Side Length Ratio Research Articles

Study on crashworthiness of square frustum lattice structure under in-plane compression load

The direction of load on the component in engineering applications is often uncertain, so the excellent crashworthiness and smooth load transfer of energy-absorbing structures in various directions is of great application value. Square frustum lattice structure (SFLS) was proposed based on the control of cell deformation mode and the improvement of in-plane strength without increasing the overall mass. Compared with multi-cell tubes commonly used in engineering and origami-patterned structure with excellent performance in research, it is found that the SFLS shows high and stable energy absorption capacity with the same structural parameters. The SEA and CFE of SFLS are 1.7 times and 3.5 times of origami structure and multi-cell tube, respectively, and the fluctuation indicator of the force displacement curve of origami structure and multi-cell tube are 1.7 times and 2.7 times of that of SFLS. In-plane quasi-static compression experiment was carried out and the finite element model was verified. The results of parametric analysis and sensitivity show that, compared with the change of cell number and cell height, the crashworthiness of SFLS under in-plane compression was most sensitive to the ratio of side length, in the range of parameters studied, the maximum SEA value of SFLS can reach 79.35 J/g for k value equal to 0.3, while the best indicator of smoothness of force-displacement curve of SFLS is found at k equal to 0.5.

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.

Comparing Ninth-Grade Students’ Approaches to Trigonometric Ratio Problems Through Real-World and Symbolic Contexts

This study investigates the problem-solving strategies employed by ninth-grade students when addressing symbolic and real-world contextual problems involving trigonometric ratios. Conducted with 46 ninth-grade students from a Turkish public high school, this research employed a worksheet consisting of six problems aligned with the Turkish ninth-grade mathematics curriculum. Three of these problems were based on real-world contexts, while the other three were conventional symbolic problems. The findings indicate that students exhibited proficiency in identifying similarity ratios using side length ratios. Additionally, the results revealed that students were more adept at solving real-world mathematical scenarios compared to purely symbolic tasks. This study offers significant insights into the problem-solving strategies of ninth-grade students when confronted with trigonometric ratio problems. It underscores crucial implications for mathematics curricula and pedagogy, highlighting the importance of preparing ninth-grade students for success in their future academic and professional endeavors. The study emphasizes the necessity for a balanced approach in teaching, integrating both real-world and symbolic problem-solving tasks to enhance students’ mathematical understanding and application. By identifying the strengths and areas for improvement in students’ problem-solving strategies, this research contributes to the development of more effective educational practices that address the diverse needs of learners.

Study on the Influence of the Cell Structure on the Pressure Drop of Gasoline Particulate Filter

The cell structure of a gasoline particulate filter (GPF) is made up of thousands of individual cells. Although the symmetric square cell structure of the GPF is commonly used internationally, several cell designs have been proposed to reduce the pressure drop in the GPF trapping process. The aim of this paper was to use AVL-Fire software to establish GPF models of different cell structures, mainly including the symmetric square cell structure, asymmetric square cell structure, and symmetric hexagonal cell structure, and analyze the GPF pressure drop characteristics of different cell structures according to the carrier structural parameters and altitude. The results show that compared with the pressure drop of the symmetric square cell structure, the pressure drop of the asymmetric cell structure with inlet/outlet side length ratios ranging from 1.1 to 1.4 is decreased by 4.61%, 9.07%, 12.19%, and 13.22%, respectively, and the pressure drop of the symmetric hexagonal cell structure is decreased by 33.17%. Both asymmetric and symmetric hexagonal cell structure GPFs can decrease the pressure drop during trapping by increasing the cell density. From 200 CPSI to 300 CPSI, the pressure drop of the asymmetric cell structure with inlet/outlet side length ratios ranging from 1.1 to 1.4 is decreased by 20.43%, 20.53%, 20.39%, and 18.56%, respectively, and the pressure drop of the symmetric hexagonal cell structure is decreased by 18.70%. The pressure drop values of GPFs with asymmetric and symmetric hexagonal cell structures show an increasing trend with an increasing filter wall thickness and inlet/outlet plug length. The pressure drop values of GPFs with asymmetric and symmetric hexagonal cell structures show an increasing trend with an increasing altitude, and the larger the inlet/outlet ratio, the more significant the increase in the pressure drop.

