Polygonal Cross-section Research Articles

Effect of Microneedle Cross-Sectional Shape on Puncture Resistance – Investigation of Polygonal and Star-Shaped Cross Sections –

The shape of the needle tip that is currently used in the medical field is a “lancet point,” which is a diagonally cut cylindrical pipe, further cut on both sides. The shape of the needle shank is typically cylindrical. In this paper, tip and shank shapes that differ from the standard shape are experimentally investigated for the purpose of reducing puncture resistance. Microneedles of various cross-sectional shapes, such as polygonal and star-like, were fabricated using stereo laser lithography. Before the needle penetrates the skin, sharp edges at the needle tip may be effective to generate a stress concentration on the skin, inducing a skin fracture. After the needle penetrates the skin, corners in the cross section of the needle shank may effectively reduce the frictional resistance because the contact area between the skin and needle is limited at the corners. A needle insertion experiment was conducted against an artificial skin made of polydimethylsiloxane. The puncture resistance decreased respectively for the circular needle, polygonal needle, and star-shaped needle. For the star-shaped needles, the maximum resistance decreased as the number of corners (N) decreased. For the polygonal needle, the maximum resistance increased as N increased from 3 to 5; however, there was no observable difference for N from 6 to 8. The experimental results show that a triangular star-shaped microneedle is the most effective in reducing the puncture resistance.

Free Vibration of AFG Circular Arch with Symmetric and Anti-symmetric Boundary Conditions at Mid-Arc

This paper studies the in-plane free vibration of axially functionally graded (AFG) circular arches with non-uniform cross-section. The geometric and material properties of circular arches with regular polygon cross-section vary symmetrically about the mid-arc along the axial direction in quadratic polynomial form. The governing differential equations of the motion are derived, and the symmetric and anti-symmetric boundary conditions of the arches are developed for applying initial and boundary value problems in the solution method. The computed results agree well with the results of the finite element software ADINA. The effects of geometrical and material parameters on the natural frequency and mode shape of AFG circular arches are investigated.

Clamped-Free Non Homogeneous Magneto Electro Elastic Plate of Polygonal Cross-Sections with Hydrostatic Stress and Gravity

In this article, the influence of hydrostatic stress and gravity on a clamped- free non homogeneous magneto electro elastic plate of polygonal cross sections is studied using linear theory of elasticity. The equations of motion based on two-dimensional theory of elasticity are applied under the plane strain assumption of prestressed and gravitated magneto electro elastic plate of polygonal cross-sections composed of non homogeneous isotropic material. The frequency equations are obtained by satisfying the boundary conditions along the irregular surface of the polygonal plate using Fourier expansion collocation method. The complex roots of the frequency equations are obtained by secant method. The numerical computations are carried out for triangular, square, pentagon and hexagon cross sectional plates. Graphical representation is given for the various physical variables via gravity and different edge boundaries and its characteristics are discussed. This result can be applied for optimum design of concrete plates with polygonal cross sections.

Free Vibration Analysis of Axially Functionally Graded (AFG) Cantilever Columns of a Regular Polygon Cross-Section with Constant Volume

This paper deals with the transverse free vibration of axially functionally graded (AFG) cantilever columns under the influence of axial compressive load. The columns possessing a regular polygon in their cross-section are tapered and their material properties vary along the axis of the column. An emphasis is placed on the columns with constant volume for admissible geometries and materials. The governing differential equation of the problem is derived and solved using the direct integral approach in conjunction with the determinant search technique. The obtained results are in good agreement with those in the available literature and computed by finite element analysis. Numerical examples for the natural frequency and mode shape of the columns are presented to investigate the effects of parameters related to geometrical nonuniformity and material inhomogeneity.

