Elliptical Section Research Articles

Utilization finite element and machine learning methods to investigation the axial compressive behavior of elliptical FRP-confined concrete columns

Nowadays, elliptical sections are among the geometric shapes that are becoming more and more popular in the architecture world. Finite element analysis (FEA) software, such as ABAQUS, is used to simulate elliptical concrete columns confined with fiber reinforced polymer (FRP) jackets based on experimental data published in the literature. The validity of the finite element modeling (FEM) approach was confirmed by comparing it to experimental data obtained from 45 specimens in existing studies, demonstrating a favorable agreement. Additionally, a parametric study was also carried out, which included simulating 40 more specimens, resulting in a total of 85 specimens for analysis. The effect of various test variables such as sectional aspect ratio, the amount of FRP layers, and concrete strength on the elliptical column’s behavior is investigated. The axial compressive strength is predicted using current models from the literature. The outcomes revealed that the higher unconfined concrete strength decreased FRP confinement efficacy. Insufficient confinement with post-peak softening is more likely in FRP-confined high strength concrete columns, especially if the confinement was not stiff enough. Also, by adding more FRP layers, the stress and strain capabilities of elliptical concrete columns confined with FRP composites are improved. Physical experiments require a significant investment of time and resources, but they can produce valuable results. Finite element analysis, on the other hand, depends heavily on the modeler's competence and can minimize the number of experiments required by employing computer simulation, but it also requires high computer settings. In recent years, there has been a major advancement in the usage of machine learning (ML) algorithms in the applications of FRP composites with different concrete components. Taking this into consideration, this investigation is extended to estimate the compressive strength of elliptical FRP-confined columns using four tree-based ML algorithms including Decision Tree, Random Forest, Gradient Boosting and XGBoost. The XGBoost model achieved the highest predictive accuracy with the R2 values of 0.95 for both the compressive strength and axial strain targets.

A numerical study on the oscillatory dynamics of tip vortex cavitation

In this paper, we numerically study the mechanism of the oscillatory flow dynamics associated with the tip vortex cavitation (TVC) over an elliptical hydrofoil section. Using our recently developed three-dimensional variational multiphase flow solver, we investigate the TVC phenomenon at Reynolds number $Re = 8.95 \times 10^5$ via dynamic subgrid-scale modelling and the homogeneous mixture theory. To begin, we examine the grid resolution requirements and introduce a length scale considering both the tip vortex strength and the core radius. This length scale is then employed to non-dimensionalize the spatial resolution in the tip vortex region, the results of which serve as a basis for estimation of the required mesh resolution in large eddy simulations of TVC. We next perform simulations to analyse the dynamical modes of tip vortex cavity oscillation at different cavitation numbers, and compare them with the semi-analytical solution. The breathing mode of cavity surface oscillation is extracted from the spatial-temporal evolution of the cavity's effective radius. The temporally averaged effective radius demonstrates that the columnar cavity experiences a growth region followed by decay as it progresses away from the tip. Further examination of the characteristics of local breathing mode oscillations in the growth and decay regions indicates the alteration of the cavity's oscillatory behaviour as it travels from the growth region to the decay region, with the oscillations within the growth region being characterized by lower frequencies. For representative cavitation numbers $\sigma \in [1.2,2.6]$ , we find that pressure fluctuations exhibit a shift of the spectrum towards lower frequencies as the cavitation number decreases, similar to its influence on breathing mode oscillations. The results indicate the existence of correlations between the breathing mode oscillations and the pressure fluctuations. While the low-frequency pressure fluctuations are found to be correlated with the growth region, the breathing mode oscillations within the decay region are related to higher-frequency pressure fluctuations. The proposed mechanism can play an important role in developing mitigation strategies for TVC, which can reduce the underwater radiated noise by marine propellers.

