Theory of Flexural Shear, Bending and Torsion for a Thin-Walled Beam of Open Section

Aspects of the general Vlasov theory are examined separately as applied to a thin-walled channel section cantilever beam under free-end end loading. In particular, the flexural bending and shear that arise under transverse shear and axial torsional loading are each considered theoretically. These analyses involve the location of the shear centre at which transverse shear forces when applied do not produce torsion. This centre, when taken to be coincident with the centre of twist implies an equivalent reciprocal behaviour. That is, an axial torsion applied concentric with the shear centre will twist but not bend the beam. The respective bending and shear stress conversions are derived for each action applied to three aluminium alloy extruded channel sections mounted as cantilevers with a horizontal principal axis of symmetry. Bending and shear are considered more generally for other thin-walled sections when the transverse loading axes at the shear centre are not parallel to the section = s centroidal axes of principal second moments of area. The fixing at one end of the cantilever modifies the St Venant free angular twist and the free warping displacement. It is shown from the Wagner-Kappus torsion theory how the end constrained warping generates an axial stress distribution that varies with the length and across the cross-section for an axial torsion applied to the shear centre. It should be mentioned here for wider applications and validation of the Vlasov theory that attendant papers are to consider in detail bending and torsional loadings applied to other axes through each of the centroid and the web centre. Therein, both bending and twisting arise from transverse shear and axial torsion applied to each position being displaced from the shear centre. Here, the influence of the axis position upon the net axial and shear stress distributions is to be established. That is, the net axial stress from axial torsional loading is identified with the sum of axial stress due to bending and axial stress arising from constrained warping displacements at the fixing. The net shear stress distribution overlays the distributions from axial torsion and that from flexural shear under transverse loading. Both arise when transverse forces are displaced from the shear centre.

GEOMETRICALLY NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS WITH GENERAL OPEN CROSS SECTION

Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.

A new finite element of spatial thin-walled beams

Based on the theories of Timoshenko＇s beams and Vlasov＇s thin-walled members, a new spatial thin-walled beam element with an interior node is developed. By independently interpolating bending angles and warp, factors such as transverse shear deformation, torsional shear deformation and their Coupling, coupling of flexure and torsion, and second shear stress are considered. According to the generalized variational theory of Hellinger-Reissner, the element stiffness matrix is derived. Examples show that the developed model is accurate and can be applied in the finite element analysis of thinwalled structures.

Nonlinear Finite Element Analysis of Thin-Walled Beam on Pre- and Post-Buckling Stiffness and Gauge Sensitivity Index

Lightweight design has a significant impact on reducing fuel consumption and harmful emission of conventional vehicles and improving driving range of electric vehicles. Reducing the thickness of components in vehicle bodies and closures is an efficient approach for weight reduction. Thickness reduction, however, will reduce structural stiffness, especially in the presence of lateral displacements of buckling when critical stress is reached. In this paper, nonlinear FEA models of a thin-walled beam with variable thickness are developed for calculating the changes of beam stiffness as to thickness reduction in the pre- and post-buckling stages. Next, these stiffness values are used to calculate gauge sensitivity of the beam, which changes with respect to beam thickness changes. It is concluded that the presence of buckling will reduce the beam stiffness, worsen the stress uniformity, and increase the gauge sensitivity value of the beam.

The Effects of the Longitudinal Axis of Loading upon Bending, Shear and Torsion of a Thin-Walled Cantilever Channel Beam

Three aluminium channel sections of US standard extruded dimension are mounted as cantilevers with x-axis symmetry. The flexural bending and shear that arise with applied axial torsion are each considered theoretically and numerically in terms of two longitudinal axes of loading not coincident with the shear centre. In particular, the warping displacements, stiffness and stress distributions are calculated for torsion applied to longitudinal axes passing through the section’s centroid and its web centre. The stress conversions derived from each action are superimposed to reveal a net sectional stress distribution. Therein, the influence of the axis position upon the net axial and shear stress distributions is established compared to previous results for each beam when loading is referred to a flexural axis through the shear centre. Within the net stress analysis is, it is shown how the constraint to free warping presented by the end fixing modifies the axial stress. The latter can be identified with the action of a ‘bimoment’ upon each thin-walled section.