A path planning and sharp corner correction strategy for wire and arc additive manufacturing of solid components with polygonal cross-sections

Pores can easily form in the geometric center and sharp corner lap joints of solid components with polygonal cross-sections fabricated by wire and arc additive manufacturing. To solve these problems, this paper proposes a composite path planning method and a sharp corner correction strategy. The composite path planning method consists of the zigzag path and the contour offsetting path. The zigzag path is used to fill the interior of the component and eliminates pores formed by traditional filling paths. The contour offset path is used to improve the geometric precision of the component. Filling paths are connected to create a closed path, which reduces arc striking and arc extinguishing during the manufacturing process. By exploring the distance between two vertices of a sharp corner lap of the outer contour path, it was found that pores form in the sharp corner lap when the angle of the sharp corner is less than 58.65°; therefore, the sharp corner correction strategy is proposed to correct the sharp corner lap path in the outer contour path. Experimental results show that the composite path filling method and the sharp corner correction strategy can eliminate pores between the geometric center and the sharp corner lap joints of components, thereby improving surface morphology and forming quality of components with complex polygonal cross-sections.

Finite element simulations of the bending resistance of square profiles with topological modifications

Bending resistance is one of the most important requirements in automobile structural members when lateral crashes occur. For this purpose, the current paper studies the bending and crashworthiness capacity of square profiles with topological modifications. Several finite element simulations were carried out using Abaqus/Explicit software. The topological modifications consisted in combining a square cross-section with polygonal and circular simple cross-sections. In all cases, the profiles evaluated were simulated with mechanical properties for aluminium alloy 6063-T5 with the same mass. The feasibility of our numerical study was validated by a three-point bending tests of a square tube using a Shimadzu universal test machine. Additional to the assessment of complex cross-sections, numerical results for simple cross-sections are presented. A better crashworthiness performance is obtained when the square section of a simple profile is reinforced with topological modifications. According to the simulation results, a complex cross-section can improve the crushing force efficiency up to 77.9% with respect to a single square profile. Regarding cross-sections with topological modifications, the best bending resistance and energy absorption capacity is obtained when the square section is combined with a square profile. This means an increase of 9.2 % of energy absorption (Ea) and 5.67% of CFE respect to the cross-section formed by square and triangular shapes.

Shape optimization for the noise induced by the flow over compact bluff bodies

A shape optimization for tonal noise generated aerodynamically at low Mach number is performed for a cylinder with polygonal cross-section. Acoustic quantities are derived from a hybrid analytical formula, with aeroacoustic sources obtained from the incompressible solution of the direct Navier-Stokes equations in 2D at Re = 150; the solid domain is modelled by an Immersed Boundary Method. The optimization is done with the Particle Swarm Optimization (PSO) technique and performed in a cluster where each cost function evaluation is an independent flow simulation. The precision on the 4 main shape parameters is set to 0.001, consistently with the convergence criteria in time, grid and swarm. Optimal shapes for minimum drag and minimum acoustic power are relatively similar. A large range between the optimal shapes is obtained: factor 1.8 for drag and 20 dB for the acoustic power. The reduction of noise is associated with long and bluffer geometries, while the louder flows are associated with highly interacting shear layers obtained with back pointing triangles. The fluctuating lift is the major quantity to control noise at fixed length, while increasing the aspect ratio tends to reduce the noise for globally all geometries. An overall correlation between mean drag and fluctuating suction is also noticed.

Diameter-dependent polygonal cross section for holey phenine nanotubes

The cross-sectional shape of the nanotube is a key factor governing fundamental mechanical properties of the nanotube and the nanotube forest. In contrast to most circular nanotubes, in the present work, we demonstrate that the holey phenine nanotubes have polygonal cross sections with diameter-dependent number of sides. The non-circular cross section is attributed to the high twistability of the continuous C–C chains in the phenine nanotube. Consequently, the phenine nanotube forest has a square lattice structure rather than the regular hexagonal lattice of the carbon nanotube forest, resulting in a smooth buckling process under biaxial compression. The buckling pattern of the phenine nanotube forest is highly ordered with the orientation determined by the initial dislocation that frequently appears in the phenine nanotube forest.