Local buckling behaviour of Q690 high strength steel press-braked elliptical hollow section stub columns: Testing, numerical modelling, and design

This paper presents comprehensive investigations on the local bucking behaviour of Q690 high strength steel (HSS) press-braked elliptical hollow section (EHS) stub columns subject to concentric compression experimentally. In comparison with conventional hot-finished EHS or cold-rolled EHS, the press-braked EHS provides high precision, great construction productivity and the fabricated geometries are not limited to production assembly instrumentation. HSS press-braked EHS fabricated through press-braking process was expected to exhibit distinct behaviour compared with their counterparts constructed from the conventional fabrication routes. Well-understanding of their performance at the levels of material, and cross-section level is essential. Material properties were obtained through tensile coupon tests. Residual stresses in both membrane and bending types were measured and recorded and their impact on structural performance was also assessed. Initial local geometric imperfection measurements were conducted for all the specimens. In conjunction with experimental studies, the finite element (FE) models of Q690 HSS press-braked EHS stub columns were developed. The accuracy of the FE model for HSS press-braked EHS stub column was asserted by comparing the numerical predictions with the tested results. An extensive parametric study was conducted to generate structural performance data with a wider range of cross-section slenderness to complement the test data bank. The cross-section classification for conventional CHS codified in existing standards and the proposed slenderness limits by various researchers were evaluated. The existing slenderness limits cannot be extended to HSS press-braked EHS investigated in this study, a new slenderness limit is proposed. Moreover, the advanced design approaches of Direct Strength Method (DSM) and Continuous Strength Method (CSM) were assessed for their applicability to the cross-section resistance predictions of the examined EHS stub columns.

Volume-Preserving Shear Transformation of an Elliptical Slant Cone to a Right Cone

One nappe of a right circular cone, cut by a transverse plane, splits the cone into an infinite frustum and a cone with an elliptical section of finite volume. There is a standard way of computing this finite volume, which involves finding the parameters of the so-called shadow ellipse, the characteristics of the oblique ellipse (the cut) and, finally, the projection of the vertex of the cone onto the oblique ellipse. This paper shows that it is possible to compute that volume just by using the information of the shadow ellipse and the height of the cone. Indeed, the finite slant cone has the same volume of an elliptic right cone, with the base being the shadow ellipse of the cut portion and with the height being the distance between the vertex of the cone and the intersection of the height of the original cone with the cutting plane. This is proved by introducing a volume-preserving shear transformation of the elliptical slant cone to a right cone, so that the standard volume formula for a cone can be straightforwardly applied. This implies a simplification in the procedure for computing the volume, since the oblique ellipse—i.e., the difficult part—can be neglected because only the shadow ellipse needs to be determined.

Dual-energy computed tomography quality control: Initial experiences with a semi-automatic analysis tool

PurposeA quality control (QC) system for dual-energy CT (DECT) was developed. The scope of the QC system was to monitor both the constancy of the CT images and the software used in calculating the DECT derived maps. Longitudinal analysis was based on a standard imaging protocol, a commercial multi-energy phantom, and a semi-automatic analysis tool. MethodsThe phantom consisted of an elliptical body section with round slots for interchangeable inserts. It was scanned with 90kVp/Sn150kVp, automatic tube current modulation, and 9.6 mGy CTDIvol. From the two conventional CT images, scanner manufacturer’s software was used to provide virtual monoenergetic images at two different energies, effective atomic number (Zeff) maps, and iodine concentration maps. The images were analyzed using an open-source tool allowing user-selected statistics of interest. The means and standard deviations of the phantom background and the iodine, calcium, and water inserts were recorded. The QC tool is available at github.com/tomakela/dectqatool. ResultsThe obtained results were generally highly consistent over time, except for the smaller diameter iodine inserts. A small change inZeff was observed after a DECT software update. The developed QC tool aided the analysis robustness: the segmentations were modifiable when needed, and small rotations or air bubbles in the water insert were easily corrected. ConclusionThe developed QC system provided easy-to-use workflow for constancy measurements. A small deviation due to change in the post-processing was detected. The proposed imaging protocol and analysis steps, and the reported measurement variations can aid in determining action levels for DECT QC.

