures.Source: ACM TRANSACTIONS ON GRAPHICS (ONLINE), vol. 42 (issue 6)
DOI: 10.1145/3618366
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| CNR IRIS | ISTI Repository | CNR IRIS | CNR IRIS
2024
Patent
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Reconfigurable mold system for the production of thin doubly-curved panels and similar applications
Rist F., Wang Z., Pellis D., Palma M., Liu D., Grinspun E., Michels D. L.
The invention provides a fully reconfigurable, zero-waste molding system for the fabrication of thin, doubly-curved, free-from elements such as pre-cast concrete panels, fiber-reinforced laminates, sandwich panels, ceramic components, plywood and sheet metal panels, and many more. The invention replaces the wasteful, time-consuming, and expensive process of machining the mold surface from a block of Polystyrene or Polyurethane foam. It can replace single- and double-surface molds in various applications across multiple industrial domains.
Rist F., Wang Z., Pellis D., Palma M., Liu D., Grinspun E., Michels D. L.
The invention provides a fully reconfigurable, zero-waste molding system for the fabrication of thin, doubly-curved, free-from elements such as pre-cast concrete panels, fiber-reinforced laminates, sandwich panels, ceramic components, plywood and sheet metal panels, and many more. The invention replaces the wasteful, time-consuming, and expensive process of machining the mold surface from a block of Polystyrene or Polyurethane foam. It can replace single- and double-surface molds in various applications across multiple industrial domains.
2024
Journal article
Open Access
A flexible mold for facade panel fabrication
Rist F., Wang Z., Pellis D., Palma M., Liu D., Grinspun E., Michels D. L.
Architectural surface panelling often requires fabricating molds for panels, a process that can be cost-inefficient and material-wasteful when using traditional methods such as CNC milling. In this paper, we introduce a novel solution to generating molds for efficiently fabricating architectural panels. At the core of our method is a machine that utilizes a deflatable membrane as a flexible mold. By adjusting the deflation level and boundary element positions, the membrane can be reconfigured into various shapes, allowing for mass customization with significantly lower overhead costs. We devise an efficient algorithm that works in sync with our flexible mold machine that optimizes the placement of customizable boundary element positions, ensuring the fabricated panel matches the geometry of a given input shape: (1) Using a quadratic Weingarten surface arising from a natural assumption on the membrane's stress, we can approximate the initial placement of the boundary element from the input shape's geometry; (2) we solve the inverse problem with a simulator-in-the-loop optimizer by searching for the optimal placement of boundary curves with sensitivity analysis. We validate our approach by fabricating baseline panels and a facade with a wide range of curvature profiles, providing a detailed numerical analysis on simulation and fabrication, demonstrating significant advantages in cost and flexibilitySource: ACM TRANSACTIONS ON GRAPHICS, vol. 43 (issue 6), pp. 1-16
DOI: 10.1145/3687906
Metrics:
Rist F., Wang Z., Pellis D., Palma M., Liu D., Grinspun E., Michels D. L.
Architectural surface panelling often requires fabricating molds for panels, a process that can be cost-inefficient and material-wasteful when using traditional methods such as CNC milling. In this paper, we introduce a novel solution to generating molds for efficiently fabricating architectural panels. At the core of our method is a machine that utilizes a deflatable membrane as a flexible mold. By adjusting the deflation level and boundary element positions, the membrane can be reconfigured into various shapes, allowing for mass customization with significantly lower overhead costs. We devise an efficient algorithm that works in sync with our flexible mold machine that optimizes the placement of customizable boundary element positions, ensuring the fabricated panel matches the geometry of a given input shape: (1) Using a quadratic Weingarten surface arising from a natural assumption on the membrane's stress, we can approximate the initial placement of the boundary element from the input shape's geometry; (2) we solve the inverse problem with a simulator-in-the-loop optimizer by searching for the optimal placement of boundary curves with sensitivity analysis. We validate our approach by fabricating baseline panels and a facade with a wide range of curvature profiles, providing a detailed numerical analysis on simulation and fabrication, demonstrating significant advantages in cost and flexibilitySource: ACM TRANSACTIONS ON GRAPHICS, vol. 43 (issue 6), pp. 1-16
DOI: 10.1145/3687906
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dl.acm.org | CNR IRIS | ACM Transactions on Graphics | CNR IRIS
2024
Conference article
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Kit-of-parts Equilateral Constant Normal Curvature (ECNC) gridshell
Man H., Wan Z., Pellis D., Schling E.
This paper investigates the design and construction of doubly-curved equilateral constant normal curvature (ECNC) gridshell structures with straight, flat, and repetitive building components. Using kit-of-parts with identical shape and size, enables standardized prefabrication. These components are connected to form a collapsible scissor-hinge grid, which can be deployed onsite to create freeform gridshells. The structure is then converted into a stable triangulated grid using diagonal elements. The angles of connections between the kit-of-parts can be adjusted to accommodate different constant normal curvature values and facilitate positive and negatively curved design shapes. This approach allows for the reuse of the same repetitive components in multiple designs and life cycles, promoting a sustainable, circular building system for energy conservation and carbon reduction.DOI: 10.1007/978-3-031-68275-9_11
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Man H., Wan Z., Pellis D., Schling E.