In-Plane Dynamic Cushioning Performance of Concave Hexagonal Honeycomb Cores

In order to further study the cushioning performance of concave hexagonal cores (CHCs) and expand their application range, the in-plane finite element model of CHCs is established in this paper. A dynamic cushioning coefficient method was proposed to characterize the cushioning performance of CHCs. The dynamic cushioning coefficient curve and minimum dynamic cushioning coefficient (MDCC) of CHCs with different impact velocities and structural parameters are obtained. The influence rules of structural parameters and impact velocities on the MDCC are analyzed; the deformation mode and transformation empirical formula are also obtained. The results show that when other parameters are constant, the MDCC of CHCs decreases with the increase of impact velocity, increases with the increase of wall thickness and side length ratio, and decreases with the increase of expansion angle. The theoretical analysis is consistent with the finite element results, which further verifies the reliability of the model. This paper provides a solid theoretical basis for the industrial application of the cushioning performance of CHCs and forms a key technical support.

Studies of Auxetic Structures Assembled from Rotating Rectangles.

The subject of the work is analysis, which presents a renowned auxetic structure based on so-called rotating polygons, which has been subject to modification. This modification entails introducing pivot points on unit cell surfaces near rectangle corners. This innovative system reveals previously unexplored correlations between Poisson's ratio, the ratio of rectangle side lengths, pivot point placement, and structural opening. Formulas have been derived using geometric relationships to compute the structure's linear dimensions and Poisson's ratio. The obtained findings suggest that Poisson's ratio is intricately tied to the structure's opening degree, varying as the structure undergoes stretching. Notably, there are critical parameter limits beyond which Poisson's ratio turns positive, leading to the loss of auxetic properties. For elongated rectangles, extremely high negative Poisson's ratio values are obtained, but only for small opening angles, while with further stretching, the structure loses its auxetic properties. This observed trend is consistent across a broad category of structures comprised of rotating rectangles.

Multi-objective optimization for snap-through response of spherical shell panels

Composite spherical shell panels are commonly used for the lightweight design of thin-walled structures in the structure, architecture, aerospace engineering. Depending on the shell panel length, thickness, curvature, and stacking sequence, the load-deflection response under lateral load can be either a completely stable equilibrium path or an unstable snap-through path. In this work, the response of simply supported cross-ply composite spherical shell panels subjected to lateral static loads is studied and optimized. The spherical shell exhibiting snap-through response is optimized to (a) maximize the load required to initiate snap-through and (b) minimize the unstable region. Meanwhile, the spherical shell exhibiting continuous response is optimized to (a) maximize the softening-hardening load and (b) minimize the shell weight. The decision variables for both constraint multi-objective optimization (CMOO) problems include layup sequence, thickness, and the radius of curvature to side length ratio. The nonlinear governing equations are derived based on Kirchhoff–Love hypotheses for thin shells and Hamilton's principle. A novel semi-analytical method is presented based on Bernstein polynomials combined with a fast iterative approach to compute the objective features of the responses. Benefiting from the high efficiency and robustness of the proposed approach, the CMOO problems are solved by the metaheuristic Multi-Objective Artificial Hummingbird Algorithm (MOAHA). Composite spherical shell panels with various geometry and lamination configurations are considered to validate the performance of the proposed method. The optimization of geometric parameters (shell curvature and thickness) in addition to the staking sequence provide a high degree of tailoring of the shell performance to meet various objectives. These parameters are taken as design variables that must be optimized to achieve some objectives and satisfy arbitrary nonlinear constraints.

Numerical Analysis of Friction-Filling Performance of Friction-Type Vertical Disc Precision Seed-Metering Device Based on EDEM

A seed-metering device is a key component for precision seeding and the core component of precision seed-metering devices. Nowadays, high-speed seeding is a trend in the development of seed-metering devices, but the filling performance of mechanical seed-metering devices decreases under the condition of high speed. Therefore, this paper explores a controllable method to improve the filling force of seeds, thereby increasing the limit operation speed of the existing mechanical seed-metering devices, so as to achieve high-speed seeding. The friction-filling method of friction vertical disc precision seed-metering devices was numerically simulated using the DEM. In this paper, the relationship between the relevant parameters and seed-filling force was confirmed via comparing theoretical formulas. The friction-filling method was studied via numerical simulation and experimental verification. This research demonstrated that during the process of friction filling, the pressure on the side wall of the tube increased with the e exponent with the change in the position of the particles. When the friction coefficient between the particles and the side wall is less than the friction coefficient between the particles, the e exponent increases. A surge occurs when the ratio of the square tube side length to the particle radius is n3+2(n=1,2,3).