Axial resistance of elliptical hollow section K-joints made of high strength steel

The present study examined the axial resistance of welded elliptical hollow section (EHS) K-joints made of high-strength steel (HSS). The axial resistance of EHS K-joints was affected by a range of factors, including the geometrical parameters, orientations, chord pre-stress levels, and the mechanical properties of the high-strength steel grades. This research aimed to investigate the performance of welded EHS K-joints made of HSS under axial loading conditions with or without chord pre-stresses. Finite element analysis was employed for numerical simulations to analyze the nonlinear behaviour of EHS K-joints with HSS. It was observed from the numerical results that the orientation types significantly affected normalised resistance ratios. In contrast, β, γ, θ, and chord pre-stress levels had minimal impact, as comparisons were based on normalised resistance ratios. However, non-dimensional geometric parameters and chord pre-stress levels notably influenced the axial joint resistance of the HSS K-joints. As for predicting the axial resistances of EHS K-joints with HSS, the numerical results indicated that the existing reduction factor might be unsafe for the equivalent RHS method to be applied in the current design guides. Therefore, a new reduction factor was proposed for EHS K-joints with HSS that yield unsafe results.

Structural behaviour of cold-formed steel elliptical hollow section stub columns after exposure to ISO-834 fire curve

The present study undertakes the post-fire stub column behaviour of cold-formed steel elliptical hollow sections (CFS-EHS) by experimental and numerical analyses. A total of 18 CFS-EHS stub column specimens made up of four cross-section series was firstly prepared, heated in a gas furnace as per the ISO-834 standard fire and then naturally cooled down to ambient temperature. Four fire exposure temperatures of 300 °C, 550 °C, 750 °C and 900 °C were adopted. Details of the experimental campaign, e.g., specimen preparation, test procedures and results, are presented. Accurate finite element (FE) model was established to mimic the experimental responses from various perspectives. Exhaustive parametric studies were subsequently conducted on 224 post-fire CFS-EHS stub columns to generate substantial data. The test and FE results were compared with the strength calculations using the equivalent diameter method and equivalent rectangular hollow section method developed for hot-finished steel elliptical hollow sections without fire exposure, the Direct Strength Method (DSM) stipulated in the American Specification AISI S100, as well as the modified DSM previously calibrated for CFS-EHS without fire exposure. By replacing the material properties obtained at ambient temperature with the post-fire material properties in the aforementioned design methods, it is shown that the equivalent section methods and the existing DSM overly underestimate the column strengths, whilst the modified DSM yields precise and reliable strength estimations. It is recommended to adopt the modified DSM for calculating the residual compressive strengths of CFS-EHS stub columns after exposure to the ISO-834 standard fire.

Determination of the optimal shape of permanent magnets of a given volume providing maximum strength of their magnetic coupling

The ponderomotive force of the adhesion of two permanent magnets depends on their shape. We present the results of determining the optimal shape of ellipsoidal magnets providing maximum magnetic adhesion between them. The interaction of two halves of a magnet, which is an ellipsoid of revolution, and a magnet in the form of a long rod with an elliptical cross section, is analyzed. Analytical formulas for the cohesion forces in these cases are obtained. For a fixed mass or volume of magnets, the problem of optimizing the adhesion force is solved and a geometric shape which provide the maximum adhesion force is determined. It is shown that in the case of a magnet in the form of an ellipsoid of revolution, the maximum adhesion force of its halves (ignoring the magnetic tension on the side surfaces) is achieved at an eccentricity of 0.625958. The magnitude of the maximum adhesion force exceeds the adhesion force of the halves of a uniformly magnetized spherical magnet of the same volume by 1.7%. In this case, the adhesion area of the ellipsoidal magnet will be less than the adhesion area of the spherical magnet by 28%. The optimal form of a bar magnet with an elliptical section with the maximum force of adhesion of its halves at a fixed volume of the magnet is determined. A formula is derived for the ponderomotive magnetostatic force of the interaction between the halves of a bar magnet with an elliptical section and the maximum force of interaction. Numerical estimates for a sintered NdFeB bar magnet showed that the ponderomotive force of interaction with a cross-sectional radius of 5 cm can reach 2 tons per 1 m of length. The results obtained can be used to improve the efficiency of devices based on permanent magnets.