Optimization of Fixture Number in Large Thin-Walled Parts Assembly Based on IPSO

There are lots of researches on fixture layout optimization for large thin-walled parts.Current researches focus on the positioning problem,i.e.,optimizing the positions of a constant number of fixtures.However,how to determine the number of fixtures is ignored.In most cases,the number of fixtures located on large thin-walled parts is determined based on engineering experience,which leads to huge fixture number and extra waste.Therefore,this paper constructs an optimization model to minimize the number of fixtures.The constraints are set in the optimization model to ensure that the part deformation is within the surface profile tolerance.In addition,the assembly gap between two parts is also controlled.To conduct the optimization,this paper develops an improved particle swarm optimization(IPSO)algorithm by integrating the shrinkage factor and adaptive inertia weight.In the algorithm,particles are encoded according to the fixture position.Each dimension of the particle is assigned to a sub-region by constraining the optional position range of each fixture to improve the optimization efficiency.Finally,a case study on ship curved panel assembly is provided to prove that our method can optimize the number of fixtures while meeting the assembly quality requirements.This research proposes a method to optimize the number of fixtures,which can reduce the number of fixtures and achieve deformation control at the same time.

Development of Fixture Layout Optimization for Thin-Walled Parts:A Review

An increasing number of researchers have researched fixture layout optimization for thin-walled part assembly during the past decades.However,few papers systematically review these researches.By analyzing existing literature,this paper summarizes the process of fixture layout optimization and the methods applied.The process of optimization is made up of optimization objective setting,assembly variation/deformation modeling,and fixture layout optimization.This paper makes a review of the fixture layout for thin-walled parts according to these three steps.First,two different kinds of optimization objectives are introduced.Researchers usually consider in-plane variations or out-of-plane deformations when designing objectives.Then,modeling methods for assembly variation and deformation are divided into two categories:Mechanism-based and data-based methods.Several common methods are discussed respectively.After that,optimization algorithms are reviewed systematically.There are two kinds of optimization algorithms:Traditional nonlinear programming and heuristic algorithms.Finally,discussions on the current situation are provided.The research direction of fixture layout optimization in the future is discussed from three aspects:Objective setting,improving modeling accuracy and optimization algorithms.Also,a new research point for fixture layout optimization is discussed.This paper systematically reviews the research on fixture layout optimization for thin-walled parts,and provides a reference for future research in this field.

Meter-Scale Thin-Walled Structure with Lattice Infill for Fuel Tank Supporting Component of Satellite:Multiscale Design and Experimental Verification

Lightweight thin-walled structures with lattice infill are widely desired in satellite for their high stiffness-to-weight ratio and superior buckling strength resulting fromthe sandwich effect.Such structures can be fabricated bymetallic additive manufacturing technique,such as selective laser melting(SLM).However,the maximum dimensions of actual structures are usually in a sub-meter scale,which results in restrictions on their appliance in aerospace and other fields.In this work,a meter-scale thin-walled structure with lattice infill is designed for the fuel tank supporting component of the satellite by integrating a self-supporting lattice into the thickness optimization of the thin-wall.The designed structure is fabricated by SLM of AlSi10Mg and cold metal transfer welding technique.Quasi-static mechanical tests and vibration tests are both conducted to verify the mechanical strength of the designed large-scale lattice thin-walled structure.The experimental results indicate that themeter-scale thin-walled structure with lattice infill could meet the dimension and lightweight requirements of most spacecrafts.

An electromagnetic semi-active dynamic vibration absorber for thin-walled workpiece vibration suppression in mirror milling

As critical components of aircraft skins and rocket fuel storage tank shells,large thin-walled workpieces are susceptible to vibration and deformation during machining due to their weak local stiffness.To address these challenges,we propose a novel tunable electromagnetic semi-active dynamic vibration absorber(ESADVA),which integrates with a magnetic suction follower to form a followed ESADVA(follow-ESADVA)for mirror milling.This system combines a tunable magnet oscillator with a follower,enabling real-time vibration absorption and condition feedback throughout the milling process.Additionally,the device supports self-sensing and frequency adjustment by providing feedback to a linear actuator,which alters the distance between magnets.This resolves the traditional issue of being unable to directly monitor vibration at the machining point due to space constraints and tool interference.The frequency shift characteristics and vibration absorption performance are comprehensively investigated.Theoretical and experimental results demonstrate that the prototyped follow-ESADVA achieves frequency synchronization with the milling tool,resulting in a vibration suppression rate of approximately 47.57%.Moreover,the roughness of the machined surface decreases by18.95%,significantly enhancing the surface quality.The results of this work pave the way for higher-quality machined surfaces and a more stable mirror milling process.

