Complex Cross-sectional Shape Research Articles

Local buckling behaviour of web perforated cold-formed steel lipped channel columns

To connect beams and bracings with storage rack uprights, closely spaced perforations are provided along the web, flanges, and rear flanges of uprights. These perforations can significantly lower the ultimate capacity of such compression members with the possible influence of its natural buckling modes. This capacity reduction can depend on various parameters such as (a) geometrical shape, proportioning of cross-section, and stiffeners; (b) perforation shape, size, spacing, and location; (b) slenderness of member, cross-section, and elements of cross-section; and (d) material properties. A thorough understanding of the influence of the above-mentioned factors is necessary for the accurate strength prediction of perforated Cold-formed steel (CFS) compression members. Even though the current design standards are updated for the accurate strength prediction of unperforated CFS compression members, they do not collectively account for the influence of all the aforementioned factors on the load-carrying capacity of the perforated CFS members, particularly for the local buckling capacity. Though the Direct Strength Method (DSM) of design is the most accepted method for accurate strength prediction of CFS members even for complex cross-sectional shapes, recent research on the strength evaluation of perforated CFS members using DSM has emphasized the need for refinement in DSM. The Modified Direct Strength Method (MDSM), which accounts for the simultaneous buckling of flanges and web, includes the cross-section aspect ratio and cross-section slenderness to predict more accurately the local buckling design strength. However, it was developed only for unperforated specimens. Hence, a systematic experimental and numerical investigation was done to understand the influence of the perforation in the local buckling behavior of the lipped channel section. In total, 14 specimens, including 2 unperforated and 12 web perforated CFS lipped channel stub columns were physically tested with fixed support conditions. The Finite Element Analysis using ABAQUS software was used to conduct an extensive parametric numerical study. The results were used to compare the strength curves of DSM and MDSM and the modification in the design curves has been proposed by considering the erosion in strength due to the presence of perforation.

Simplification of the calculation scheme for determining the stress state of non-thin cylindrical shells with a complex cross-sectional shape ellipticity

An alternative to full-scale experiments is computer simulation, which allows studying a variety of states, phenomena, processes, etc. occurring in the environment.
 Conducting a computational experiment is an integral part of the design phase of new structures and their elements. One of the important issues is the choice of research model, feasible calculation scheme and possibility of its simplification.
 This research investigates orthotropic non-thin cylindrical shells with corrugated ellipses as cross sections, which has the two-parameter deviation of the cross-section shape from a circular one. Considered are shells, for which the cross-section curvature radius of the reference surface has the positive sign. The shells are subjected to internal pressure under conditions of simple support on the ends.The subject of the study is the stress state of shells and, as a consequence, the establishment of the relationship between the geometric parameters of the reference surface of the cross sections and the possibility of simplifying the calculation scheme (excluding from consideration the parameter characterizing ellipticity).The problem is solved using the spatial model of linear elasticity theory based on the method of approximation of functions by discrete Fourier series.For the class of considered shells, we find the limits of possible simplification of the calculation scheme during calculations on durability with use of the fourth theory of durability (the theory of the greatest specific potential energy), due to exclusion from consideration of the parameter, which characterizes ellipticity of corrugated cylindrical shells.The cross-sectional radius of curvature of the reference surface in the zone of greatest rigidity was chosen as a criterion for the possibility of using a simplified scheme. It is found that a simplified scheme can be used when the cross-section curvature radius of the reference surface of elliptical corrugated cylindrical shells in this section differs from that for circular corrugated shells by no more than 17%.

Design of an Intermediate Die for the Multi-Pass Shape Drawing Process.