Experimentally investigating the instability onset in closed polygonal containers

The article investigates the instability onset in the vortex flow in the stationary container with a rotating lid and polygonal cross-sections. Transition to unsteady flow regime is determined in closed containers with square, pentagonal and hexagonal cross-sections. The onset of flow unsteadiness is measured by combining the high spatial resolution of PIV and the temporal accuracy of LDA. A detailed transition scenario from steady and axisymmetric flow to unsteady flow with discrete rotational symmetry is investigated for the aspect ratio of 2.5 ≤ h ≤ 6.0. The results show that at steady conditions there are no asymmetric distortions of the flow topology due to the non-axisymmetric effect of the polygonal geometry of the used containers. It is found that reducing the number of cross-section angles shifts the instability onset to smaller aspect ratios and the vortex breakdown bubble stabilizes and shifts the flow instability onset to higher Reynolds numbers. The features of the flow structure formation in the polygonal containers are shown to be similar to those in the axisymmetric configuration. It is proved that the onset of the unsteadiness in polygonal configurations is based on the appearance of rotating vortex multiplets, which is similar to the cylindrical container.

Torsional Capacity of Slip Joints with Polygonal Hollow Sections

ABSTRACTPolygonal steel sections are widely used for lighting towers and are more and more adopted for transmission line towers. They convince with an inconspicuous appearance compared to steel lattice towers. Therefore, instead of flange connections “invisible” joints are preferred, such as slip joints. The European design rules for overhead electrical lines (1) cover the use of these joints very generally by a constant ratio of the overlapping length L and the section's diameter D. It is neither distinguished between load conditions nor between cross‐sectional shapes. The ratio value L/D = 1.5 is based on bending tests without regard to torsional moments. In the design of transmission line pylons, torsional loading occurs in the load case of a single‐side loss of a transmission line. Thus, there is a need to improve the knowledge on the load bearing effect of a slip joint connection within this special load case.In this paper the torsional capacity of slip joints is investigated to identify the capability of polygonal cross sections to carry this additional load, particularly in comparison with circular hollow sections. On the basis of numerical and analytical analysis, an adaption for the design of the slip joints is proposed.

An investigation into the effect of regular polygonal cross-sections on thethermal performance of microchannel heat sinks

An investigation into the effect of regular polygonal cross-sections on thethermal performance of microchannel heat sinks

An analytical solution for the estimate of the mean crushing force of structures with polygonal and star-shaped cross-sections subjected to axial load

The present work is focused on the development of an analytical solution for the estimate of the mean crushing force for structures with polygonal and star-shaped cross-section. The geometrical analysis revealed that polygonal and star-shaped cross-sections could be obtained using a consistent set of equations. A theoretical model for the mean crushing force that can be applied for this entire range of structures was developed, based on the hypothesis of an extensional model applied to the collapse pattern. Literature data were collected and used as a reference for an analysis of the results. For each case, a specific material model was assigned, and crushing process parameter like the effective crushing distance was discussed. A nondimensional analysis of the mean crushing force was performed in order to evaluate the results overall data collected. Finally, the proposed solution was compared with existing, specific, analytical solutions used for the estimate of the mean crushing force and values of the mean crushing force from the literature. The linear regression model applied to the dataset consisting of analytical estimates resulted in a coefficient of determination R2 = 0.983 while for the dataset comprising experimental values, a coefficient of determination R2 = 0.965 was obtained. These results show that this analytical solution can be used, with confidence, to provide a preliminary estimate of the mean crushing force while allowing variations of the shape of the cross-section and, without the need of a specific or particular analytical formula.

A new homo-polygonal multi-cell structures under axial and oblique impacts; considering the effect of cell growth in crashworthiness

In this paper, groups of new homo-polygonal multi-cell tubes are introduced and investigated under both axial and oblique loads via studying the effect of cell growth on energy absorption characteristics. Finite element models has been developed and validated by experimental tests as well as a new developed theoretical procedure for multi-cell tubes. The new developed homo-polygonal multi-cell structures are investigated considering the effect of cell growth to find the most efficient topology. Different polygonal cross-sections including pentagonal, hexagonal and octagonal are considered while each cross-section has cells in corners form that have the same shape as their own cross-section. Obtained results point out that there is a distinct connection between cell’s size and absorbed energy and cell growth could affect the energy absorption characteristics in a perceptible manner. When cells start to manifest in tubes the peak crush force increases and then drops to its original value as cells reaches their maximum possible size. Acquiring the numerical data of all the structures, by using the COPRAS multi-criteria decision-making method, the best structure is distinguished. Next, the best thickness in the best impact angle of crash found using the relevant RSM as an optimisation method.