Stability and design of stainless steel hollow section columns at elevated temperatures

This paper investigates the stability and design of stainless steel circular, elliptical, square and rectangular hollow section (CHS, EHS, SHS and RHS) columns at elevated temperatures. Nonlinear shell finite element models are employed to conduct comprehensive parametric studies whereby extensive benchmark structural performance data on the behaviour and resistance of stainless steel hollow section columns at elevated temperatures is generated. In total, 26,760 cold-formed and hot-rolled austenitic, duplex and ferritic stainless steel CHS, EHS, SHS and RHS columns at elevated temperatures are taken into account, considering various member slendernesses, cross-section geometries, cross-section slendernesses and elevated temperature levels. New flexural buckling design rules are put forward for stainless steel hollow section columns in fire, which consistently considers the elevated temperature strength at 2% total strain f2,θ as the reference material strength for all cross-sections classes. The accuracy, safety and reliability of the proposed new design rules are assessed for a wide range of cases. Comparisons are also made against the results obtained through the column fire design rules of the European structural steel fire design standard EN 1993-1-2 [1]. It is demonstrated that the proposed new design rules furnish more accurate, safe-sided and reliable flexural buckling resistance predictions for stainless steel hollow section columns at elevated temperatures relative to the column fire design provisions of EN 1993-1-2 [1].

Cold-formed stainless steel elliptical hollow sections under combined biaxial bending and axial compression - Numerical modeling and design

This paper aims to investigate the cross-section response of cold-formed stainless steel (CFSS) elliptical hollow sections (EHS) under combined biaxial bending and axial compression. In the present study, an advanced finite element (FE) model was adopted to perform a comprehensive parametric study for CFSS EHS under combined biaxial bending and axial compression, with different stainless steel alloys, as well as a broad range of cross-section sizes, aspect ratios, loading eccentricities and angles. Numerical results obtained from the parametric study were compared with the design strengths calculated by the current design rules in European code EN 1993-1-4, American specification SEI/ASCE 8-02 and Australian/New Zealand standard AS/NZS 4673. In addition, the Continuous Strength Method (CSM) for CFSS circular hollow sections (CHS) under combined actions, was also evaluated for the design of CFSS EHS under combined actions. The comparisons revealed that the current design codes EN 1993-1-4, SEI/ASCE 8-02 and AS/NZS 4673 provided conservative and very scattered predictions for CFSS EHS under combined actions. The existing CSM can provide more accurate predictions than the current design codes (i.e., AS/NZS 4673, EN 1993-1-4 and SEI/ASCE 8-02), but a further improvement is needed. In the present study, a modified CSM is proposed for CFSS EHS under combined actions, which can achieve reliable and accurate design predictions.

Machine learning models for predicting the axial compression capacity of cold‑formed steel elliptical hollow section columns

Machine learning models for predicting the axial compression capacity of cold‑formed steel elliptical hollow section columns

Structural response and design of stainless steel hollow section columns at elevated temperatures

AbstractThis paper investigates the flexural buckling behaviour and design of stainless steel circular, elliptical, square and rectangular hollow section (CHS, EHS, SHS and RHS) columns at elevated temperatures through numerical modelling. Shell finite element models are utilised to perform numerical parametric studies whereby benchmark structural performance data are generated. A large number of cold‐formed and hot‐rolled austenitic, duplex and ferritic stainless steel CHS, EHS, SHS and RHS columns at elevated temperatures are taken into account, considering various cross‐section and member slendernesses. Since the fire design provisions provided in the European fire design standard EN 1993‐1‐2 for stainless steel columns are largely based on those originally developed for carbon steel columns, they typically lead to rather inaccurate ultimate resistance predictions for stainless steel columns at elevated temperatures. To address this, in the present study, a new flexural buckling design method for stainless steel hollow section columns at elevated temperatures is put forward. The accuracy, safety and reliability of the proposed design method and the provisions in EN 1993‐1‐2 are assessed. It is observed that the proposed fire design method leads to more accurate, safe‐sided and reliable flexural buckling resistance predictions for stainless steel hollow section columns at elevated temperatures relative to the provisions in EN 1993‐1‐2.