The multi-pass shape drawing process is mainly used in metal forming processes to manufacture long components with constant arbitrary cross-sectional shapes along their lengths. The cross-roller guide is a typical component that is manufactured by a multi-pass shape drawing process. The cross-roller guide is mostly used in optical measurement equipment where high-precision movement is required. Therefore, the dimensional accuracy of the cross-roller guide is very important since it can influence precision linear motion. However, the unfilled defects can occur in a case where the product has a complex cross-sectional shape. In this study, a new design method for an intermediate die is suggested by using an equal-radial-velocity variation method in order to reduce the unfilled defects. The proposed design method can reduce the unfilled defects by minimizing the radial velocity variation in the deformation zone of the drawing die. The intermediate die was designed by geometrical information of the final product without prior finite element (FE) analysis. The suggested method was applied to design the multi-pass shape drawing process for manufacturing the cross-roller guide. FE analysis was performed to validate the effectiveness of the proposed method in comparison to the conventional design method that uses equipotential lines in the multi-pass shape drawing process. Finally, a shape drawing experiment was performed to compare the target shape and the FE analysis with the experimental data.

Influence of the punch with concave cutting-edge on the blanking force in micro punching process

Micro blanking machining is a promising manufacture technology to realize mass production of micro parts efficiently. In the process of blanking, the blanking force is significant to the punch, die, and sheet workpiece. In order to investigate the influence of cutting-edge shape of the punch on the micro blanking process, a self-developed micro combined EDM and blanking machine tool is applied in this paper. A punch with concave cutting-edge is capable to be fabricated online through a series of processing based on micro EDM: 3D milling, wire electrical discharge grinding and reverse EDM copy machining techniques. Then the punch and die are accurately matched online due to the preparation of them in the same coordinate system. Micro blanking parts and punching parts with the complex cross-sectional shape is obtained by using the online fabricated punch with flat cutting-edge and concave cutting-edge respectively in the workpiece of stainless steel SUS304 foil. The characteristic of blanking force varying with time indicates that the blanking force is significantly reduced in the case of concave cutting-edge, meanwhile, both blanking parts and punching parts have the high quality.

Pseudo-static simplified analytical solution for seismic response of deep tunnels with arbitrary cross-section shapes

Tunnels located in seismic active areas must support not only static loads exerted by the ground under gravity but also seismic loads from earthquake events. Current analytical solutions for seismic analysis of tunnel structures are limited to circular or rectangular tunnels but not available for tunnels with other complex cross-section shapes, such as straight-wall-arch-shaped or semi-rectangular-shaped tunnels. This paper presents a unified simplified analytical solution for deep tunnels with arbitrary cross-section shapes subjected to seismic loading. Since the cross-section dimension of tunnels is normally much smaller than the wavelength of ground peak velocities, the structure can be designed using the pseudo-static approach. The ground and the tunnel liner are assumed to be elastic, homogeneous, and isotropic in plane strain condition. Two different contact conditions, no-slip and full-slip conditions, are considered at the liner-ground interface. The complex variable theory combined with the conformal mapping technique are employed to obtain closed-form solutions for tunnel deformation and stresses. The proposed solution is verified by providing comparisons between its results and those from the finite element program ABAQUS. Furthermore, parametric analyses are carried out to investigate the influence of soil-structure relative stiffness ratio, cross-section shape, height-span ratio and thickness of middle wall on tunnel responses.

METHODOLOGY OF THE TESTS OF FRAGMENTS OF MULTI-HOLLOW SLABS OF FORMLESS MOLDING WITH PINCHED SUPPORT ZONES

The problem of determining the moment of formation of normal cracks in bending reinforced concrete elements with a complex cross-sectional shape, clamped at one end in brickwork and operating under the action of a negative bending moment is considered. A technique for testing prototypes of hollow-core slabs without formwork is presented. The purpose of the experiment is to determine the angles of rotation of the support nodes of hollow-core slabs without formwork, embedded in brickwork. The design of an installation for testing experimental specimens until the moment of cracking is presented. A diagram of the arrangement of measuring instruments is given to determine the deformation of the support unit at the place where the slab is embedded in the masonry, the defl ection of the prototype at the place of load application, the deformation of the brickwork simulating the wall of a multi-storey building.