Quasi-static impact of origami crash boxes with various profiles

The crash box is a structural component which is widely used in transport vehicles. It is designed to collapse and absorb kinetic energy in a low-speed collision. In this paper, we present a family of new origami crash boxes with rectangular, polygonal cross sections, and tapered shapes, through pre-folding the surface of thin-walled tubes according to a set of developable origami patterns. We have demonstrated through quasi-static impact experiments and numerical simulation that these origami crash boxes collapse into a diamond-shaped mode with a doubled number of traveling plastic hinge lines. The proposed optimal design leads to a maximum increase of 107.1% in terms of the energy absorption per unit mass and a maximum reduction of 68.3% of the initial peak force when compared with the conventional crash box. The substantial gain in overall energy absorption and the decrease in peak reaction force makes the proposed origami patterns attractive for energy absorption applications.

A Compromise Reveals Buckling Resistance Strategy of a Naturally Slender Tibia

AbstractIn nature, slender tibiae of stick insects have an excellent performance in resisting buckling, which raises the questions why the natural evolution chooses the pentagonal shape as the tibiae's cross section to resist buckling? Why is the proximal base round but the distal end pentagonal in adult tibiae? In this study, 3D geometrical models of the tibiae in stick insects are reconstructed aimed at investigating the buckling resistance strategy of the biological composite with different polygonal cross sections. The numerical result is consistent with the experimental observation. Based on large deflection theory, corresponding mechanical models proposed herein can accurately predict the structural response and mechanical behavior at buckling (including both Euler buckling and local buckling). Eventually, with the help of numerical and theoretical analysis, this article might have found the reason for the tibiae of stick insects naturally evolving to form the cross section with a pentagonal shape. In conclusion, the nature's choice of pentagon (S5) cross section could be a best compromise strategy to balance both Euler buckling and local buckling resistance capability. The knowledge gained from this work will inspire the designs of new advanced materials and structures.

Effect of radial clearance and holes as crush initiators on the crashworthiness performance of bi-tubular profiles

The use of bi-tubular structures has gained importance in the design of energy absorption systems for protection of passengers in train collisions. Therefore, it is critical to improve the crashworthiness performance of bi-tubular profiles. For this purpose, the effect of cross-section, bi-tubular clearance and holes as crush initiators is evaluated using finite element simulations. To get reliable outcomes, special emphasis was set on the progressive damage modelling of aluminum 6063-T5 by a Johnson-Cook (J-C) failure model. During the cross-section study, bi-tubular arrangements based on polygonal and circular cross-section were evaluated by quasi-static compression loads. The results indicate that the circular shapes showed better crashworthiness performance or crush force efficiency (CFE) up to 12.28% respect to a square base structure. A 10.72% improvement in CFE was obtained when the non-dimensionalized clearance between profiles is increased from λ=20 to λ=40. The effect of holes on crashworthiness performance was evaluated by drilling holes at different locations both in the inner and outer profiles. The results show that the use of holes increased the crush force efficiency and energy absorption (Ea) capability even more than the effect of clearance alone. Improvements in the order of 2.50% and 12.96% for Ea and CFE respectively were computed when holes were placed at the top end of a BC-3 profile with a non-dimensional clearance of λ=40. Considering all effects simultaneously, an increase of 24.6% and 26.31% for Ea and CFE respectively was calculated. Finally, an application to a crash buffer in a railway transport system is considered. Likewise, its improved crashworthiness behavior is presented.

A non-linear model for analysis and design of slender reinforced-concrete columns

The purpose of this paper is to present a non-linear model for analysis and design of slender reinforced-concrete columns subjected to uniaxial and biaxial bending. This model considers both material and geometric non-linearities, as well as creep effects. The structural analysis is performed by the finite-element method associated with an iterative process to solve the system of non-linear equations. The column may have an arbitrary polygonal cross-section, including openings. Green's theorem is used to perform the integration at the level of the cross-sections, which is greatly simplified with the use of a new parabola–rectangle diagram proposed for concrete in compression. This new diagram provides the correct value of the tangent modulus of elasticity of concrete, allowing its use for non-linear analysis of slender columns. By changing the strain value corresponding to the maximum stress, it is possible to use a single stress–strain diagram for displacement calculation and rupture verification, which facilitates the design of slender columns. The accuracy of the method is demonstrated through the analysis of several columns tested experimentally by other authors.