Local buckling response and design of stainless steel hollow sections at elevated temperatures

AbstractThe structural behaviour and design of stainless steel hollow sections in fire, including stainless steel (i) circular hollow sections (CHS), (ii) elliptical hollow sections (EHS), (iii) square hollow sections (SHS) and (iv) rectangular hollow sections (RHS), are explored in this paper. Shell finite element models of stainless steel CHS, EHS, SHS and RHS able to replicate their structural response at elevated temperatures are created. Numerical parametric studies are performed on cold‐formed and hot‐rolled austenitic, duplex and ferritic stainless steel CHS, EHS, SHS and RHS subjected to (i) pure compression, (ii) pure bending, (iii) combined axial compression and bending and (iv) combined bending and shear in fire, covering different cross‐section slendernesses and elevated temperature levels. Calibrated against the benchmark structural performance data obtained from the numerical parametric studies, the new design proposals for predicting the ultimate resistances of stainless steel CHS, EHS, SHS and RHS in fire put forward in Quan and Kucukler [1,2] are set out. It is demonstrated that relative to the design recommendations provided in the European structural steel fire design standard EN 1993‐1‐2, the proposed cross‐section design methods provide more accurate and safe‐sided ultimate resistance predictions for stainless steel CHS, EHS, SHS and RHS at elevated temperatures.

Gas-dynamic and mixing analysis of under-expanded hydrogen jets: effect of the cross section shape

Green hydrogen is expected to have a key role in the transition towards a carbon-neutral society, particularly in the transportation sector. Exploration of novel solutions for the direct injection of hydrogen in internal combustion engines (ICEs) is a main topic for both academia and industry. Here, the authors explore the gas-dynamic and mixing features of hydrogen under-expanded jets exiting from non-axisymmetric cross-sections, with the aim to provide guidelines for designing novel generations of ICE hydrogen injectors. Triangular and star shapes have been compared with elliptical and rectangular sections with different aspect ratios. Differences in the shock wave systems are reported, and explanations of the gas-dynamic mechanisms developed by each section are proposed. Non-uniformity in the radial expansion of the jet boundary has been noticed in all of the non-axisymmetric sections, leading to an axis switching of the jet in some cases. Differences in the radial mixing and axial jet penetration have been reported too, and a robust correlation with the vorticity distribution along the jet boundary has been observed.

Improving the Mechanical Properties of a Lattice Structure Composed of Struts with a Tri-Directional Elliptical Cylindrical Section via Selective Laser Melting.

In recent years, lattice structures produced via additive manufacturing have been increasingly investigated for their unique mechanical properties and the flexible and diverse approaches available to design them. The design of a strut with variable cross-sections in a lattice structure is required to improve the mechanical properties. In this study, a lattice structure design method based on a strut cross-section composed of a mixture of three ellipses named a tri-directional elliptical cylindrical section (TEC) is proposed. The lattice structures were fabricated via the selective laser melting of 316L alloy. The finite element analysis results show that the TEC strut possessed the high mechanical properties of lattice structures. Compression experiments confirmed that the novel lattice structure with the TEC strut exhibited increases in the elastic modulus, compressive yield strength, and energy absorption capacity of 24.99%, 21.66%, and 20.50%, respectively, compared with the conventional lattice structure at an equal level of porosity.

Geometric Characteristics of Simply Connected Planar Sections With Application to Airfoils

The presented work is to develop a numerical computation program to determine the geometrical characteristics of arbitrary simply connected planar sections and applications to airfoils. In the literature, there are exact analytical solutions only for some simple geometry such as circular, rectangular and elliptical sections. Hence our interest is focused on the search of approximate numerical solutions for more complex sections used in aeronautics. The used method is to subdivide the section in the infinitesimal triangular section with a single observer within the area having a suitable position. The characteristics of any triangle, given by the positions of these three nodes are known in the literature. Using the principle of compound surfaces, one can determine the geometric characteristics of the airfoil surface. The analytic function of the airfoil boundary is obtained by using the cubic spline interpolation because the airfoil is given in the form of tabulated points. An error estimation is done to determine the accuracy of the numerical computation.