Performance investigation of a novel composite channel considering tapered-3D wavy structure

In this study, a novel composite flow channel was proposed to address issues of gas transport obstruction, poor water removal performance, high pressure drop, and low current density within the cathode flow channel of proton exchange membrane fuel cells (PEMFCs). The flow channel could optimize performance by combining a tapered design with a 3D wave structure. Based on a controlled variable method and three-dimensional (3D) multiphase computational fluid dynamics (CFD) simulations, the effects of the flow channel inlet and outlet side length ratio LD/d, amplitude A, and wavelength λ on PEMFC performance were investigated. As shown by results, appropriate decrease of LD/d, increase of A, and reduction of λ could increase convective mass transfer in the flow channel, improve the uniformity of the reaction gas distribution, and enhance the Water removal performance. Moreover, the optimal performance was achieved when LD/d=1/3, A = 0.3 mm and λ=4 mm for PEMFC. Finally, when the cell output voltage was 0.4 V, the current density of the novel composite flow channel was up to 6.26% higher than that of the traditional 3D wave-shaped flow channel.

Effects of parameters on postbuckling failure of composite sandwich panels loaded axially: Function form and applications

Based on the refined first-order shear theory (simplified zig-zag model), using quasi-conforming finite element method with path-following and switching approach, the postbuckling behaviors and postbuckling bearing capacity (PBC) of composite sandwich panels (CSPs) axially loaded were studied and discussed in detail. To utilize the carrying potential of CSPs in postbuckling, the effects of the key parameters on postbuckling behaviors of the CSPs were analyzed by finite element method. The numerical results show that the PBC of CSPs increases with the increase of face sheets thickness, core thickness and core shear modulus, but it is insensitive to the change of the side length ratio. The enhancement of core shear strength can increase the PBC of CSPs and change the failure mode, but it is found there is a threshold value, beyond which, the PBC will no longer or slightly increases with the increase of core shear strength. The failure of CSPs is mainly determined by the tensile strength in the direction perpendicular to the fiber. Finally, a parameter selection optimization approach is proposed to effectively improve the PBC of CSPs under axial compression.

Model for calculating local bearing capacity of concrete with spiral stirrups

This study evaluates the mechanical and failure modes of 30 concrete specimens under local compression. The experimental results indicate that the specimens undergo three types of local compressive failure modes. These modes primarily depend on the strengths of the tensile and compression regions. Based on the test results, a calculation model for the local bearing capacity of concrete with spiral stirrups Fl is formulated. In the model, the local compressive failure of concrete with spiral stirrups is classified into tension and compression. The yielding of spiral stirrups in the tensile region is regarded as tensile failure, and compressive failure is considered to have occurred when the strain value in the compression region reaches 0.002. To simplify the model calculation, the spacing s, diameter d, and yield strength fy of spiral stirrup as well as the local compression area ratio Ab/Al (ratio of the concrete bearing area Ab to the loading area Al) are comprehensively analyzed. Based on the analysis results, a formula for the bearing capacity of the reinforcement Ns is derived. The independent variables of the formula are yield force of spiral stirrup fyAssl, stirrup spacing s, and ratio of specimen side length to loading plate side length h/a. A simplified formula for calculating the tensile failure of the specimen is derived. To ensure simultaneous tensile and compressive failures, a critical reinforcement ratio of the spiral stirrup ρvu is proposed based on the calculation model. Test data from similar axial local compression tests are collected to verify the accuracy of the calculation model. The local bearing capacity of concrete is recalculated according to the calculation method proposed in this study. Results show that the calculation model is highly accurate. Accordingly, it may be used as reference for calculating the local bearing capacity.

Constitutive Law of Rectangular Concrete with Carbon Fiber Sheet Confinement

This paper investigates the stress-strain relationship of a rectangular cross-section concrete element reinforced with Carbon fiber Sheet (CFS). In order to verify the confinement effect of the carbon fiber sheet over the concrete, an experiment was conducted using concrete elements with CFS by changing the ratio of side length of the cross section, the ratio of the height to the short side and the amount of CFS layers. In total, 16 concrete specimens were tested under compressive monotonic loading. In the experiment, the compressive strength decreases, and the ultimate strain increases as the ratio of side length increases. Furthermore, we proposed an evaluation formula for a rectangular cross-section concrete element reinforced with CFS. The proposed formula corresponds well to the experimental results.