Substantiation of the influence of the channel shape and the roughness of machine canals on the pressure loss of irrigation pumping stations

To take into account the influence (on the value of head losses) of the channel cross-sectional shape and the presence of a flow with a free surface in it, additional correction factors are introduced (when using the concept of hydraulic radius), as well as new dependencies and formulas for determining the coefficient of hydraulic friction are presented, taking into account the influence of the morphometric elements of the channel on the hydraulic resistance of the machine channels of pumping stations. The article presents the results of hydraulic studies in free-flow and pressure water pipelines, the results of which showed that the dependencies obtained for calculating hydraulic resistance in round pressure pipes cannot be extended without appropriate adjustments to the pressure-free channels (provided that the pipe diameter is replaced in the corresponding calculations D-value 4R, where R-hydraulic radius). This position is justified by the presence of a number of factors that distinguish the pressure movement of liquid in pipes from its free-flow movement in the channels, where there is a free flow surface, a wider range of roughness of the channel bottom and walls, a different (than in pipes) distribution of tangential stresses along the wetted perimeter, the possibility of two different flow states (depending on the slope of the channel bottom). The work also considers the general equation of fluid motion in free-flow channels and the functional dependences of the hydraulic friction coefficient on the Reynolds number, relative roughness and on the shape of the free section of the channel; resistance formulas, first for the simplest channels with respect to the cross-sectional shape (round and infinitely wide rectangular), and then for channels with a more complex cross-sectional shape.

Constrained optimization of anti-symmetric cold-formed steel beam-column sections

Flexibility in the manufacturing of cold-formed steel (CFS) cross-sectional shapes provides a unique opportunity to improve the load-carrying capacity of these elements, leading to more efficient and economic structural systems. This paper presents a practical constrained optimization methodology for pin-ended anti-symmetric CFS beam-columns members with different lengths subjected to various combinations of axial compression and bending moment. The optimization process is carried out using a Genetic Algorithm (GA) with respect to buckling resistance of CFS elements determined according to the Direct Strength Method (DSM). In total, 132 CFS beam-columns with three different lengths (1000, 2000 and 3000 mm) and eleven different cross-sections are optimized under concentrically compressive loads with different levels of eccentricities varying from 0 to 30 mm. Each cross-section is formed using a certain number of fold-lines of steel plate, while the length and angle of the constituent elements of the cross-section are considered as the main design variables. To provide more practical beam-column elements, end-use constraints as well as a range of practical manufacturing and construction limitations are imposed on the selected cross-sections during the optimization process. A standard commercially available anti-symmetric Z section is taken as a starting point of optimization and used to assess the efficiency of the optimized sections. The results show that, for the given plate width and thickness, the adopted optimization process can significantly increase the strength of beam-column members on average 62%, 92%, and 188% for the short, medium and long length elements, respectively, compared to those with the standard section. It is also demonstrated that using more complex cross-sectional shapes does not necessarily provide higher strength for beam-column members. Finally, to verify the efficiency of the optimized sections, detailed nonlinear finite element models are developed using ABAQUS software. The developed models should prove useful for the efficient design of CFS beam-column elements in practice.

3D simulation of single bubble dynamics in a microchannel with a complex cross-sectional shape

The relevance of a study of bubbly liquid dynamics in porous media is due to a wide range of their use in technological and industrial processes. This work is dedicated to the numerical study of the dynamics of single incompressible bubbles in a viscous fluid flow in a microchannel with a cross-section in the shape of a deltoid. This geometry is due to the similarity with the domain between closely packed cylindrical fibers, forming a porous medium, for example, in the manufacturing of composite materials. In the present study for solving the considered problems, the boundary element method (BEM) was chosen as a basis of the numerical approach, since all calculations were associated only with boundaries. BEM is effective in studying 3D problems in the domains with complex geometry and modelling objects with arbitrary deformation. The influence of the initial radius of the bubble, its position relative to the channel centerline on the bubble deformation, relative velocity of the mass center of the bubble to the average flow velocity in the channel is considered.