Static strengths of cold-formed steel elliptical hollow section X-joints

The newly emerged elliptical hollow section (EHS) has a vast of structural and architectural merits and is favorable for engineers and designers. This paper presents an experimental investigation concerning the structural behavior of cold-formed steel EHS X-joints. Thirty elliptical hollow section X-joints with three different brace-chord orientations were carefully designed, fabricated by robotic gas metal arc welding and tested with the braces axially compressed. The width ratio between brace and chord (β) ranged from 0.29 to 1. The brace-to-chord thickness ratio (τ) ranged from 0.58 to 1.83 and the chord width-to-thickness ratio (2γ) ranged from 10.1 to 52.6. The static strengths, failure modes and load-deformation responses are discussed. The current codified design provisions do not cover the design of cold-formed steel elliptical hollow section X-joints investigated in this study. As the performance of EHS lies between the circular and rectangular hollow sections, the feasibility of the design provisions initially calibrated for conventional X-joints as specified in the CIDECT and Eurocode 3 with incorporation of equivalent section methods as well as the design recommendations previously proposed for hot-rolled steel elliptical joints was evaluated. In general, these design methods provide accurate strength predictions for cold-formed steel elliptical hollow section X-joints. Nevertheless, the scattering of predictions is still a concern and the design method shall be further improved.

Detection Accuracy of Colorimetric Water Quality Analyzer

The accuracy of the titration device for colorimetric water quality analysis is the key to its detection accuracy. In order to solve the problem of excessive titration of traditional Chinese medicine in the traditional titration method, a structure optimization scheme of a micro-peristaltic pump applied to a water quality analyzer was designed. By analyzing the phenomenon of periodic water backflow and the “creep” of the pump tube when the peristaltic pump is working, the pump tube is changed from a traditional circular section to an elliptical section; the eccentricity of the pump tube section is adjusted to improve the pressure characteristics of the pump tube and reduce the effect of the “creep”; Ansys is used for solid-fluid coupling and simulation and compared with the experimental results, and the reasons for the differences are analyzed. The experiment proves that the design scheme can improve the stability of the output flow compared with the original design, and the degree of reflux is also reduced to 20.72%, which meets the need of improving the detection accuracy of the water quality analyzer.

Study on the effect of inflow direction on the hydrodynamic characteristics of underwater manipulators

When operating in water, an underwater manipulator is subjected to different directions of flows. Thus, its hydrodynamic performance and flow-field evolution vary. Herein, the hydrodynamic coefficients and flow field characteristics of an underwater manipulator with different incoming flow directions in a subcritical range are studied. The effects of the different inflow directions on the hydrodynamic coefficients and the flow field evolution of the sectional shape, spacing, and arrangement order are numerically investigated. Results indicate that the hydrodynamic coefficients of the upstream circular section decrease at γ = 60° as the angle of the inflow direction increases. The root-mean-square value of the lift coefficient of the downstream elliptical section increases by a factor 1.5 with an increase in the inflow angle. When the elliptical section is upstream, the working attitude of the underwater manipulator is relatively stable. The research conclusions of this work will provide help for the precise positioning and fishing of underwater manipulators in the ocean.

Strength enhancement and stub-column behavior of cold-formed stainless steel elliptical hollow sections

This paper aims to investigate the strength enhancement, local geometric imperfections, and stub-column behavior of cold-formed (CF) stainless steel elliptical hollow sections (EHS) by using finite element methods. In the present study, an advanced numerical approach was used to conduct a comprehensive parametric study for CF stainless steel EHS with a wide range of cross-section dimensions and slenderness values as well as different stainless steel alloys. By analyzing the generated numerical data from the parametric study, the effects of cold-forming and material parameters on the strength enhancement were examined. Predictive models of the strength enhancement as well as the local geometric imperfections for CF stainless steel EHS are proposed. The slenderness limits for CF stainless steel circular hollow sections (CHS) and CF steel EHS in the existing design methods were assessed for CF stainless steel EHS. New slenderness limits are proposed for CF stainless steel EHS. In addition, the existing equivalent diameter method, the Continuous Strength Method (CSM) and the Direct Strength Method (DSM) were evaluated for the design of CF stainless steel EHS. Modifications on these existing design methods are proposed for CF stainless steel EHS, which can improve their accuracy.