Abstract : This mini-symposium is based on the JSIAM activity group “Geometric Shape Generation”, and aims at exhibiting the latest research in this activity group and relevant researchers, especially putting its focus on the structures, mechanics and analysis. We discuss origami structures and applications, discrete surfaces and shell structures, geometric modeling of specific surfaces and vibration analysis.
Organizer(s) : Miyuki Koiso, Makoto Ohsaki, Jun Mitani, Kento Okuda
Abstract : We introduce a geometric modeling method of the umbrella by defining the rib curves as the intersection of two bilinear patches. Furthermore, we investigate various differential geometric properties of the umbrella surface and introduce a method to unfold it onto a plane that can be used to fabricate a wooden template for cutting canopy fabrics.
[04221] Geometrical and structural design of pseudo-geodesic gridshells
Format : Talk at Waseda University
Author(s) :
Romain Mesnil (Ecole des Ponts ParisTech)
Olivier Baverel (Ecole des Ponts ParisTech)
Abstract : Gridshells are efficient structures built using a network of straight members that are deformed into doubly curved shapes. In this presentation, we propose to construct gridshells with pseudo-geodesic curves, which are characterized by the equality between torsion and geodesic torsion. We show that existence of parametrization by pseudo-geodesic network is impossible when integral of Gaussian curvature is superior to an upper bound. Structural performance and fabrication are discussed with the case-study of an architectural pavilion.
[02774] Preliminary research on shape searching method for curved crease origami using bending deformation
Format : Talk at Waseda University
Author(s) :
Tianhao Zhang (The University of Tokyo)
Ken'ichi Kawaguchi (The University of Tokyo)
Abstract : Curved crease origami is focused on by the researchers and designers in the field of building structure owing to the foldability and mechanical properties. In this paper, a shape searching method is proposed based on an optimization approach. This approach can form a shape close to the target surface defined by the designers. This research aims to search the shape concerning bending deformation to explores the application of curved origami to architectural structures.
[02924] Shape design of free-form shells with specified projected membrane forces
Format : Talk at Waseda University
Author(s) :
Makoto Ohsaki (Kyoto University)
Yusuke Sakai (Sony Computer Science Laboratories)
Taku Nakajima (Kyoto University)
Riree Takeoka (Takenaka Corporation)
Abstract : A shape design method is proposed for membrane free-form shells modeled as a graph surface. The distribution of membrane forces projected to the plane is specified to satisfy horizontal equilibrium as a function of shear stress. The shape is determined as a solution to the vertical equilibrium equations discretized by the finite difference method. The shape is iteratively corrected to achieve the specified projected stress distribution considering the material property.
[05391] Singularity of Arc- and Spiral-shaped Miura-ori as Rigid-Flat-Foldable Origami Pattern
Format : Talk at Waseda University
Author(s) :
Hiroyuki Tagawa (Mukogawa Women's University)
Abstract : Arc- and spiral-shaped Miura-ori is rigid flat-folding Origami pattern and one variational type of Miura-ori. Geometric folding lines of the spiral-shaped Miura-ori are obtained by arraying quadrilaterals with identical internal angles in the same column. The arc-shaped Miura-ori is obtained by setting equal edge lengths of the quadrilaterals in the radial direction. This study investigates the singularity of an arc- and spiral-shaped Miura-ori among the generalized Miura-ori.
[03876] A first-order method for large-scale eigenvalue optimization problems in topology optimization
Format : Talk at Waseda University
Author(s) :
Akatsuki Nishioka (The University of Tokyo)
Mitsuru Toyoda (Tokyo Metropolitan University)
Mirai Tanaka (The Institute of Statistical Mathematics)
Yoshihiro Kanno (The University of Tokyo)
Abstract : Eigenvalue optimization problems arise in many situations in topology optimization when considering robustness, vibration and buckling. As topology optimization problems are often very large-scale, the semidefinite programming approach is sometimes too computationally costly. We propose an efficient optimization algorithm based on the smoothing method for large-scale eigenvalue problems. The proposed method only uses the first-order derivative of the objective function, and thus has low computational cost per iteration. It also has convergence guarantee.
