Concave Angles Research Articles

A Special Corner Element for Solving Heat Conduction Problems

A hybrid Trefftz finite element method is proposed for solving heat conduction problems in a domain with concave or convex angles. In this method, two temperature fields are independently assumed, one of which is the intra-element field defined inside the element and the other is the frame field defined on the boundary. The corner effects embed in the truncated complete solutions which are used to construct the internal interpolation function for approximating the intra-element field. It is able to accurately analyze the problems with particular corners. The key characteristics lie in the finite element formulation which is evaluated along the element boundary. Compared with the conventional FEM, the corner element does not lose any accuracy by using a small number of elements. Numerical examples demonstrate that the proposed method exhibits low sensitivity to mesh distortion. Compared with ABAQUS, the proposed method also exhibits higher accuracy and a faster convergence rate.

Low-velocity impact response of sandwich plates with corrugation star-shaped honeycomb hybrid core

Compared with traditional lightweight corrugation and honeycomb cores, the novel cellular structure exhibiting a negative Poisson's ratio possesses distinctive mechanical deformation features, making it suitable for modeling lightweight sandwich structures. Therefore, the concept of combining the auxetic honeycomb core with folded corrugations is proposed to construct a new type of corrugation star-shaped honeycomb (SSH) hybrid core for studying the dynamic behavior of sandwich panels subjected to low-velocity impact. Integrate Hertz elasticity theory and first-order shear deformation theory (FSDT) to develop an equivalent analytical model, and derive the equations of motion through Hamilton principle. To model contact force interactions during dynamic processes, a spring-mass model is utilized. Analytical solutions are derived for predicting transverse displacement with Duhamel's principle and Navier's method. Numerical simulations are conducted using the Abaqus commercial software, and the validity of the results is confirmed by comparing them with findings in the existing literature. Based on this, effective strategies for enhancing the sandwich panel's resistance to low-velocity impacts are proposed by examining the influence of different side length ratios, thickness ratios, and cell concave angles. In comparison to the corrugation re-entrant hexagonal honeycomb hybrid core sandwich panel structure, the corrugation SSH hybrid core sandwich panel structure reduces transverse displacement by 33.6 % at the same impact velocity.

Application of a novel machine learning model for the prediction and optimization of anti-blast performance of sandwich honeycomb blast walls

Sandwich honeycomb blast wall with the superior energy absorption characteristics could be applied to anti-blast protection of offshore oil and gas platform. Recently, machine learning technique, as an alternative to traditional Finite Element Analysis (FEA), is becoming a powerful tool in understanding structural performance. The aim of this study is to propose a novel data-driven model for fast predictions of structure response of sandwich blast wall under explosion, including the maximum deformation δmax, the maximum internal energy Emax and the energy absorption ratio RE. FEA was firstly conducted to generate sample data for the proposed model by using LS-DYNA software. An improved artificial electric field algorithm (IAEFA) was combined with artificial neural network (ANN) to develop an IAEFA-ANN model. In case studies, the prediction results of IAEFA-ANN approximate the results of FEA well, and comparison results of 9 different ANN models demonstrate that IAEFA-ANN model has the best performance. Then, the effects of explosion parameters (including explosive charge mass Me, stand-off distance d and concave angles θ) on structural response prediction results were investigated by using the proposed model. Moreover, the IAEFA-ANN model was applied to conducting optimal design of the blast wall to obtain optimum anti-blast performance.

Study on quasi-static axial compression performances and energy absorption of four-star double arrow honeycomb

A four-star double arrow honeycomb (FS-DAH) is proposed. Firstly, representative cell of FS-DAH is chosen by adopting asymptotic homogenization method. Then, in-plane large deflection equations along X and Y compression directions are constructed by utilizing elliptic integral approach, elastic modulus, Poisson's ratio and platform stress of FS-DAH are derived.Subsequently, finite element model (FEM) of FS-DAH is constructed, and quasi-static axial compression simulation analysis is executed. To further verify the accuracy of theoretical predictions and FEM, samples with PLA material are manufactured by employing 3D printing technology, and quasi-static compression test is conducted. The results indicate that FS-DAH exhibit “zigzag” deformation mode along transverse direction and “wave” deformation mode along longitudinal direction under Y compression and “><” deformation mode appears under X compression, which are both consistent with simulation analysis. Moreover, there exist two platform regions and one platform zone along Y and X directions for stress–strain curves accordingly, the errors of simulation and theoretical results are within allowable range compared with test in terms of elastic modulus, platform stress and Poisson’s ratio. Eventually, FEMs with various concave angles and cell number are investigated, and its unit mass energy absorption decreases with the increment of concave angle and cell number.