Effect of multi-point roller dies on the forming accuracy of profile in flexible 3D stretch bending technology

With the increasing demand for parts with large sizes and complex cross-sectional shapes, the required target shapes are increasingly difficult to meet. In this paper, a flexible 3D stretch bending device has been developed, which can form complex cross-sectional 3D parts with 2 degrees of freedom at one time and can form large sizes 3D parts. Compared with traditional monolithic molds, discrete molds using in flexible 3D stretch bending forming are more convenient for shape adjustment of target profile. The multi-point roller dies are composed of multiple different roller-type die units. In order to better evaluate the forming accuracy of 3D parts, the influence of the number, shape, and surface of the roller dies on the forming results is discussed. The influence of different parameters on the forming accuracy is studied by numerical simulation, and the results are compared with the experimental results. From the perspective of forming accuracy, the influence of FSBR process and different parameters on the forming result is analyzed. Analysis of the dimple and shape errors of the FSBR parts shows that the number, shape, and surface of RDU directly affect the forming accuracy. By modifying the die parameters, the surface dimples can be reduced and the forming accuracy can be improved.

Analytical Sensitivity Analysis Method of Cross-Sectional Shape for Thin-Walled Automobile Frame Considering Global Performances

At the conceptual design stage, thin-walled beams (TWBs) with the complex cross-sectional shapes are extensively used to compose the automobile frame. Thus, the performances of automobile frame are determined by cross-sectional shapes of TWBs. Currently, the modifications of complex cross-sectional shapes depend on the experience of engineers, which often causes the design risk. Meanwhile, to our knowledge, the previous studies mainly focused on the regular cross sections and paid little attention for the complex cross-sectional shape for the automobile frame. Therefore, this paper proposes an analytical sensitivity analysis method to modify the complex cross-sectional shapes. This method regards the coordinates of points and the thicknesses of sheets as design variables to describe the cross-sectional shapes. The bending stiffness, torsional stiffness and frequency are used to evaluate the performances of automobile frame. Finally, an example of the RAV4 automobile frame verifies that the analytical sensitivity analysis method can effectively guide the modification of the cross-sectional shape and achieve the lightweight automobile frame.

Multi-objective cross-sectional shape and size optimization of S-rail using hybrid multi-criteria decision-making method

This study proposes a multi-objective lightweight and crashworthiness optimization design of complex cross-sectional shape and size of S-rail employing a hybrid multi-criteria decision-making (HMCDM) method. Several S-rails with special cross-sectional shapes of the reinforcement plate are established and compared. Response surface models with different orders are established considering the complex cross-sectional shapes and sizes. The objective function chosen for the two objectives is the specific energy absorption (SEA) and the peak force (PF). Meanwhile, the metrics for the three-objective are the PF, the total mass (M), and the energy absorption (EA). Two-objective Pareto fronts are obtained by the three-objective optimization confronting. Different multi-criteria decision-making methods are used to find the trade-off optimum points from the Pareto fronts. Results indicate that the proposed HMCDM method, including the technique for order preferences by similarity to ideal solution, gray relational analysis, and entropy weight, demonstrates a good trade-off frontier solution. In the case of a slight increase in M, the EA and SEA performances of the optimal model are greatly improved compared with the S-rail without a stiffener. Compared with the initial optimization model, the M of the optimal model is reduced by 25.62%, and the performance is improved. Therefore, the design of the cross-sectional shape and size of the S-rail and hybrid method can improve the crashworthiness.

Influence of the shape of the pressureless trapezoidal channel and roughness on the pressure loss of the machine channels of the pumping stations

In this work, we consider the general equation of fluid motion in pressureless channels and the functional dependences of the coefficient of hydraulic friction on the Reynolds number, relative roughness, and the shape of the live section of the channel, as well as the resistance formulas for the simplest channels with respect to the cross-sectional shape (round and infinitely wide rectangular), and then for channels with a more complex cross-sectional shape. To take into account the effect (on the pressure loss) of the channel cross-sectional shape and the presence of a flow with a free surface in it, additional correction factors are introduced (using the hydraulic radius concept). In conclusion, it is concluded that the values of the mentioned correction factors can and should be refined only as a result of the relevant experiments. The work also examined the patterns of hydraulic resistance in engine channels of the correct form of a live section with uniform turbulent fluid motion. Formulas of hydraulic resistance in the machine channels of a simple and complex outline of a live section are given.

