Regular Polygonal Cross-section Research Articles

Simulations of shaping and reducing effects of image charge attraction on ion transmission through untilted mica capillaries

We simulated transmission of 7-keV Ne7+ ions through untilted mica capillaries to study the influence of the image charge attraction. In simulations, the repulsive interaction of incident ions with the charges accumulated on the capillary surface was also considered. The capillaries used have various regular polygonal cross sections. Our results clearly show that the image attraction greatly reduces the ion transmission. Moreover, the shaping effect, already reported previously, is also reproduced. For a regular polygonal shaped capillary the transmitted angular distribution remains regular polygonal, but its orientation with respect to the capillary differs by some angle. An analytic model calculation was conducted to describe the reduction of the image attraction on the transmitted ion fraction through the untilted capillary, agreeing well with the simulated results. The reducing effect of the image attraction on ion transmission was found to be strong for the combination of low-energy ions and capillaries with large aspect ratios (length/diameter).

Estimation of critical thickness of insulation for regular polygon cross-section ducts/conductors

In some areas, due to geometry or space constraints, the outer structures of ducts or conductors are non-circular or are of regular polygonal shape. Determination of critical thickness of insulation for these ducts or conductors is difficult. The critical thickness of insulation, in case of circular cross section duct depends on the thermal conductivity of the material and heat transfer coefficient surrounding the duct. Authors in this work have attempted to estimate the critical thickness of insulation in case of regular polygonal cross-section. It is attempted to determine the critical thickness, leading to maximum heat loss, in case of various polygonal cross section. In this work the authors have estimated a correction factor that can multiplied to the critical thickness if the conductor is circular in cross section. It is observed that correction factor goes on increasing as the number of sides goes on increasing. The proposed work is relevant to the heat transfer community. Wire and solar plate manufacturers will be directly benefited from the outcome of this project to improve their design.

Tubes of non-circular cross-section to destabilize liquid plugs in heat transfer devices

The stability of a liquid plug inside a vertical tube depends on the balance between the weight of the liquid and the capillary forces. Contact angle hysteresis is required for a liquid plug to be at equilibrium; it has a stabilizing effect. On the other hand, capillary drainage into corners or grooves destabilizes liquid plugs and may lead to their dislocation. Following a detailed literature review about the influence of the tube cross-section on plug stability, this paper provides original numerical and experimental results obtained in tubes of circular, regular polygonal and fluted cross-sections. The cross-section may affect stability either through direct modification of the menisci curvature, or through that of apparent contact angle hysteresis. The latter was characterized experimentally for the first time to our knowledge in tubes of non-circular cross-section. Among the studied shapes, the fluted and triangular ones are the most promising for destabilizing liquid plugs. They both promote capillary drainage. Besides, fluted tubes reduce stability by a direct effect on curvature, while triangular tubes decrease apparent contact angle hysteresis. These findings could help improve the performance of two-phase closed thermosyphons of small dimensions by mitigating liquid hold-up in the condenser section. Indeed, recent advances in additive manufacturing processes enable the fabrication of thermosyphons with very complex shapes. Other devices such as fuel cells could also benefit from the optimization of their geometry to prevent channel occlusion.

Free vibration and buckling of heavy column with regular polygon cross-section

This paper deals with the free vibration and buckling of heavy column, considering its own self-weight. The column has a regular polygonal cross-section with a constant area. The column is applied to an external axial load as well as the self-weight. The five end conditions of the column are considered. Based on equilibrium equations of the column element, differential equations governing the vibrational and buckled mode shapes of column are derived. In solution methods, differential equations are numerically integrated by the direct integration method and eigenvalues of the natural frequency, buckling load and self-weight buckling length are calculated by the determinant search method. The numerical results of this study were in good agreement with those of the reference. Parametric study of the end condition, side number and self-weight on the natural frequency and buckling load was carried out.

Torsional rigidity for regular polygons

We present a simple lower bound for the torsional rigidity of a beam with regular polygonal cross-section. The methods used are applicable to other cross-sections, in particular to other tangential polygons.

