Optimal design of watt six-bar transmission mechanism for morphing trailing edge

The morphing trailing edge could realize a continuous smooth deformation compared with conventional trailing edge, which effectively improves the aerodynamic performance. In this paper, a multi-step optimization design of watt six-bar transmission mechanism for morphing trailing edge is proposed. In the first optimization stage, the most effective aerodynamic shape and bar position in the middle of the morphing trailing edge is determined. In the second optimization stage, a watt six link transmission mechanism is proposed by using genetic algorithm to match the optimal shape from the first optimization stage. Result shows that the optimal design could achieve the determined aerodynamic shape in the first optimization stage perfectly.

Log smooth deformation theory via Gerstenhaber algebras

We construct a $$k\left[ \!\left[ Q\right] \!\right] $$ k Q -linear predifferential graded Lie algebra $$L^{\bullet }_{X_0/S_0}$$ L X 0 / S 0 ∙ associated to a log smooth and saturated morphism $$f_0: X_0 \rightarrow S_0$$ f 0 : X 0 → S 0 and prove that it controls the log smooth deformation functor. This provides a geometric interpretation of a construction in Chan et al. (Geometry of the Maurer-Cartan equation near degenerate Calabi-Yau varieties, 2019. arXiv:1902.11174) whereof $$L^{\bullet }_{X_0/S_0}$$ L X 0 / S 0 ∙ is a purely algebraic version. Our proof crucially relies on studying deformations of the Gerstenhaber algebra of polyvector fields; this method is closely related to recent developments in mirror symmetry.

Semi-continuity of the Diederich–Fornaess and Steinness indices

In this paper, we prove the semi-continuity theorem of Diederich–Fornaess index and Steinness index under a smooth deformation of pseudoconvex domains in Stein manifolds.

Regularity of minimal surfaces with lower-dimensional obstacles

We study the Plateau problem with a lower-dimensional obstacle in {\mathbb{R}^{n}}. Intuitively, in {\mathbb{R}^{3}} this corresponds to a soap film (spanning a given contour) that is pushed from below by a “vertical” 2D half-space (or some smooth deformation of it). We establish almost optimal {C^{1,\frac{1}{2}-}} estimates for the solutions near points on the free boundary of the contact set, in any dimension {n\geq 2}. The {C^{1,\frac{1}{2}-}} estimates follow from an ε-regularity result for minimal surfaces with thin obstacles in the spirit of the De Giorgi’s improvement of flatness. To prove it, we follow Savin’s small perturbations method. A nontrivial difficulty in using Savin’s approach for minimal surfaces with thin obstacles is that near a typical contact point the solution consists of two smooth surfaces that intersect transversally, and hence it is not very flat at small scales. Via a new “dichotomy approach” based on barrier arguments we are able to overcome this difficulty and prove the desired result.

A soft Oka principle for proper holomorphic embeddings of open Riemann surfaces into (ℂ*)2

Let X be an open Riemann surface. We prove an Oka property on the approximation and interpolation of continuous maps X \to (\mathbb{C}^{*})^{2} by proper holomorphic embeddings, provided that we permit a smooth deformation of the complex structure on X outside a certain set. This generalises and strengthens a recent result of Alarcón and López. We also give a Forstnerič–Wold theorem for proper holomorphic embeddings (with respect to the given complex structure) of certain open Riemann surfaces into {(\mathbb{C}^{*})^{2}} .

EXPERIMENTAL INVESTIGATION OF DEFLECTED MODE OF THE RIENFORCED CONCRETE BEAMS WITH ORGANIZED CRACKS UNDER LONG-TERM LOADING

Introduction. Evaluation of the influence level of the pre-organized cracks in tensile zone of the reinforced concrete beams on their crack resistance, deformability under long-term loading is investigated in the article.Materials and methods. Concrete for specimen was produced in laboratory and factory on portland cement of the 500-grade at W/C=0,71; concrete composition 1:1,9:4 (by weight); strength of cube at 28th days – 13,85 MPa; strength of prism with dimensions 10/10*40 cm – 11,48 MPa; span calculation – 78 cm; steel rebar grade – A400 with diameter of 10 mm. Organized crack was formed by installing plate with thickness of 0,5 mm and height of 30 mm on the rebar in the zone of maximum moments.Results. The experiments confirmed the hypothesis about the beams rigidity with pre-organized cracks in comparison with stochastic cracks under the influence of long-term loading. As a result, the beams with pre-organized cracks provide the smaller deflection after long-term period than the beams without organized cracks. Thus, the proposed method of the deflections calculation of the reinforced concrete beams with pre-organized cracks under the long-term loading helps to reduce deflection to 33%.Discussion and conclusion. The findings of this study suggest that the presence of pre-organized cracks reduces the beams deflections in comparison with the specimens of section, and such method actually regulates the stress-strain state of reinforced concrete structures and leads to the smooth deformation at all stages under the influence of long-term loading.