The effects of morphometric elements of the channel on hydraulic resistance of machine channels of pumping stations

Presents the results of hydraulic studies in pressureless and pressure water conduits, the results of which showed that the dependences obtained for calculating the hydraulic resistance in round pressure pipes cannot be distributed without the corresponding adjustments of pressureless channels (provided that the diameter of the pipe is replaced in the corresponding calculations with a value where hydraulic radius). In particular, it follows (and this is confirmed by the data of the corresponding experimental studies published in the literature) that in the case of pressureless channels, the pressure loss coefficient, and therefore the pressure loss, depends not only on the relative roughness and Reynolds number, but also on the shape of the cross section the channel. Moreover, if for hydraulically smooth pressureless channels this dependence can be considered to a first approximation clarified, then for channels whose wetted surface is characterized by the presence of a certain roughness, the question of its influence, as well as the shape of the channel cross section on the pressure loss, is far from roughly approximate solution. The paper also considers the general equation of fluid motion in pressureless channels and the functional dependences of the coefficient of hydraulic friction on the Reynolds number, relative roughness, and on the shape of the living section of the channel; resistance formulas are first for the simplest with respect to the cross-sectional shape of the channels (round and infinitely wide rectangular), and then for channels with a more complex cross-sectional shape. To take into account the effect (on the pressure loss) of the channel cross-sectional shape and the presence of a flow with a free surface in it, additional correction factors are introduced (using the hydraulic radius concept) as well as new dependencies and formulas for determining the hydraulic friction coefficient are given, s taking into account the influence of morphometric elements of the channel on the hydraulic resistance of the machine channels of pumping stations.

High-Throughput Particle Concentration Using Complex Cross-Section Microchannels.

High throughput particle/cell concentration is crucial for a wide variety of biomedical, clinical, and environmental applications. In this work, we have proposed a passive spiral microfluidic concentrator with a complex cross-sectional shape, i.e., a combination of rectangle and trapezoid, for high separation efficiency and a confinement ratio less than 0.07. Particle focusing in our microfluidic system was observed in a single, tight focusing line, in which higher particle concentration is possible, as compared with simple rectangular or trapezoidal cross-sections with similar flow area. The sharper focusing stems from the confinement of Dean vortices in the trapezoidal region of the complex cross-section. To quantify this effect, we introduce a new parameter, complex focusing number or CFN, which is indicative of the enhancement of inertial focusing of particles in these channels. Three spiral microchannels with various widths of 400 µm, 500 µm, and 600 µm, with the corresponding CFNs of 4.3, 4.5, and 6, respectively, were used. The device with the total width of 600 µm was shown to have a separation efficiency of ~98%, and by recirculating, the output concentration of the sample was 500 times higher than the initial input. Finally, the investigation of results showed that the magnitude of CFN relies entirely on the microchannel geometry, and it is independent of the overall width of the channel cross-section. We envision that this concept of particle focusing through complex cross-sections will prove useful in paving the way towards more efficient inertial microfluidic devices.

UV-NIR femtosecond laser hybrid lithography for efficient printing of complex on-chip waveguides.

We propose UV-IR femtosecond laser hybrid lithography for the efficient printing of complex on-chip waveguides, which offers good performance in terms of processing efficiency and accuracy. With this three-dimensional printing technology, waveguides with complex cross-section shapes, such as owls and kittens, can be easily fabricated with an efficiency increased by 1500% (for ${6}\;\unicode{x00B5} {\rm m}\; \times \;{6}\;\unicode{x00B5} {\rm m}$6µm×6µm). In addition, a circular cross-section waveguide with an extremely low birefringence and complex ${8} \times {8}$8×8 random walk networks were quickly customized, which implies that in the design and preparation of the large-scale optical chips, the proposed maskless method allows for the preparation of highly customized devices.