Research on shear capacity of Dense-Steel-Column wall structure

Based on the previous experimental study on the shear capacity of the dense-steel-column wall (DSCW), to reveal the failure mechanism of DSCW under seismic load, the finite element analysis (FEA) of six test specimens from the experimental study is carried out, and the FEA results are compared with that of the experimental study. To further study the influences of different factors on the seismic behavior of DSCW and to calculate the shear capacity of DSCW, the parametric study is performed with 90 FEA models considering different parameters such as axial compression ratio (μ), column side length (l), and spacing to side length ratio (l/b). The results show that the local buckling failure of the columns occurs at the bottom of the wall with obvious in-plane bending deformation. Adding diagonal bracings greatly increases the stiffness of the wall, and the shear capacity of the wall with diagonal bracings decreases more slowly under the cyclic load. From the hysteresis curves and skeleton curves, it is seen that all specimens have good energy dissipation capacity and high shear capacity. With the constraint of the out-of-plane wall limb, the L-shaped and T-shaped walls have less deflection, higher shear capacity, and better energy dissipation capacity compared with that of than the |-shaped wall. The parametric study shows that the ductility decreases with the increase of axial compression ratio. The shear capacity of the wall increases with the increase of the column side length and with the decrease of the column spacing to side length ratio. In the end, the calculating formula of the shear bearing capacity of DSCW was put forward, the calculated values are in good aggreement with those of finite element analysis.

Mesoscale synergistic effect mechanism of aggregate grading and specimen size on compressive strength of concrete with large aggregate size

In this paper, a 2D finite element model with a mesoscale level was established. The effects of content, maximum particle size, and shape of aggregate on the strength of concrete were simulated. In addition, five mesoscopic models of aggregate gradation and specimen side length (100–450 mm) were established to investigate the influence law of aggregate grading and model size on the compressive strength of concrete. The simulation results were also compared and verified with four theoretical size-effect models. The results showed that the compressive strength shows a trend of decreasing and then increasing with the increase of aggregate content and falling with the growth of maximum aggregate size dmax. The peak stress of convex polygonal aggregates is higher than that of round and elliptical. In addition, when the ratio of model side length to the maximum aggregate particle size is about 3.5, the compressive strength gradually decreases with the increase of specimen size, up to 27.65 % decreased, showing a pronounced size effect. After comparative analysis, the simulated data in this paper fitted well with the Bažant’s Type-2, Kim’s modified, Jin’s modified, and Carpinteri’s size effect law (SEL). In addition, the data obtained from the simulation of this paper would better reflect the existing test conclusions. The mesoscale model established in this paper can significantly improve the effectiveness and efficiency of full-graded concrete modeling, and better simulate the strength difference between full-graded and wet-screened specimens. The difficulties in the mesoscale numerical simulation are solved to a certain extent.

Experimental study on the flat-wise compression of foldcore sandwich paperboard

Foldcore sandwich structures have aroused considerable research interest in recent years. While foldcores made of metal or composite have been studied extensively, paper-based foldcore are relatively rare. In this paper, we focus on the flat-wise compression properties of foldcore sandwich paperboard with the Miura-ori pattern in the field of packaging and logistics engineering. The flat-wise compression properties and affecting factors of foldcore sandwich paperboard are identified experimentally. Among these factors, the side length ratio (a/b) of the Miura-ori unit significantly influences the deformation mode of the foldcore sandwich paperboard, thus affecting the load-carrying performance and energy-absorption properties. Moreover, the foldcore sandwich paperboard is compared with the conventional corrugated paperboard. The results indicated that although the specific peak stress of foldcore sandwich paperboard and conventional B-flute corrugated paperboard are approximately equal at the same profile angle, the specific energy absorption of the former was 2.06 times higher than the latter. What is more, the specific peak stress and specific energy absorption of the foldcore sandwich paperboard are 1.93 times and 3.24 times higher than those of B-flute corrugated paperboard by merely increasing the sector angle from 60° to 75°. These findings may provide the potential for practical application of paper-based foldcore sandwich panels, thus facilitating the structural design of multilayered cushioning paper pads.