[03320] Recent advances on tension-compression mixed shell form-finding
Format : Talk at Waseda University
Author(s) :
Masaaki Miki (The University of Tokyo)
Abstract : In architecture, thin surface structures that can withstand gravity with no bending action are called shells. Shells have special geometries that enable them to stream gravitational force toward the ground along their forms with in-plane stresses only; the process of finding these special forms is called form-finding. Researchers have pointed out that in shell form-finding, the problem can be formulated using two surfaces: the shell itself and another surface called Airy's stress function. In 2022, a novel NURBS-based computational approach that can properly handle mixed tension–compression stress states was presented by Miki et al. (note that similar methods were first introduced in Ciang Yu-Chou). Because the solutions are repretented by NURBS, the partial derviatvies can be computed at any point. This enables many kind of computations. In this talk, we present what kind of compuation turns possible based on the solutions obatined by the proposed method.
[02771] Developable surfaces with curved folds
Format : Talk at Waseda University
Author(s) :
Miyuki Koiso (Kyushu University)
Abstract : Developable surfaces are surfaces which can be unfolded into the plane preserving the length of all curves on the surface. Since developable surfaces with curved folds are constructed by bending a flat sheet, they have many applications in manufacturing objects. In this talk, we give conditions of piecewise-smooth surfaces for being developable in terms of curvatures. We also discuss variational problems for developable surfaces, geometric characterizations of their optimal solutions, and their applications to architecture.
[02773] Variational principle for generating discrete surfaces with piecewise constant Gaussian curvatures
Format : Talk at Waseda University
Author(s) :
Kazuki Hayashi (Kyoto University)
Yoshiki Jikumaru (Kyushu University)
Makoto Ohsaki (Kyoto University)
Takashi Kagaya (Muroran Institute of Technology)
Yohei Yokosuka (Kagoshima University)
Abstract : We derive a method to generate triangular meshes with piecewise constant Gaussian curvatures, in which the connection between the patches is G0 continuous. Gaussian curvature flows at interior vertices and those at the internal boundary are derived from the variational principle of the energy functional. The proposed method can generate the shape of the whole surface integrally using the derived flows.
[02776] Geometric shape generation of hanging membranes
Format : Talk at Waseda University
Author(s) :
Yoshiki Jikumaru (Toyo University)
Yohei Yokosuka (Kagoshima University)
Abstract : In this talk, we present a differential geometric formulation of hanging membranes based on the equilibrium equations in the shell membrane theory and the variational principle.
We also propose a geometric shape generation of hanging membranes.
[05556] Proposal for a temporary structure with a mechanism capable of curved folding
Format : Talk at Waseda University
Author(s) :
Yohei Yokosuka (Kagoshima University)
Miyuki Koiso (Kyushu University)
Kento Okuda (National Institute of Technology, Sasebo College)
Toshio Honma (Kagoshima University)
Jun Mitani (University of Tsukuba)
Abstract : Temporary housing requires the rapid supply of numerous houses after a disaster. Therefore, it is useful to use architectural structures that utilizes curved folding, which enables the immediate development of a flat board into a three-dimensional structure.
In this presentation, a pillow type box that maximizes the inner volume is adopted for the design shape, we demonstrate numerical analysis of rigid folding and scaled models of temporary structures with a mechanism capable of curved folding.
[05623] Topology of vibrating shapes
Format : Talk at Waseda University
Author(s) :
Konrad Polthier (FU Berlin)
Jakub Rondomanski (FU Berlin)
Carlos Andres Palma (HU Berlin)
José D. Cojal González (HU Berlin)
Jürgen P. Rabe (HU Berlin)
Abstract : Vibrations of a parameter dependent set of physical shapes exhibit characterizing topological properties.
We will discuss the topology of such vibrations based on a carefully selected metric and its holonomy.
Overall, the choice of the metric embarks beyond the classical Berry connection. Applications aim
at a better understanding of the topology of vibrating crystals.
