Beam Cross Section Research Articles

An efficient approach for free vibration analysis of functionally graded sandwich beams of variable cross-section

In this research paper, a powerful numerical method is implemented to examine the free vibration analysis of functionally graded (FG) sandwich beams of variable cross-section. The core of the beam is considered to be made from homogenous isotropic material and the faces of the sandwich beam are considered to be made of FG materials. The effect of the shear strain is considered in the formulations based on the first-order shear deformation theory (FSDT). The governing canonical equations for the dynamic response of FG sandwich beams are derived with the aid of the canonically conjugate momentums for the first time. To solve these equations numerically the Complementary Functions Method (CFM) is implemented. The free vibration behavior of the symmetric and asymmetric FG sandwich beams is investigated for different boundary conditions. The presented efficient numerical method is validated with the available literature. Moreover, detailed parametric studies are conducted to demonstrate the influence of layers, geometric constants, material volume fraction indexes, and beam slenderness on the natural frequencies of FG sandwich beams.

An analytical method for beam hardening correction in thermal-neutron radiography

The effect of polychromatic nature of thermal neutrons on neutron radiography was studied through experiments and simulations on borated and non-borated stainless steel with homogeneous composition. The results were compared to theoretical neutron-transmission results obtained for a monochromatic neutron beam.The evolution of total cross sections, neutron-transmission and gray level in neutron radiography image indicate the important effect of beam hardening.For that, an analytical procedure has been established for thermal cross section determination and beam hardening correction of the experimental and simulated data. The corrected data values agree well with those calculated theoretically indicating the effectiveness of the developed correction method.

Load-Bearing Capacity of Reinforced Concrete and Fiber Concrete Cross-Beam Systems

The results of experimental studies and computer modeling of reinforced concrete and fiber concrete cross-beam systems are presented. The authors have made a special stand, the design of which allows to carry out researches of bearing capacity and deformability of such systems under the concentrated and distributed static loads. Samples made of reinforced concrete and steel fiber concrete and consisting of four mutually perpendicular beams of rectangular cross-section were tested. The specimens were reinforced in the lower zone with longitudinal reinforcement of 8 mm in diameter, two rods in each beam. Steel-fiber concrete specimens have an additional dispersed reinforcement of steel fiber with bent ends in an amount of 1% by volume of concrete. A procedure of finite-element modeling and calculation of cross-beam systems in the licensed program ANSYS 17.1 was developed, and a comparison of the results obtained experimentally and on the basis of computer modeling was performed. The tests showed that dispersed reinforcement of the cross-beam system with steel fiber leads to an increase in its bearing capacity by 1.23 times. During modeling and finite-element analysis in the ANSYS 17.1 program, the increase in bearing capacity was 1.18 times. At the same time, the load-carrying capacity of the reinforced concrete cross-beam system obtained by the finite-element method was 13% lower than in the experiment, and that of the fiber-reinforced concrete system was 15% lower. At the same time, the discrepancy in the approaches considering torsion and not taking it into account is about 5% for all the samples studied in the work.

Generalized strain-based finite element for non-linear stability analysis of beams with thin-walled open cross-section

Based on the generalized strain theory a shear-deformable finite element is developed for nonlinear stability analysis of thin-walled open-section beams in multibody systems. In this formulation a finite number of deformations, characterized as generalized strains, is defined which are related to dual stress resultants in a co-rotational frame. The stiffness formulation is based on a second-order approximation of the local elastic displacement field. Timoshenko’s beam theory and Vlasov’s modified thin-walled beam theory are used to include the shear strain effects due to non-uniform bending and restrained warping torsion and their mutual coupling effects. Axial shortening associated with the Wagner Hypothesis is taken into account such that the nonlinear behaviour of the beam is predicted accurately, especially under large torsion. Coupling between bending and torsional deformation due to non-coincident centroid and shear centre is modelled using a second-order cross-section transformation matrix. Cubic Hermitian polynomials are used as shape functions for the lateral displacements and twist rotation to derive the elastic and geometric stiffness matrices. Geometric nonlinearities associated with axial elongation and bending curvatures are described by additional torsion, bending and warping-related quadratic deformation terms yielding a set of modified deformations. The inertia properties of the beam are described using both consistent and lumped mass formulations. The latter is used to model rotary and warping inertias of the beam cross-section. The accuracy and the computational efficiency of the new beam element is demonstrated in several static and dynamic examples.