Numerical Analysis of Cold-Formed Thin-Walled Steel Short Columns with Pitting Corrosion during Bridge Construction

Pitting corrosion is harmful during bridge construction,which will lead to uneven roughness of steel surfaces and reduce the thickness of steel.Hence,the effect of pitting corrosion on the mechanical properties of cold-formed thin-walled steel stub columns is studied,and the empirical formulas are established through regression fitting to predict the ultimate load of web and flange under pitting corrosion.In detail,the failure modes and load-displacement curves of specimens with different locations,area ratios,and depths are obtained through a large number of non-linear finite element analysis.As for the specimens with pitting corrosion on the web,all the specimens are subject to local buckling failure,and the failure mode will not change with pitting corrosion,but the failure location will change with pitting corrosion location;the size,location,and area ratio of pitting corrosion have little influence on the ultimate load of cold-formed thin-walled steel short columns,but the loss rate of pitting corrosion section area has a greater impact on the ultimate bearing capacity.As for the specimen with flange pitting corrosion,the location and area ratio of pitting corrosion have less influence on the ultimate load of cold-formed thin-walled steel short columns,and the section area loss rate has greater influence on the ultimate bearing capacity;the impact of web pitting corrosion on the ultimate load is greater than that of flange pitting corrosion under the same condition of pitting corrosion section area.The prediction formulas of limit load which are suitable for pitting corrosion of web and flange are established,which can provide a reference for performance evaluation of corroded cold-formed thin-walled steel.

Restrained torsion of open thin-walled beams including shear deformation effects

A first-order torsion theory based on Vlasov theory has been developed to investigate the restrained torsion of open thin-walled beams. The total rotation of the cross section is divided into a free warping rotation and a restrained shear rotation. In first-order torsion theory, St. Venant torque is only related to the free warping rotation and the expression of St. Venant torque is derived by using a semi-inverse method. The relationship between the warping torque and the restrained shear rotation is established by using an energy method. The torsion shear coefficient is then obtained. On the basis of the torsion equilibrium, the governing differential equation of the restrained torsion is derived and the corresponding initial method is given to solve the equation. The relationship between total rotation and flee warping rotation is obtained. A parameter λ, which is associated with the stiffness property of a cross section and the beam length, is introduced to determine the condition, under which the St. Venant constant is negligible. Consequently a simplified theory is derived. Numerical examples are illustrated to validate the current approach and the results of the current theory are compared with those of some other available methods. The results of comparison show that the current theory provides more accurate results, In the example of a channel-shaped cantilever beam, the applicability of the simplified theory is determined by the parameter study of λ.

Modeling and Free Vibration Behavior of Rotating Composite Thin-walled Closed-section Beams with SMA Fibers

Smart structure with active materials embedded in a rotating composite thin-walled beam is a class of typical structure which is using in study of vibration control of helicopter blades and wind turbine blades. The dynamic behavior investigation of these structures has significance in theory and practice. However, so far dynamic study on the above-mentioned structures is limited only the rotating composite beams with piezoelectric actuation. The free vibration of the rotating composite thin-walled beams with shape memory alloy（SMA） fiber actuation is studied. SMA fiber actuators are embedded into the walls of the composite beam. The equations of motion are derived based on Hamilton＇s principle and the asymptotically correct constitutive relation of single-cell cross-section accounting for SMA fiber actuation. The partial differential equations of motion are reduced to the ordinary differential equations of motion by using the Galerkin＇s method. The formulation for free vibration analysis includes anisotropy, pitch and precone angle, centrifugal force and SMA actuation effect. Numerical results of natural frequency are obtained for two configuration composite beams. It is shown that natural frequencies of the composite thin-walled beam decrease as SMA fiber volume and initial strain increase and the decrease in natural frequency becomes more significant as SMA fiber volume increases. The actuation performance of SMA fibers is found to be closely related to the rotational speeds and ply-angle. In addition, the effect of the pitch angle appears to be more significant for the lower-bending mode ones. Finally, in all cases, the precone angle appears to have marginal effect on free vibration frequencies. The developed model can be capable of describing natural vibration behaviors of rotating composite thin-walled beam with active SMA fiber actuation. The present work extends the previous analysis done for modeling passive rotating composite thin-walled beam.