On impact behaviors of 3D concave structures with negative Poisson’s ratio

Lattice structures with high mechanical properties and lightweight performance attracted increasing attention to the application of automotive, railway vehicle, and aerospace industries. This work developed a novel three-dimensional concave lattice structure using a hyper-elastic soft photopolymer via the digital light processing technique. The axial low-velocity impact behaviors of the proposed structures were investigated by a drop hammer machine and numerical simulation. The results showed that the novel 3D concave structures could present continuous auxetic behaviors with large negative Poisson’s ratios. The structural design parameters such as concave angle and thickness had significant effects on Poisson’s ratio and energy absorption. Specifically, the structures with concave angles from 10° to 20° and with thicknesses from 0.5 mm to 1.0 mm presented the higher negative Poisson’s ratio. The highest negative Poisson’s ratio of −0.86 was obtained. This work offered a new insight into designing novel meta-lattice structures with improved impact resistance.

Crashworthiness and optimization of novel concave thin-walled tubes

In this work, a new type of energy-absorbing thin-walled tubes with concave angles is proposed by a unique structural design method to improve the crashworthiness performance of the traditional hexagonal thin-walled tube (TH). These concave tube structures (CTSs) are named CTS1, CTS2, and CTS3 respectively, while CTS1 is developed by a common design method. The crushing behaviors of the CTS3 are investigated by quasi-static compression experiments and numerical simulations. The crashworthiness and energy dissipation mechanism of all the tubes are investigated, and the results demonstrate that the CTS3 exhibits superior energy absorption capability than the other proposed tubes and TH with the same mass. Then, the mean crush resistance of the CTSs is predicted by theoretical analysis, and the influences of slenderness rate, boundary condition, and loading rate on the crushing responses of CTS3 are performed by numerical analysis. Besides, the comparative analysis of performances of the CTS3 and the typical concave tubes (TCTs) is carried out, and the results indicate that the CTS3 has the best energy absorption capacity among these tubes. In addition, the optimal structure parameters of CTS3 are explored to enhance the capacity of energy absorption further.

Domain merging in LaBGeO5 single crystals

LaBGeO5 crystals emerged as the most promising candidates for UV laser sources based on a frequency conversion. Creation of periodical domain structures in LaBGeO5 for frequency conversion requires control of domains merging. Here, we studied domain structure evolution during domain merging with Cherenkov-type SHG microscopy. In low fields, two scenarios of domain merging were distinguished: “shape stability effect” and “jerky wall motion effect”. The formation of concave angles after merging led to appearance of fast domain walls. In high fields, the difference between slow and fast wall velocities diminished and merging did not result in domain wall acceleration.

On equidistant polytopes in the Euclidean space

An equidistant polytope is a special equidistant set in the space $\mathbb{R}^n$ all of whose boundary points have equal distances from two finite systems of points. Since one of the finite systems of the given points is required to be in the interior of the convex hull of the other one we can speak about inner and outer focal points of the equidistant polytope. It is of type $(q, p)$, where $q$ is the number of the outer focal points and $p$ is the number of the inner focal points. The equidistancy is the generalization of convexity because a convex polytope can be given as an equidistant polytope of type $(q, 1)$, where $q\geq n+1$. In the paper we present some general results about the basic properties of the equidistant polytopes: convex components, graph representations, connectedness, correspondence to the Voronoi decomposition of the space etc. Especially, we are interested in equidistant polytopes of dimension $2$ (equidistant polygons). Equidistant polygons of type $(3,2)$ will be characterized in terms of a constructive (ruler-and-compass) process to recognize them. In general they are pentagons with exactly two concave angles such that the vertices, where the concave angles appear at, are joined by an inner diagonal related to the adjacent sides of the polygon in a special way via the three reflection theorem for concurrent lines. The last section is devoted to some special arrangements of the focal points to get the concave quadrangles as equidistant polygons of type $(3,2)$.