Approximate determination of shear stresses for a 2D beam made of a non-Green elastic solid

Shear stresses for a two-dimensional (2D) beam are calculated modifying the classical method developed by Jouravski, for the case the linearized strain tensor is assumed to be a nonlinear function of the Cauchy stresses. Two problems are studied, namely, the case of a cantilever beam with a point load on its free edge (considering a rectangular and a circular cross-section) and the three-point flexural test for a beam of rectangular cross-section. Numerical results are obtained for the particular case of a bimodular constitutive model for rock, and the results for the shear stresses are compared with the predictions of the classical theory of strength of materials for such problems, assuming a linearized elastic body.

FIB line marking as a tool for local erosion/deposition/fuzz formation measurements in ASDEX Upgrade during the He campaign

Tungsten (W) is the prime candidate for the plasma facing material in present and future fusion devices. When exposed to a plasma containing He ions, W can exhibit creation of sub-surface nano-bubbles leading to formation of nano-tendrils called fuzz. Formation of W fuzz was confirmed by many laboratory experiments including He loading in linear plasma devices. There is, however, limited experience related to the parameter space for fuzz formation and re-erosion in a tokamak environment. For this reason, a dedicated experiment was carried out in ASDEX Upgrade (AUG) during its 2022 He campaign to study the evolution of fuzz-like W structures.Twelve tungsten samples were mechanically polished to a mirror-like surface finish. Six of them were subsequently exposed to a He plasma in the PSI-2 linear device in order to establish a fuzz layer with a thickness of 600 – 800 nm. Before exposure in AUG, all samples were pre-characterized by Focused Ion Beam (FIB) cross-sectioning. In total 48 FIB cross-sections with line markings for quantification of local erosion, deposition and fuzz formation were prepared – 4 on each sample. The samples were placed in two parallel poloidal rows spanning a range of 20 cm around the outer strike line position (OSP). They were subsequently exposed in AUG to a series of 14 consecutive discharges, 8 in H-mode and 6 in L-mode.Detailed analysis by means of electron microscopy revealed on the samples regions of erosion, deposition and fuzz formation. Below the H-mode OSP, homogeneous co-deposits containing W and O, with a thickness up to 400 nm, were found. In the close vicinity of the H-mode OSP, significant erosion of pre-exposure PSI-2 fuzz was observed. The erosion reached up to 100 – 250 nm, depending on the location. In addition, the initially polished samples did not show any newly formed fuzz in that zone. Above the H-mode OSP, new fuzz was formed with a thickness of up to 1 μm. There was no Mo found in the newly formed fuzz. Pre-exposure PSI-2 fuzz was either removed or modified.

Influence of flexural-torsional couplings and rotational effects on vibration behaviour of tapered thin-walled anisotropic biconvex beam

Accurate modelling and prediction of dynamic characteristics for rotating thin-walled blades have drawn attention as it is an essential part of structural health monitoring for various engineering and civil applications such as wind turbine, helicopter and aeroplane blades. With the advent of structural tailoring techniques, various non-classical effects and couplings implicitly affecting the behaviour of such structures are yet not fully explored. In this regard, the present work proposes a numerical model for finding the free vibration characteristics of anisotropic tapered biconvex closed cross-section beam under rotating conditions. The model is derived based on energy method following the Ritz approximation. Circumferentially asymmetric stiffness (CAS) ply configuration is considered in order to study the impact of flexural torsional coupling on the vibration characteristics. Transverse shear effects, primary and secondary warping were also included in the current model. Mode switching phenomenon is dissected elaborately for the first few frequencies under rotating and nonrotating conditions. The impact of rotational effects like centrifugal acceleration, centrifugal warping, inertial warping on the first few frequencies is also demonstrated. An iterative technique is adapted to solve the equations having these rotational effects. Modal Assurance Criterion (MAC) is done in order to judge the consistency of the modes at different rotating speeds.

Quasi-one-dimensional treatment of heat transfer in beams of non-uniform cross-section

We test performance of a quasi-one-dimensional approach to steady state heat transfer in broadening beams, characterized by variable cross-sectional area. The results obtained analytically and by solving the governing equation numerically in Python, for three different instances, are compared to FEM simulations. We demonstrate that the quasi-one-dimensional model gives accurate predictions for beam suitably averaged temperatures but the range of Biot numbers for which it can be accurately applied to is currently limited by a crucial parameter.

