Application of Interactive Deformation to Assembled Mesh Models for CAE Analysis

Author(s):  
Hiroshi Masuda ◽  
Kenta Ogawa

Mesh deformation, which is sometimes referred to as mesh morphing in CAE, is useful for providing various shapes of meshes for CAE tools. This paper proposes a new framework for interactively and consistently deforming assembly models of sheet structure for mechanical parts. This framework is based on a surface-based deformation, which calculates the vertex positions so that the mean curvature normal is preserved at each vertex in a least squares sense. While existing surface-based deformation techniques cannot simultaneously deform assembly mesh models, our method allows us to smoothly deform disconnected meshes by propagating the rotations and translations through disconnected vertices. In addition, we extend our deformation technique to handle non-manifold conditions, because shell structure models may include non-manifold edges. We have applied our method to assembly mesh models of automobile parts. Our experimental results have shown that our method requires almost the same pre-processing time as existing methods and can deform practical assembly models interactively.


2020 ◽  
Vol 18 (1) ◽  
pp. 1518-1530
Author(s):  
Xuesen Qi ◽  
Ximin Liu

Abstract In this paper, we discuss the monotonicity of the first nonzero eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow (MCF). By imposing conditions associated with the mean curvature of the initial hypersurface and the coefficient function of the forcing term of a forced MCF, and some special pinching conditions on the second fundamental form of the initial hypersurface, we prove that the first nonzero closed eigenvalues of the Laplace operator and the p-Laplace operator are monotonic under the forced MCF, respectively, which partially generalize Mao and Zhao’s work. Moreover, we give an example to specify applications of conclusions obtained above.





Author(s):  
M. S. Longuet-Higgins

Imagine a nearly horizontal, statistically uniform, random surface ζ(x, y), Gaussian in the sense that the second derivatives , , have a normal joint distribution. The problem considered is the statistical distribution of the quantitywhere J and Ω denote the mean curvature and total curvature of the surface, respectively, and ν is a constant parameter.





2014 ◽  
Vol 70 (6) ◽  
pp. o717-o718 ◽  
Author(s):  
Channappa N. Kavitha ◽  
Manpreet Kaur ◽  
Jerry P. Jasinski ◽  
Hemmige S. Yathirajan

In the title salt, C6H13N2O+·C6H2N3O7−(systematic name: 4-acetylpiperazin-1-ium 2,4,6-trinitrophenolate), the piperazin-1-ium ring has a slightly distorted chair conformation. In the picrate anion, the mean planes of the twoo-NO2andp-NO2groups are twisted with respect to the benzene ring by 15.0 (2), 68.9 (4) and 4.4 (3)°, respectively. In the crystal, N—H...O hydrogen bonds are observed, linking the ions into an infinite chain along [010]. In addition, weak cation–anion C—H...O intermolecular interactions and a weak π–π stacking interaction between the benzene rings of the anions, with an inter-centroid distance of 3.771 (8) Å, help to stabilize the crystal packing, giving an overall sheet structure lying parallel to (100). Disorder was modelled for one of the O atoms in one of theo-NO2groups over two sites with an occupancy ratio of 0.57 (6):0.43 (6).



Author(s):  
Hironori Kumura

Let UB(p0; ρ1) × f MV be a cylindrically bounded domain in a warped product manifold := MB × fMV and let M be an isometrically immersed submanifold in . The purpose of this paper is to provide explicit radii of the geodesic balls of M which first exit from UB(p0; ρ1) × fMV for the case in which the mean curvature of M is sufficiently small and the lower bound of the Ricci curvature of M does not diverge to –∞ too rapidly at infinity.



2017 ◽  
Vol 320 ◽  
pp. 674-729 ◽  
Author(s):  
Juan Dávila ◽  
Manuel del Pino ◽  
Xuan Hien Nguyen


2018 ◽  
Vol 2018 (743) ◽  
pp. 229-244 ◽  
Author(s):  
Jingyi Chen ◽  
John Man Shun Ma

Abstract Let F_{n} : (Σ, h_{n} ) \to \mathbb{C}^{2} be a sequence of conformally immersed Lagrangian self-shrinkers with a uniform area upper bound to the mean curvature flow, and suppose that the sequence of metrics \{ h_{n} \} converges smoothly to a Riemannian metric h. We show that a subsequence of \{ F_{n} \} converges smoothly to a branched conformally immersed Lagrangian self-shrinker F_{\infty} : (Σ, h) \to \mathbb{C}^{2} . When the area bound is less than 16π, the limit {F_{\infty}} is an embedded torus. When the genus of Σ is one, we can drop the assumption on convergence h_{n} \to h. When the genus of Σ is zero, we show that there is no branched immersion of Σ as a Lagrangian self-shrinker, generalizing the rigidity result of [21] in dimension two by allowing branch points.



2018 ◽  
Vol 62 (9) ◽  
pp. 1793-1798 ◽  
Author(s):  
Zhuhong Zhang


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