Boundary Element Analysis forModeⅢCrack Problems of Thin-Walled Structures from Micro-to Nano-Scales

This paper develops a new numerical framework for modeⅢcrack problems of thin-walled structures by integrating multiple advanced techniques in the boundary element literature.The details of special crack-tip elements for displacement and stress are derived.An exponential transformation technique is introduced to accurately calculate the nearly singular integral,which is the key task of the boundary element simulation of thin-walled structures.Three numerical experiments with different types of cracks are provided to verify the performance of the present numerical framework.Numerical results demonstrate that the present scheme is valid for modeⅢcrack problems of thin-walled structures with the thickness-to-length ratio in the microscale,even nanoscale,regime.

A geometrical and physical nonlinear finite element model for spatial thin-walled beams with arbitrary section

Based on the theories of Bernoulli-Euler beams and Vlasov's thin-walled members,a new geometrical and physical nonlinear beam element model is developed by applying an interior node in the element and independent interpolations on bending angles and warp,in which factors such as traverse shear deformation,torsional shear deformation and their coupling,coupling of flexure and torsion,and second shear stress are all considered.Thereafter,geometrical nonlinear strain in total Lagarange(TL) and the corresponding stiffness matrix are formulated.Ideal plastic model is applied to physical nonlinearity to comply with the yield rule of Von Mises and incremental relationship of Prandtle-Reuss.Elastoplastic stiffness matrix is derived by numerical integration on the basis of the finite segment method.Examples show that the developed model is feasible in analysis of thin-walled structures with high accuracy.

Miniature tunable Airy beam optical meta-device

Tunable Airy beams with controllable propagation trajectories have sparked interest in various fields,such as optical manipulation and laser fabrication.Existing research approaches encounter challenges related to insufficient compactness and integration feasibility,or they require enhanced tunability to enable real-time dynamic manipulation of the propagation trajectory.In this work,we present a novel method that utilizes a dual metasurface system to surpass these limitations,significantly enhancing the practical potential of the Airy beam.Our approach involves encoding a cubic phase profile and two off-axis Fresnel lens phase profiles across the two metasurfaces.The validity of the proposed strategy has been confirmed through simulation and experimental results.The proposed meta-device addresses the existing limitations and lays the foundation for broadening the applicability of Airy beams across diverse domains,encompassing light-sheet microscopy,laser fabrication,optical tweezers,etc.

Fully automatic AI segmentation of oral surgery-related tissues based on cone beam computed tomography images

Accurate segmentation of oral surgery-related tissues from cone beam computed tomography(CBCT)images can significantly accelerate treatment planning and improve surgical accuracy.In this paper,we propose a fully automated tissue segmentation system for dental implant surgery.Specifically,we propose an image preprocessing method based on data distribution histograms,which can adaptively process CBCT images with different parameters.Based on this,we use the bone segmentation network to obtain the segmentation results of alveolar bone,teeth,and maxillary sinus.We use the tooth and mandibular regions as the ROI regions of tooth segmentation and mandibular nerve tube segmentation to achieve the corresponding tasks.The tooth segmentation results can obtain the order information of the dentition.The corresponding experimental results show that our method can achieve higher segmentation accuracy and efficiency compared to existing methods.Its average Dice scores on the tooth,alveolar bone,maxillary sinus,and mandibular canal segmentation tasks were 96.5%,95.4%,93.6%,and 94.8%,respectively.These results demonstrate that it can accelerate the development of digital dentistry.

Microstructures and Properties of 550 MPa Grade High Strength Thin-walled H-beam Steel

The microstructures and mechanical properties of 550 MPa grade lightweight high strength thin-walled H-beam steel were experimentally studied. The experimental results show that the microstructure of the air-cooled H-beam steel sample is consisted of ferrite, pearlite and a small amount of granular bainites as well as fine and dispersive V（C,N） precipitates. The microstructure of the water-cooled steel sample is consisted of ferrite and bainite as well as a small amount of fine pearlites. The microstructure of the water-cooled sample is finer than that of the air-cooled sample with the average intercept size of the surface grains reaching to 3.5 gna. The finish rolling temperature of the thin-walled high strength H-beam steel is in the range of 750 ~C-850 ~C. The lower the finish rolling temperature and the faster the cooling rate, the finer the ferrite grains, the volume fraction of bainite is increased through water cooling process. Grain refinement strengthening and precipitation strengthening are used as major strengthening means to develop 550 MPa grade lightweight high strength thin- walled H-beam steel. Vanadium partially soluted in the matrix and contributes to the solution strengthening. The 550 MPa grade high-strength thin-walled H-beam steel could be developed by direct air cooling after hot rolling to fully meet the requirements of the target properties.