Post-buckling behaviour of thin-walled regular polygonal tubular columns undergoing local-distortional interaction

This work presents and discusses numerical results of an ongoing investigation concerning the elastic post-buckling behaviour and imperfection sensitivity of regular convex polygonal cross-section (RCPS) tubular columns affected by local-distortional (L-D) interaction. This investigation is conducted by means of geometrically non-linear Generalized Beam Theory (GBT) analyses, extending the knowledge on the “pure” local and distortional post-buckling behaviours of RCPS tubes recently reported by Martins et al. [1]. Due to their inherent modal nature, the GBT analyses make it possible to acquire in-depth knowledge on the structural behaviour of RCPS tubes and also to include, in a straightforward fashion, arbitrary member initial geometrical imperfections. Columns with distortional-to-local critical buckling load ratios (i) close to 1 (“true L-D interaction” – the most trivial L-D interaction type) and (ii) significantly above 1 (“secondary-distortional bifurcation L-D interaction” – the most relevant L-D interaction type) are investigated. Local/distortional critical-mode initial geometrical imperfections and (linear) combinations of both are considered in the former columns, while only local initial imperfections are dealt with in the latter ones – several amplitudes are dealt with to assess the imperfection sensitivity. For comparison and validation purposes, ABAQUS shell finite element analysis results are also reported.

3D Gravity Analysis in the Spatial Domain: Model Simulation by Multiple Polygonal Cross-Sections Coupled with Exponential Density Contrast

An automatic 3D modeling technique is developed in the spatial domain to analyze the gravity anomalies produced by a concealed density interface with mass density contrast differing exponentially with depth. The sedimentary column above the interface is described with a stack of multiple vertical polygonal sections of unit thickness each. For such a case, the depth ordinates of the vertices of the cross-sections become the unknown parameters to be estimated from gravity data. Forward solution of the model space is realized in the spatial domain by a technique that combines both analytic and numeric approaches. Initial depths to the interface are calculated based on the Bouguer slab approximation and subsequently improved, iteratively, based on the ratio of the product of the observed gravity anomaly and existing depth parameter to the corresponding model gravity response. The iterative process continues until one of the predefined termination criteria is accomplished. Unlike the existing methods, the advantage of the proposed method is that the observed gravity anomalies need not necessarily be sampled/available at regular spatial grid intervals. The applicability of the proposed model is exemplified with a set of noisy gravity anomalies attributable to a synthetic structure before being applied to a real world gravity data. In the case of the synthetic example, the method has yielded a structure that was compatible with the assumed structure even in the presence of random noise. Application of the proposed method to the gravity data set from the Los Angeles Basin, California, using a prescribed exponential density function has yielded a model that concurs reasonably well with the published models.

On the local and distortional post-buckling behaviour of thin-walled regular polygonal tubular columns

This paper presents and discusses numerical results concerning the (i) elastic local and distortional post-buckling behaviours and (ii) imperfection sensitivity of regular convex polygonal cross-section (RCPS) simply supported tubes under uniform compression (columns). Although it was shown recently that the local and distortional buckling behaviours may be often characterised by duplicate bifurcation modes, knowledge concerning the corresponding post-buckling behaviour is still lacking. The results presented are obtained through a geometrically non-linear Generalised Beam Theory (GBT) formulation previously reported by the authors. This GBT formulation is first employed to characterise the column bifurcation behaviour, namely by helping to pinpoint the occurrence of the above two distinct buckling behaviours. Then, post-buckling results are presented and discussed for (i) different combinations of the local-to-distortional buckling load ratio and the (ii) amplitude of the critical-mode initial geometrical imperfections, in order to characterise the RCPS column imperfection sensitivity. Such results provide the evolution, along given equilibrium paths, of the column deformed configurations (expressed in GBT modal form), relevant displacement profiles and participation diagrams based on either stress resultant strain energies or amplitude functions. For comparison and validation purposes, ABAQUS shell finite element values are reported.