Sedimentation of general shaped particles using a multigrid fictitious boundary method

In this paper, a direct numerical simulation technique, the Finite Element Fictitious Boundary Method (FBM), is used to simulate fluid–solid two-phase flows of different general shaped particles. The momentum interactions between solid and fluid phases are handled by using the FBM. The continuity and momentum equations are solved on a fixed Eulerian grid that is independent of flow features by using a discrete projection scheme inside a multi-grid finite element approach. A detailed description is presented for the geometric representation and modeling of two-dimensional particles of different general shapes, i.e., circular, elliptical, square, rectangular, triangular, and pentagonal shapes inside the fluid. We discussed the effects of particle shapes and the influences on the settling behavior of the particles. A comparison of the settling trajectories of the particles of the same mass but with different shapes is presented. Moreover, depending upon the particle’s shape, some interesting facts are discovered, which have a great influence on the particles’ trajectory and settling velocity. Some very important correlations between the drag force coefficient and particle’s Reynolds numbers with different density ratios of particles are obtained. Furthermore, we also studied the settling behavior of elliptical and rectangular particles with different axis ratios and a boomerang particle with different concave angles. The authors of the article agree to the retraction of the article effective AUGUST 20, 2021.

Pancharatnam-Berry phase algorithm to calculate the area of arbitrary polygons on the Poincaré sphere.

We introduce a very efficient noniterative algorithm to calculate the signed area of a spherical polygon with arbitrary shape on the Poincaré sphere. The method is based on the concept of the geometric Berry phase. It can handle diverse scenarios like convex and concave angles, multiply connected domains, overlapped vertices, sides and areas, self-intersecting polygons, holes, islands, cogeodesic vertices, random polygons, and vertices connected with long segments of great circles. A set of MATLAB routines of the algorithm is included. The main benefits of the algorithm are the ability to handle all manner of degenerate shapes, the shortness of the program code, and the running time.

Robust atlas generation via angle-based segmentation

We present a robust method to generate atlases with low isometric distortion and high packing efficiency. Given a surface that has been cut to disk topology, the algorithm contains four steps: (1) computing a bijective parameterization with low isometric distortion; (2) partitioning the input parameterized charts into a set of rectangle-like patches; (3) mapping rectangle-like patches onto rectangles that are packed into a rectangular domain; and (4) reducing parameterization distortion while maintaining high packing efficiency and bijection. Since there have been elegant and robust solutions for the first, third, and fourth steps, we focus on the second step. Central to the second step is a novel and robust segmentation technique. To improve the robustness of the segmentation, we first deform the parameterized charts to straighten their boundaries while aligning with the axes as much as possible, bounding the deformation distortion, and not introducing intersecting boundaries. Since rectangle-like patches are preferred for the third and fourth steps, we segment the deformed charts by decomposing concave interior angles into several interior angles close to π2 or π. To this end, we develop four types of operations: (i) bridging operation, (ii) extension operation, (iii) vertical line operation, and (iv) bisector operation. The pre-deformation process makes our heuristic segmentation very simple and effective. We demonstrate the efficacy of our method on various complex models. Compared to other state-of-the-art methods, our method achieves higher robustness.

Multi-sided Bézier surfaces over curved, multi-connected domains

A new multi-sided, control point based surface formulation is proposed, extending the principles of the Generalized Bézier patch published by Várady et al. (2016). The surface is constructed from side interpolants given in Bézier form. The boundary curves may have different degrees, and the cross-derivatives can ensure arbitrary G-continuity with adjacent patches. The representation is capable of handling boundary curves with high curvature variations and concave angles. The surfaces are C∞-continuous and may have holes in their interior.The most distinctive feature of the patch is that it is defined over a planar domain with curved boundaries that mimic the shape of the 3D boundary curves. Local parameters, derived from harmonic barycentric coordinates, are associated with each side of the domain. The control points are multiplied by Bernstein functions and additional rational terms that provide the same degree of freedom for shape design as their quadrilateral counterparts.The paper introduces the full construction of Curved Domain (CD) Bézier patches including domain generation, parameterization, basis functions, and methods for additional interior shape control. Specific problems related to CD surfaces are also discussed with many examples that demonstrate the peculiarity and usefulness of the scheme.

Behaviour Analysis of Reinforced Soil Retaining Wall According to Laboratory Scale Test