Wideband subwavelength acoustic edge detection via trapped modes with breaking structural periodicity

The wave manipulation through acoustic metamaterials and the application in realizing the super-resolution edge detection has been achieved by the trapped resonance coupling with evanescent waves. Here, we numerically and experimentally demonstrate that the working bandwidth of such edge detection can be effectively broadened by increasing the side length ratio of the narrow segments to the wide segments, and the imaging resolution is mainly determined by the size of the first narrow segment of the edge detector. By breaking the periodicity of these segments, the wide working bandwidth (∼900 Hz) and the imaging resolution of 0.11λ are experimentally verified.

Curved-line cleft lip repair in unilateral complete cleft lip patients: Comparative analysis of lip dimensions after cheiloplasty

This study aimed to restore upper lip symmetry and minimize tissue sacrifice using a curved line design and wire technique and analyze the postoperative outcomes. In this retrospective study, medical records of patients with complete unilateral cleft lip who underwent unilateral cheiloplasty between August 2017 and February 2019 were reviewed. The postoperative clinical photos were analyzed to determine vertical, diagonal philtral heights and the horizontal lengths of the upper lip. The average of the cleft side to non-cleft side length ratios were compared between the curved line group and conventional group. At 3, 6, and 12 months, the average vertical length ratios were significantly greater in the curved line group than in the conventional group (0.927–0.823, p = 0.007; 0.940 to 0.885, p = 0.037; and 0.947 to 0.883, p = 0.040, respectively), but the average horizontal length ratios were not significantly different between the two groups. Within the limitations of the study it seems that curved line cheiloplasty aids in preventing short lip deformity development at regular term without significantly sacrificing the horizontal length and, therefore, should be adopted whenever appropriate.

Dividing the Perimeter of a Triangle into Unequal Proportions

We fully describe the envelope of all line segments that divide the perimeter of a triangle into the ratio α : 1 − α as α varies from 0 to 1 / 2 . If α is larger than the ratio of the longest side length to the perimeter, then the envelope is a 12-sided closed curve consisting of six line segments and six parabolic arcs. For other values of α , the envelope is the union of one to three parabolic arcs and possibly a 5- or 9-sided nonclosed curve consisting of line segments and parabolic arcs.

Numerical investigation and ANN-based prediction on compressive strength and size effect using the concrete mesoscale concretization model

The concrete mesoscale concretization model (CMCM) is proposed using the statistical distribution and local spatial correlation theory to describe the randomization, continuum, and correlation of the material properties of mesoscale components. The distribution of material properties was obtained by stochastic discretization, spatial correlation correction, and remapping operations. The hypotheses of elastic modulus control (EMC) and characteristic deformation control (CDC) are used to describe the variation of mechanical parameters in the concrete damage plasticity model. The uniaxial compression behavior and size effect of concrete with different side lengths, aspect ratios, aggregate contents, air contents, and contact frictions are simulated using the above model. Without the contact frictions, the size effect of the sample’s side length is apparent, while the size effect of aspect ratio is not observed. The increase of size effect degree is contributed by the increase of air content rather than aggregate content. When the loading boundaries are constrained by friction, both the side length and aspect ratio of samples show the size effect. The increase of aggregate content leads to the increase of size effect degree, while the increase of air content leads to a minor increase of size effect degree. The developed CMCM can capture the mechanical responses, and the ANN-based prediction model is applicable to explore the relationship between compressive strength and sample parameters.

Boundary element analysis of thin structures using a dual transformation method for weakly singular boundary integrals

This paper focuses on the weakly singular integrals in thin structures of 3D boundary element method. In the pioneering woks for the weakly singular integrals, the singularities are eliminated through introducing transformations whose Jacobian at the singular point is zero. When using these methods for weakly singular boundary integrals on elements with a large-angle and large side length ratio, near singularity will appear. In this paper, a dual transformation method is proposed to accurately calculate weakly singular integrals in which the near singularity is also considered. The numerical implementation is divided into several steps. Firstly, the (α, β) coordinate transformation method is used to eliminate the weak singularity by introducing the α factors in the transformation Jacobian. Then extract the integral form with near singularities about β. Finally, a corresponding distance transformation is constructed to eliminate its near singularity. The results show that the proposed method can accurately integrate for arbitrary element shape and source point position. The dual transformation method may be a good choice to evaluate weakly singular integral for thin structural problem.