Unobstructed symplectic packing for tori and hyper-Kähler manifolds

Let [Formula: see text] be a closed symplectic manifold of volume [Formula: see text]. We say that the symplectic packings of [Formula: see text] by balls are unobstructed if any collection of disjoint symplectic balls (of possibly different radii) of total volume less than [Formula: see text] admits a symplectic embedding to [Formula: see text]. In 1994, McDuff and Polterovich proved that symplectic packings of Kähler manifolds by balls can be characterized in terms of the Kähler cones of their blow-ups. When [Formula: see text] is a Kähler manifold which is not a union of its proper subvarieties (such a manifold is called Campana simple), these Kähler cones can be described explicitly using the Demailly and Paun structure theorem. We prove that for any Campana simple Kähler manifold, as well as for any manifold which is a limit of Campana simple manifolds in a smooth deformation, the symplectic packings by balls are unobstructed. This is used to show that the symplectic packings by balls of all even-dimensional tori equipped with Kähler symplectic forms and of all hyper-Kähler manifolds of maximal holonomy are unobstructed. This generalizes a previous result by Latschev–McDuff–Schlenk. We also consider symplectic packings by other shapes and show, using Ratner’s orbit closure theorem, that any even-dimensional torus equipped with a Kähler form whose cohomology class is not proportional to a rational one admits a full symplectic packing by any number of equal polydisks (and, in particular, by any number of equal cubes).

STRUCTURAL BEHAVIOR OF R/C SHELL CONSIDERING THE POSITION OF EDGE BEAM

Reinforced Concrete (R/C) shell has been constructed to cover large public spaces and large industrial buildings. RC shell is originally a continuous structure and shows the large load bearing capacity. To apply these structures to such purpose, the structure is cut at any particular portion and loses their continuum properties. Therefore, edge beams must be placed to avoid the stress concentration and a local failure. In this paper, R/C cylindrical shell with edge beam on meridional free edges was analyzed by use of FEM. RC shell had 960 x 960 mm plan and the thickness was 10 mm. The radius and the depth of the shell were 688 mm and 190 mm, respectively. As the edge beam, three kinds of rectangular beams, which had 2 cm width and 4 cm depth, were arranged. One was connected to the shell at the gravity center of the beam and the others were connected at the bottom or the top of the beam. From the numerical analyses, the deformation and the stress distribution of the shell mentioned above were analyzed precisely. The shell connected with the gravity center of the beam showed the smooth deformation and the stress distributions.

Total Variation Filtered Demons for Improved Registration of Sliding Organs

We present a new approach to regularize the displacement field of the accelerated Demons registration algorithm. The accelerated Demons algorithm uses Gaussian smoothing to penalize oscillatory motion in the displacement fields during registration. This regularization approach is often applied and ensures a smooth deformation field. However, when registering images with discontinuities in their motion field such as from organs sliding along the chest wall, the assumption of a smooth deformation field is invalid. In this work, we propose using total variation based smoothing that is known to better retain the discontinuities in the deformation field. The proposed approach is a first step towards automatically recovering breathing induced organ motion with good accuracy.

Physical Model for Interactive Deformation of 3D Plant

Modeling the deformation of 3D plant is a challenge in computer graphics. This paper presents a simulation method for physically simulating interactive deformation of 3D plant models. This method creates a tetrahedral mesh from the initial triangular plant model, the tetrahedral mesh is then used for dynamic response calculation of collision or interaction, the original triangular mesh is deformed along with the tetrahedral mesh. A capsule-based method and a spatial hashing based method are used for efficient and accurate collision detection. Smooth deformation effects and real-time simulation on 3D plant models demonstrate the effectiveness of our method. The main contribution of this paper is the proposed method can handle the geometric complexity of various plants by a simple model.