arXiv subjects

Kentaro Hayakawa

Publications and source records attributed to Kentaro Hayakawa.

5 recordsLinked to original sources

arXiv2026

Michell-Prager type truss structures constructed from integrable discrete power function and discrete logarithmic function

The Michell-Prager type truss structures are constructed from the integrable discrete power and logarithmic functions. It is demonstrated that specific sublattices, subject to suitable boundary conditions, yield approximate Michell trusses, which are theoretically optimal structures achieving force equilibrium with material economy. The result of shape optimization minimizing the Michell functional is provided for numerical evidence of their optimality.

math.DG↗

arXiv2025

Laguerre geometry for optimization of gridshell with specified force distribution

For the design of gridshells consisting of continuous beams in two directions and quadrilateral faces to cover a large space of architecture, it is important to arrange each row and column of beams along a planar curve and ensure planar faces for constructability and cross-sectional compatibility at joints. It is also important that the gridshell is in equilibrium mainly with axial forces against the design loads; i.e., bending deformation should be avoided. In this study, we first find a continuous shell surface where the principal curvature lines coincide with the principal directions of membrane forces. For this purpose, we utilize the L-isothermic surface, which is a kind of membrane O-surface. Specifically, the generalized Dupin cyclide is used as the reference surface, which has an explicit form of membrane forces with a single arbitrary parameter against normal loads. Various force distributions are obtained as the parameter is adjusted without changing the surface shape. Next, the shell is discretized into a gridshell, and target axial forces are obtained from the section length of the covering region of each node. The axial forces are adjusted by optimizing the cross-sectional radii of the beams with pipe sections to realize the specified target force distribution. Since the Laguerre transformation preserves geometric and static properties of the L-isothermic surface, the force can be adjusted by a simple process without re-optimization to obtain an approximate optimal solution of the gridshell after transformation. The ratio of out-of-plane shear force to the normal load at the node is also evaluated to investigate the effect of deformation on the force distribution.

math.OC↗

arXiv2025

Infinitely refinable generalization of quad-mesh rigid origami: from linear and equimodular couplings

A quad-mesh rigid origami is a continuously deformable panel-hinge structure where planar, rigid, zero-thickness quadrilateral panels are connected by rotational hinges in the combinatorics of a grid. This article provides a comprehensive exposition of two new families of infinitely refinable quad-mesh rigid origami, generated from linear and equimodular couplings. These constructions expand the current landscape beyond well-known variations such as the Miura-ori, V-hedron (discrete Voss surface or eggbox pattern), anti-V-hedron (flat-foldable pattern), and T-hedron (trapezoidal pattern). We conjecture that as the mesh is refined to infinity, these quad-mesh rigid origami converges to special ruled surfaces in the limit, supported by multiple lines of evidence.

math.MG↗

arXiv2024

Real and complexified configuration spaces for spherical 4-bar linkages

This note is a complete library of symbolic parametrized expressions for both real and complexified configuration spaces of a spherical 4-bar linkage. Building upon the previous work from Izmestiev, (2016, Section 2), this library expands on the expressions by incorporating all four folding angles across all possible linkage length choices, along with the polynomial relation between diagonals (spherical arcs). Furthermore, a complete MATLAB app script is included, enabling visualization and parametrization. The derivations are presented in a detailed manner, ensuring accessibility for researchers across diverse disciplines.

cs.GR↗

arXiv2024

Non-parametric structural shape optimization of piecewise developable surfaces using discrete differential geometry

We propose a two-level structural optimization method for obtaining an approximate optimal shape of piecewise developable surface without specifying internal boundaries between surface patches. The condition for developability of a polyhedral surface onto a plane is formulated using the area of discrete Gauss map formed by unit normal vectors at the faces adjacent to each vertex. The objective function of the lower-level optimization problem is the sum of square errors for developability at all interior vertices. The contribution of large error to the objective function is underestimated by filtering with hyperbolic tangent function so that the internal boundary between the surface patches can naturally emerge as a result of optimization. Vertices are located non-periodically to generate the internal boundaries in various unspecified directions. Simulated annealing is used for the upper-level optimization problem for maximizing stiffness evaluated by the compliance under the specified vertical loads. The design variables are the heights of the specified points. It is shown in the numerical examples that the compliance values of the surfaces with a square and a rectangular plan are successfully reduced by the proposed method while keeping the developability of each surface patch. Thus, a new class of structural shape optimization problem of shell surfaces is proposed by limiting the feasible surface to piecewise developable surfaces which have desirable geometrical characteristics in view of fabrication and construction.

math.OC↗