Reinforced soil retaining wall are ground structures that can be readily seen all around us. The development of reinforcements to these walls and their demand have increased rapidly. These walls are advantageous because they can be used not only in simple construction compared with reinforced concrete retaining walls but also when the height of the wall needs to be higher. However, unlike reinforced concrete retaining walls, in which the walls are integrated and resist the earth pressure on the back, the block-type reinforced earth retaining wall method secures its structural stability by frictional force between the buried land and reinforcements. A phenomenon in which a block is cracked or dropped owing to deformation has been frequently reported. In particular, this phenomenon is concentrated at the curved parts of a reinforced soil retaining wall and is mainly known as a stress concentration. However, to date, the design of reinforced soil retaining walls has been limited by the two-dimensional plane strain condition and has not considered the characteristics of the curved part. There is a lack of research on curved part. Therefore, this research determines the behavioural characteristics of curved-part reinforced soil retaining walls with regard to the shape (convex or concave) and angle (60°, 90°, 120°, and 150°). The displacement generated in the straight part and the curved part was analysed through an Laboratory Scale Test. The results showed that the horizontal displacement of the curved part increases as a convex angle becomes smaller, and the horizontal displacement of the curved part decreases as a concave angle becomes smaller. At the center (D and H have the same length, but H represents the height and D represents the separation distance from the center of the curved part) of the convex curve, the horizontal displacement of the 0.5 D section decreased to 13.8%; it decreased to 41.0% in the 1.0 D section. For concave angles, it was revealed that the horizontal displacement from the center 0.0 D to the 0.5 D section of the curved part increased by 25%, and from the 1.0 D section, by 75%. It was confirmed that the displacement difference was largely based on the value of 0.5 D. It was judged that this can be used as basic data for the design and construction guidelines for reinforced soil retaining wall of reinforced soil retaining walls.

A computed tomography-based spatial reference for pedicle screw placement in adolescent idiopathic scoliosis

Study designCross-sectional.ObjectivesTo determine semiautomatically the 3D position of the pedicle axis in operative adolescent idiopathic scoliosis (AIS) patients relative to the operating table and the lamina, as orientation for pedicle screw placement for better understanding and reference of spine surgeons.Summary of background dataPedicle morphology is well described as the angle between the convex and concave pedicle. However, the pedicle angle as relative to the neutral anterior–posterior axis or to an easy-to-use intravertebral landmark, remained unknown.MethodsThe pedicles of the apex and two adjacent vertebrae cranial and caudal to the apex of 86 right-sided primary thoracic AIS curves were evaluated using semiautomatic 3D software on high-resolution CT scans, in the same prone position as during surgery. Pedicle vectors were obtained and calculated as transverse and sagittal angles, as relative to the neutral axis (corresponding with an axis perpendicular to the operating table) and to an axis perpendicular to the lamina.ResultsAt the apex, the mean convex and concave transverse pedicle angles were 14.3º (95% confidence interval [95% CI]: 12.0–16.6) and 30.4º (95% CI: 28.1–32.8) to the right. The angles decreased toward the adjacent levels cranial and caudal to the apex (p < 0.001) and linearly increased with a higher Cobb angle (r ≥ 0.472; p < 0.001). The mean transverse pedicle–lamina angles, sagittal pedicle angles and the sagittal pedicle–lamina angles differed along the curve as well (p < 0.001).ConclusionsPedicle angulation differs between convex and concave and depends on the position of the vertebra relative to the apex, as well as the curve severity. The transverse and sagittal pedicle angles, as relative to the operating table and laminae, could provide useful reference for better understanding of the distorted 3D morphology, and the angles, as given in this study, could serve as an approximate guideline for the expected direction of the pedicle screw.Level of evidenceLevel IV.

Potential of Morphology Repair: Experimental Research on the Regeneration of Incomplete Crystallographic KH2PO4 Crystal Enclosed by Singular Face (Crystal Research and Technology 8/2019)

Crystal Research and TechnologyVolume 54, Issue 8 1970024 Cover PictureFree Access Potential of Morphology Repair: Experimental Research on the Regeneration of Incomplete Crystallographic KH2PO4 Crystal Enclosed by Singular Face (Crystal Research and Technology 8/2019) First published: 12 August 2019 https://doi.org/10.1002/crat.201970024AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Graphical Abstract Mingwei Li and co-workers (article no. 1800240) have examined the regeneration characteristics of incomplete crystals of crystallographic potassium dihydrogen phosphate (KH2PO4) in supersaturated solution. The designed crystals were enclosed by singular faces and thus provided surface conditions for ordinary layer-by-layer growth, however, thin surface layers grew from crystal edges or concave angles to repair the crystals to convex polyhedrons. It is assumed that the incomplete crystal possesses a "potential of morphology repair", which drives the thin surface layer growth. Volume54, Issue8August 20191970024 RelatedInformation

Experimental Research on the Regeneration of Incomplete Crystallographic KH2PO4 Crystal Enclosed by Singular Face

AbstractThe phenomenon of thin surface layer growth during the regeneration of incomplete crystallographic potassium dihydrogen phosphate crystal has not been thoroughly elucidated to date. In the present study, four sets of incomplete crystallographic KH2PO4 crystals enclosed by singular faces are designed to observe their regeneration characteristics in supersaturated solution. In all the crystals, even though every crystal face is singular surface, thin surface layers still grow from crystal edges or concave angles to repair themselves to convex polyhedrons. Through surface energy calculation, it is found that the thin surface layer growth encounters higher growth barrier than ordinary layer‐by‐layer growth. Here, an assumption is proposed that the incomplete crystal possesses a “potential of morphology repair”, which drives the thin surface layers growing to repair itself into complete form. This assumption is confirmed to some extent by a thin surface layer fragments experiment. The experiment implies that thin surface layer is the same as the ordinary crystal seed once separated from incomplete crystal, and its growth rate is one order slower than in incomplete crystal.