Post-buckling behaviour of thin-walled regular polygonal tubes subjected to bending

This work presents and discusses numerical results concerning the elastic post-buckling behaviour and imperfection sensitivity of regular convex polygonal cross-section (RCPS) tubular beams buckling in local, distortional and mixed local–distortional modes, a topic currently lacking research. This study is carried out in the framework of Generalised Beam Theory (GBT) geometrically non-linear analyses, enriched with a branch switching technique, and takes advantage of the GBT intrinsic modal nature to shed new light on the mechanics underlying the post-buckling behaviour of these members. Due to the small half-wavelength of all the buckling phenomena addressed, only simply supported members under uniform bending are investigated. In particular, this work investigates the post-buckling behaviour and imperfection sensitivity of RCPS beams (i) exhibiting several wall numbers (6, 8, 10, 14, 20, 30) with distinct combinations of circumradius-to-thickness ratios (ii) having distinct lengths, and (iii) containing critical-mode initial geometrical imperfections with several amplitudes. Relevant displacement profiles and modal participation diagrams are provided along trivial and non-trivial equilibrium paths, in order to draw meaningful conclusions concerning the post-buckling behaviour of RCPS tubes under bending. For comparison and validation purposes, ABAQUS shell finite element results are also presented.

Large deflection stability of axially functionally graded tapered cantilever column

This article studies the large deflection stability of axially functionally graded (AFG) cantilever column for analyzing post-buckling behavior. Consideration is given to a nonlinearly tapered column with a regular polygon cross section, whose volume is constant. The governing differential equations of the problem are derived based on the large deflection beam theory. To calculate the elastica and buckling load of the AFG column, the differential equations are solved with the direct integration method together with the nonlinear solution method. The computed results are compared with those reported in literature and obtained from finite element method. Numerical examples are provided to ascertain the effects of the geometric and material parameters on the elastica and buckling load. The elastica shape is shown to depend on applied load and column properties, and the optimal shape such that the AFG column with fixed volume enables to bear the maximum buckling load is discussed.

Buckling optimization of axially functionally graded columns having constant volume

ABSTRACT In this article, the buckling optimization of axially functionally graded (AFG) columns to maximize the buckling capacity is studied. Consideration is given to an AFG column having a tapered regular polygon cross section and variable material properties. The governing differential equation is derived based on Euler–Bernoulli beam theory with the relevant boundary conditions and is solved using the direct integration method combined with a determinant search algorithm. The computed buckling loads are compared with those presented in the literature and obtained from finite element analysis. Numerical examples for buckling load and buckled mode shape are given to highlight the effect of parameters related to the Young's modulus, cross-sectional shape, tapering and column volume. In particular, the geometry and material parameters that provide buckling optimization at constant volume of the column are analysed.

Cushioning energy absorption of paper corrugation tubes with regular polygonal cross-section under axial static compression

Abstract The paper corrugation tube is an innovative kind of energy absorbing structure and shock absorber which can play an important role on the cushioning energy absorption for airdrop equipments and transportation packaging. The deformation characteristics and failure modes of the regular triangle, quadrangle, pentagon and hexagon paper corrugation tubes were comparatively studied by a series of axial static compression experiments, the cushioning energy absorption was evaluated by the seven characteristic parameters (e.g. initial peak force, mean crush force, total energy absorption, specific energy absorption, crush force efficiency, unit area energy absorption and stroke efficiency), and the influences of tube direction, cross-sectional shape, tube length and compression rate on failure modes and cushioning energy absorption were analyzed and compared. These researches showed that the tubes along X direction only have the accordion deformation mode, yet the tubes along Y direction have four deformation modes including steady state progressive buckling, Euler buckling, angular tear and transverse shear. For the paper corrugation tubes along Y direction, the cross-sectional shape has obvious influence on the cushioning energy absorption of structures, and the specific energy absorption and unit area energy absorption of regular triangle and pentagon tubes are better than those of the tubes with regular quadrilateral and hexagonal cross-section at compression rates of 12 and 48mm/min. The tube length of 150 mm or compression rate of 72 mm/min would cause the increase of contribution proportion of non-ideal deformation mode and the decrease of cushioning properties. The paper corrugation tubes along X direction have more stable and controllable deformation mode, yet the paper corrugation tubes along Y direction have better cushioning energy absorption.

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.

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.