This paper investigates the design and construction of doubly-curved equilateral constant normal curvature (ECNC) gridshell structures with straight, flat, and repetitive building components. Using kit-of-parts with identical shape and size, enables standardized prefabrication. These components are connected to form a collapsible scissor-hinge grid, which can be deployed onsite to create freeform gridshells. The structure is then converted into a stable triangulated grid using diagonal elements. The angles of connections between the kit-of-parts can be adjusted to accommodate different constant normal curvature values and facilitate positive and negatively curved design shapes. This approach allows for the reuse of the same repetitive components in multiple designs and life cycles, promoting a sustainable, circular building system for energy conservation and carbon reduction.DOI: 10.1007/978-3-031-68275-9_11
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doi.org | CNR IRIS | CNR IRIS | link.springer.com
2024
Journal article
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Alignable lamella gridshells
Pellis D.
Alignable lamella gridshells are 3D grid structures capable of collapsing into a planar strip. This feature significantly simplifies on-site assembly and also ensures compactness for efficient transport and storage. However, designing these structures still remains a challenge. This paper tackles the inverse design problem of alignable lamella gridshells leveraging concepts from differential geometry and Cartan's theory of moving frames. The study unveils that geodesic alignable gridshells, where lamellae are disposed tangentially to the surface, are limited to forming shapes isometric to surfaces of revolution. Furthermore, it demonstrates that alignable gridshells with lamellae arranged orthogonally to a surface can be realized only on a specific class of surfaces that meet a particular curvature condition along their principal curvature lines. Finally, drawing on these theoretical findings, this work introduces novel computational tools tailored for the design of these structures.Source: ACM TRANSACTIONS ON GRAPHICS, vol. 43 (issue 6), pp. 1-21
DOI: 10.1145/3687898
Project(s): SUN
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Pellis D.
Alignable lamella gridshells are 3D grid structures capable of collapsing into a planar strip. This feature significantly simplifies on-site assembly and also ensures compactness for efficient transport and storage. However, designing these structures still remains a challenge. This paper tackles the inverse design problem of alignable lamella gridshells leveraging concepts from differential geometry and Cartan's theory of moving frames. The study unveils that geodesic alignable gridshells, where lamellae are disposed tangentially to the surface, are limited to forming shapes isometric to surfaces of revolution. Furthermore, it demonstrates that alignable gridshells with lamellae arranged orthogonally to a surface can be realized only on a specific class of surfaces that meet a particular curvature condition along their principal curvature lines. Finally, drawing on these theoretical findings, this work introduces novel computational tools tailored for the design of these structures.Source: ACM TRANSACTIONS ON GRAPHICS, vol. 43 (issue 6), pp. 1-21
DOI: 10.1145/3687898
Project(s): SUN
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dl.acm.org | ACM Transactions on Graphics | CNR IRIS | CNR IRIS
2024
Journal article
Open Access
The geometry of principal symmetric structures
Pellis D., Pottmann H.
We introduce a novel class of quadrilateral gridshell structures in axial force equilibrium where rods are aligned symmetrically with the principal stress directions of a limit membrane shell. These structures exhibit a distinctive property where the axial forces in the four connected rods at each node are nearly equal. This characteristic enables a more uniform distribution of forces within the structure, particularly in cases where stresses exhibit significant anisotropy. In contrast, conventional gridshells often result in numerous rods remaining nearly unloaded in such scenarios. We begin by studying the equilibrium of rod networks that are symmetric to principal stress directions. Next, we explore the geometric properties of these networks in relation to the isotropic geometry of their Airy stress surface. We introduce then a computational pipeline for designing principal symmetric structures through quadrilateral remeshing of a surface in membrane equilibrium and subsequent optimization. Finally, we present some of the achieved results.Source: STRUCTURES, vol. 60
DOI: 10.1016/j.istruc.2024.105972
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Pellis D., Pottmann H.
We introduce a novel class of quadrilateral gridshell structures in axial force equilibrium where rods are aligned symmetrically with the principal stress directions of a limit membrane shell. These structures exhibit a distinctive property where the axial forces in the four connected rods at each node are nearly equal. This characteristic enables a more uniform distribution of forces within the structure, particularly in cases where stresses exhibit significant anisotropy. In contrast, conventional gridshells often result in numerous rods remaining nearly unloaded in such scenarios. We begin by studying the equilibrium of rod networks that are symmetric to principal stress directions. Next, we explore the geometric properties of these networks in relation to the isotropic geometry of their Airy stress surface. We introduce then a computational pipeline for designing principal symmetric structures through quadrilateral remeshing of a surface in membrane equilibrium and subsequent optimization. Finally, we present some of the achieved results.Source: STRUCTURES, vol. 60
DOI: 10.1016/j.istruc.2024.105972
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CNR IRIS | www.sciencedirect.com | Structures | IRIS Cnr | CNR IRIS | CNR IRIS | IRIS Cnr