Geometric Accuracy and Energy Absorption Characteristics of 3D Printed Continuous Ramie Fiber Reinforced Thin-Walled Composite Structures

The application of continuous natural fibers as reinforcement in composite thin-walled structures offers a feasible approach to achieve light weight and high strength while remaining environmentally friendly.In addition,additive manufacturing technology provides a favorable process foundation for its realization.In this study,the printability and energy absorption properties of 3D printed continuous fiber reinforced thin-walled structures with different configurations were investigated.The results suggested that a low printing speed and a proper layer thickness would mitigate the printing defects within the structures.The printing geometry accuracy of the structures could be further improved by rounding the sharp corners with appropriate radii.This study successfully fabricated structures with vari-ous configurations characterized by high geometric accuracy through printing parameters optimization and path smoothing.Moreover,the compressive property and energy absorption characteristics of the structures under quasi-static axial compression were evaluated and compared.It was found that all studied thin-walled structures exhibited progressive folding deformation patterns during compression.In particular,energy absorption process was achieved through the combined damage modes of plastic deformation,fiber pullout and delamination.Furthermore,the com-parison results showed that the hexagonal structure exhibited the best energy absorption performance.The study revealed the structure-mechanical property relationship of 3D printed continuous fiber reinforced composite thin-walled structures through the analysis of multiscale failure characteristics and load response,which is valuable for broadening their applications.

Properties of focused Laguerre–Gaussian beam propagating in anisotropic ocean turbulence

We analyze the properties of a focused Laguerre–Gaussian(LG)beam propagating through anisotropic ocean turbulence based on the Huygens–Fresnel principle.Under the Rytov approximation theory,we derive the analytical formula of the channel capacity of the focused LG beam in the anisotropic ocean turbulence,and analyze the relationship between the capacity and the light source parameters as well as the turbulent ocean parameters.It is found that the focusing mirror can greatly enhance the channel capacity of the system at the geometric focal plane in oceanic turbulence.The results also demonstrate that the communication link can obtain high channel capacity by adopting longer beam wavelength,greater initial beam waist radius,and larger number of transmission channels.Further,the capacity of the system increases with the decrease of the mean squared temperature dissipation rate,temperature-salinity contribution ratio and turbulence outer scale factor,and with the increase of the kinetic energy dissipation rate per unit mass of fluid,turbulence inner scale factor and anisotropy factor.Compared to a Hankel–Bessel beam with diffraction-free characteristics and unfocused LG beam,the focused LG beam shows superior anti-turbulence interference properties,which provide a theoretical reference for research and development of underwater optical communication links using focused LG beams.

Generation of structured light beams with polarization variation along arbitrary spatial trajectories using tri-layer metasurfaces

Conventionally,the spatially structured light beams produced by metasurfaces primarily highlight the polarization modulation of the beams propagating along the optical axis or the beams'spatial transmission trajectory.In particular,along the optical axis,the polarization state is either constant or varies continuously in each output plane.Here,we develop innovative spatially structured light beams with continually changing polarization along any arbitrary spatial transmission trajectories.With tri-layer metallic metasurfaces,the geometric characteristics of each layer structure can be adjusted to modulate the phase and polarization state of the incident terahertz(THz)wave.The beam will converge to the predefined trajectory along several paths to generate a Bessel-like beam with longitudinal polarization changes.We demonstrate the versatility of the approach by designing two THz-band structured light beams with varying polarization states along the spatial helical transmission trajectory.Continuous linear polarization changes and linear polarization to right circular polarization(RCP)and back to linear polarization changes are realized respectively.The experimental results are basically consistent with the simulated results.Our proposal for arbitrary trajectory structured light beams with longitudinally varying polarization offers a practical method for continuously regulating the characteristics of spatial structured light beams with non-axial transmission.This technique has potential uses in optical encryption,particle manipulation,and biomedical imaging.