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

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.

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.

A model for functionally graded materials

Abstract Modelling the mechanical properties of functionally gradient materials (FGMs) is central for engineers to accurately predict their mechanical behaviors. Beam models for FGMs with regular polygonal cross-sections are developed. It is assumed that material properties of the inner core are constant, and the outer shell gradually change by a power-law throughout the height of the regular polygonal cross-section. The analytical solutions of bending, buckling and free vibration behaviors of proposed FG beams modelled by the Euler‒Bernoulli beam theory and refined Timoshenko beam theory are obtained. In addition, the effects of aspect ratio, Young's modulus ratio, power-law index and topology number on the mechanical behaviors of the FG beams are investigated.

Large Deflections and Buckling Loads of Cantilever Columns with Constant Volume

This paper deals with the large deflections and buckling loads of tapered cantilever columns with a constant volume. The column member has a solid regular polygonal cross-section. The depth of this cross-section is functionally varied along the column axis. Geometrical nonlinear differential equations, which govern the buckled shape of the column, are derived using the large deflection theory, considering the effect of shear deformation. The buckling load of the column is approximately equivalent to the load under which a very small tip deflection occurs. In regard to the numerical results, both the elastica and buckling loads with varying column parameters are discussed. The configurations of the strongest column are also presented.

On the buckling of elastic rings by external confinement.

We report the results of an experimental and numerical investigation into the buckling of thin elastic rings confined within containers of circular or regular polygonal cross section. The rings float on the surface of water held in the container and controlled removal of the fluid increases the confinement of the ring. The increased compressive forces can cause the ring to buckle into a variety of shapes. For the circular container, finite perturbations are required to induce buckling, whereas in polygonal containers the buckling occurs through a linear instability that is closely related to the canonical Euler column buckling. A model based on Kirchhoff-Love beam theory is developed and solved numerically, showing good agreement with the experiments and revealing that in polygons increasing the number of sides means that buckling occurs at reduced levels of confinement.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

The vibration behaviour of thin-walled regular polygonal tubes

This paper addresses the free vibration behaviour of single-cell thin-walled tubes with regular convex polygonal cross-section (RCPS) and provides an extensive analysis of the resulting natural frequencies and associated vibration mode shapes. A semi-analytical approach is adopted, which is based on the generalised beam theory (GBT) specialisation for RCPS recently proposed by Gonçalves and Camotim (2013) [1] and subsequently employed to obtain insightful conclusions concerning the buckling behaviour of RCPS tubes (Gonçalves and Camotim (2013) [2,3]). This approach makes it possible to obtain closed-form analytical solutions and also acquire in-depth knowledge concerning the mechanics of the vibration problem, through the well-known GBT modal decomposition features. Attention is paid to local (plate-like), extensional, torsional and distortional vibration modes, as well as their interaction.

Surface effects on the persistence length of nanowires and nanotubes

Surface effects on the persistence length of quasi-one-dimensional nanomaterials are investigated by using the theory of surface elasticity and the core–shell model of nanobeams. A simple and unified expression is provided to determine the persistence length of nanowires and nanotubes with any regular polygonal cross-sections. It is demonstrated that surface effects have a distinct influence on the persistence length when the characteristic sizes of materials shrink to nanometers. This work is helpful not only for understanding the size-dependent behavior of nanomaterials but also for the design of devices based on nanotubes or nanowires.

Principle Analysis of Profiled Bar Turning Peeling Machine

Through the study of regular polygon cross section continuous forming processing technology of rotary cutting machine, this article designed a profiled bar turning peeling machine. This machine is mainly composed of workpiece axis, cutter axis, feed device and pulling device, etc . Parallel mounted, workpiece axis and cutter axis rotate at a rotational speed ratio in the same direction so as to form complex turning motions, during which the cutting track of the knifepoint relative to workpiece axis forms a shape of approximate linear closed curve, at the same time, feed device and pulling device pull workpiece moving along the axis, through which this machine can complete a turning finish of a whole workpiece at a time. This article analyzed the turning peeling principle of profiled bar, established a motion trajectory equation for the knifepoint relative to the workpiece axis, analyzed the processing straightness error of turned profiled bar, and then derived the error calculation formula.