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2023
Journal article
Closed Access
Deployable strip structures
Liu D., Pellis D., Chiang Y-C., 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 42 (2023): 1–16. doi:10.1145/3592393
DOI: 10.1145/3592393
Metrics:
Liu D., Pellis D., Chiang Y-C., 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 42 (2023): 1–16. doi:10.1145/3592393
DOI: 10.1145/3592393
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dl.acm.org 
| ACM Transactions on Graphics | CNR ExploRA
2023
Conference article
Closed Access
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: IWSS 2023 - Italian Workshop on Shell and Spatial Structures, pp. 359–368, Turin, Italy, 26-28/06/2023
DOI: 10.1007/978-3-031-44328-2_37
Metrics:
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: IWSS 2023 - Italian Workshop on Shell and Spatial Structures, pp. 359–368, Turin, Italy, 26-28/06/2023
DOI: 10.1007/978-3-031-44328-2_37
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link.springer.com | CNR ExploRA
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) 42 (2023). doi:10.1145/3618366
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) 42 (2023). doi:10.1145/3618366
DOI: 10.1145/3618366
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ISTI Repository 
| dl.acm.org | CNR ExploRA