Superfast domain wall motion in lithium niobate single crystals. Analogy with crystal growth

In this paper, we studied the superfast domain walls that appear after domain merging during polarization reversal in congruent lithium niobate single crystals by in situ optical visualization with a high temporal resolution. The superfast domain walls were observed during the fast transformation of the domain shape from concave polygonal that appears after merging to the convex polygonal one with slow domain walls only. Orientations and velocities of superfast domain walls were measured during transformation of an artificial polygonal X-shaped domain (with all concave angles appearing after merging) to a hexagonal one. The “convex” growth of isolated hexagonal domains was governed by the slowest domain walls, while the “concave” growth after domain merging—by the superfast walls with three orders of magnitude higher velocity. We reconstructed experimentally the v-plot (kinetic Wulff plot) for domain wall motion by analysis of both convex and concave domain growth. The slowest walls (Y-walls) correspond to the v-plot deep cusps having six-fold symmetry, whereas the superfast walls correspond to the v-plot maxima having three-fold symmetry with a difference between Y+ and Y− crystallographic directions. The field dependences of the velocities of the superfast domain walls followed the activation law, taking into account the existence of the bias field.

Multi-sided Bézier surfaces over concave polygonal domains

A new multi-sided, control point based surface representation is introduced, based on the Generalized Bézier patch [1]. While the original surface is based on convex polygonal domains and a specific, uniform arrangement of control points, the new construction permits domains with concave angles and supports a more general control point structure, where independent “half-Bézier” interpolants, or ribbons, are blended together. The ribbons may have arbitrary degrees along the boundary and also in the cross-derivative direction; the related control points ensure tangent- or curvature-continuous connection to adjacent quadrilateral Bézier patches and permit shape editing and optimization, when needed.The surface comprises four components: (i) a concave domain generated from a 3D loop of boundary edges, (ii) half-Bézier interpolants, (iii) parameterizations that cover the full domain for each interpolant, and (iv) blending functions that guarantee both Bézier-like behavior along the boundaries and a smooth, C∞-continuous composition in the interior of the patch. Editing concave Bézier patches using additional control points is also discussed. A few interesting test examples illustrate the benefits of the method.

Low-Temperature Cu–Cu Direct Bonding Using Pillar–Concave Structure in Advanced 3-D Heterogeneous Integration

Low-temperature Cu–Cu bonding utilizing pillar and concave on silicon substrate with and without polymer layer is successfully implemented at 200 °C under atmospheric pressure. Finite-element method (FEM) simulations on stress and deformation generated during bonding process are also presented in order to discuss their influence on bonding result of several pillar diameters and of concave sidewall angles originating from the manufacturing process. The alteration of parameters in FEM simulations would also be investigated to enhance the bonding outcome. The parameters include the diameter of pillar, the sidewall angle of concave, the shape of the concave opening, the addition of extra polymer layer under Cu concave layer, the bonding temperature, and the pitch of the pillar–concave structure. The implementation of Cu–Cu bonding using pillar–concave structure could have a prospective effect on existing packaging methods in semiconductor industry with benefits of applicability to various sorts of substrates and low bonding temperature.

Plane wave refraction on convex and concave angles in geometric acoustics approximation

An exact analytical solution to the eikonal equation for a plane wave refracted on a boundary comprising both convex and concave obtuse angles has been built. Under the convex angle summit the solution has a line of discontinuity in the ray vector field and in the first derivatives of the first arrival times, and under the concave angle it has a cone of waves diffracted on this angle. This cone corresponds to the Keller diffraction cone in the geometric diffraction theory. The relation between the eikonal equation and the resultant Hamilton–Jacoby equation for arrival times of downward waves and the ray parameter conservation equation is investigated. Solutions to these equations coincide for pre-critical incidence angles and differ for super-critical angles. It is shown that the arrival times of maximum amplitude waves, which are of the greatest practical interest, coincide with the times calculated from the ray parameter field for the ray parameter conservation equation. The numerical algorithm proposed for calculation of these times can be used for arbitrary speed models.