Fabrication of micro punching mold for micro complex shape part by micro EDM

Micro punching process is suitable for mass production of micro parts. It is a challenge to fabricate micro punching mold with complex cross-sectional shape on-machine. The micro punching system’s structure design has to meet the requirement of large punching force. In this study, a micro punching system has been developed with a micro electrical discharge machining (EDM) module. A series of machining operations, from the fabrication of micro molds to punching, have been completed with no secondary clamping error. The micro die and reversed electrode are prepared using micro EDM milling. The micro punch is fabricated using reversed electrode. The punching clearance is around 11 μm. Complex shape punched holes and blanked parts have been successfully fabricated on copper, brass, 304 stainless steel, and 3J21 alloy. After punching, there was no damage on the edges of micro die and micro punch. The key dimensional error of blanked part varies by different materials, which is less than 2.5 μm.

Analysis of fully developed flow and heat transfer through n-sided polygonal ducts with round corners using the Galerkin weighted residual method

The Galerkin weighted residuals method is extended solve the laminar, fully developed flow and heat transfer of Al2O3-water nanofluid inside polygonal ducts with round corners for the constant heat flux and uniform wall temperature boundary conditions. Using the method, semi-analytical, closed-form solutions are obtained for the friction coefficient and the Nusselt number in terms of the radius of the round corners for the triangular, rectangular, hexagonal, and octagonal ducts. The effects of varying the radius of the round corners and the volume fraction of the nanoparticles on the friction coefficient and the Nusselt number are analyzed. The results show that the friction factor and the average Nusselt number increase with increasing the radius of the round corners. The study indicates that the Galerkin weighted residuals method is an accurate and efficient technique to obtain closed-form solutions for the flow and temperature fields in ducts with complex cross sectional shapes.

On turbulent friction in straight ducts with complex cross-section: the wall law and the hydraulic diameter

We develop predictive formulae for frictional resistance in ducts with complex cross-sectional shape based on the use of the log law and neglect of wall shear stress non-uniformities. The traditional hydraulic diameter naturally emerges from the analysis as the controlling length scale for common duct shapes such as triangles and regular polygons. The analysis also suggests that a new effective diameter should be used in more general cases, yielding corrections of a few percent to friction estimates based on the traditional hydraulic diameter. Fair, but consistent, predictive improvement is shown for duct geometries of practical relevance, including rectangular and annular ducts, and circular rod bundles.

Design of Experiment as a powerful tool when applying Finite Element Method: a case study on prediction of hot rolling process parameters

The ultimate goal in hot roll pass design is to manufacture a rolled product with the required dimensional accuracy, defect free surface, and mechanical properties. The proper selection of process parameters is crucial to meet increasing requirements for desired quality and geometrical properties of rolled products. Due to the complex behavior of the metal flow at high temperatures and the severe plastic deformations in shape rolling, most efforts that have been made so far only rely upon the practical experience gained by operators. The large number of variables involved and the difficulty in investigating the process characteristics, make the use of finite element (FE) tools an effective and attractive opportunity towards a thorough understanding of the rolling process. In this work, Design of Experiment (DOE) is proposed as a powerful and viable method for the prediction of rolling process parameters while reducing the computational effort. Nonlinear 3D FE models of the hot rolling process are developed for a large set of complex cross-section shapes and validated against experimental evidences provided by real plant products at each stage of the deformation sequence. Based on the accuracy of the validated FE models, DOE is applied to investigate the flat rolling process under a series of many parameters and scenarios. Effects of main roll forming variables are analyzed on material flow behavior and geometrical features of a rolled product. The selected DOE factors are the workpiece temperature, diameter size, diameter reduction (draught), and rolls angular velocity. The selected DOE responses are workpiece spread, effective stresses, contact stresses, and rolls reaction loads. Eventually, the application of Pareto optimality (a Multi-Criteria Decision Making method) allows to detect an optimal combination of design factors which respect desired target requirements for the responses.