The Mechanism of the Formation of the Spin Hall Effect in a Sharp Focus

We have shown how the spin Hall effect is formed in a tight focus for two light fields with initial linear polarization. We have demonstrated that an even number of local subwavelength regions appear in which the sign of the longitudinal projection of the spin angular momentum (the third Stokes component) alternates. When an optical vortex with topological charge n and linear polarization passes through an ideal spherical lens, additional optical vortices with topological charges n + 2, n − 2, n + 1, and n − 1 with different amplitudes are formed in the converged beam. The first two of these vortices have left and right circular polarizations and the last two vortices have linear polarization. Since circularly polarized vortices have different amplitudes, their superposition will have elliptical polarization. The sign of this elliptical polarization (left or right) will change over the beam cross section with the change in the sign of the difference in the amplitudes of optical vortices with circular polarization. We also have shown that optical vortices with topological charges n + 2, n − 2 propagate in the opposite direction near the focal plane, and together with optical vortices with charges n + 1, n − 1, they form an azimuthal energy flow at the focus.

Shear strength assessment of reinforced recycled aggregate concrete beams without stirrups using soft computing techniques

This paper presents a study to predict the shear strength of reinforced recycled aggregate concrete beams without stirrups using soft computing techniques. The methodology involves the development of a Multi-Objective Genetic Algorithm Evolutionary Polynomial Regression (MOGA-EPR) and Gene Expression Programming (GEP) models. The input variables considered are the longitudinal reinforcement ratio, recycled coarse aggregate ratio, beam cross-section dimensions, and concrete compressive strength. Data collected from the literature were used to train and validate the models. The results showed that the MOGA-EPR and GEP models can accurately predict the shear strength of beams without stirrups. The models also performed better than equations from the codes and literature. This study provides an alternative approach to accurately predict the shear strength of reinforced recycled aggregate concrete beams without stirrups.

Features of the formation and diagnostics of powerful metal ion beams with submillisecond duration

The article presents the results of experimental studies on the formation of repetitively-pulsed beams of titanium ions with submillisecond pulse duration from the continuous vacuum arc discharge plasma. The influence of ion-electron emission on the overestimation of the measured ion current with a power density of tens and hundreds of kilowatts per square centimeter was studied using various methods. It has been established that at an average energy of titanium ions of about 80 keV, due to ion-electron emission, the measured current is three times higher than the real ion beam current. Complicating the measurement of the current and energy parameters of the ion beam, the ion-electron emission ensures the neutralization of its space charge during the entire duration of the pulse. An increase in the ion current density due to ballistic focusing to more than 1 A/cm2 does not change the ion-electron emission coefficient. It is shown that, as a result of incomplete ion beam space charge neutralization, its crossover is shifted by 20 mm beyond the geometric focus of the system. The possibility of forming submillisecond high-intensity titanium ion beams with a current density exceeding 2.8 A/cm2, a power density exceeding 200 kW/cm2, and a pulse energy exceeding 100 J has been experimentally demonstrated. Data are obtained on the change in the current density over the ion beam cross-section depending on the accelerating voltage amplitude, the vacuum arc discharge current, and the distance from the focusing electrode.

On the equivalent flexural and shear moduli of laminated beams: Definition and determination by bending tests

Equivalent flexural and shear moduli of laminated beams of rectangular cross-section made of orthotropic layers are defined by an analytical approach. Equivalent flexural and shear modulus are defined as those that would correspond to a homogenous beam. In order to check the suitability of the moduli defined, three-point bending tests varying the span are carried out in a sandwich material and in hybrid laminates. In the case of the sandwich material, it is shown that a three-point bending test could be considered a shear test from the stiffness point of view. In the case of hybrid materials, virtual tests are carried out by the Finite Element Method. The agreement between equivalent moduli obtained from the analytical approach and the bending tests has been checked, being quite good in all cases. Finally, the effect of dimension uncertainty in three-point bending tests is analyzed by a Monte Carlo simulation.

Buckling analysis of multi-span non-uniform beams with functionally graded graphene-reinforced foams

This paper conducts the buckling analysis of multi-span functionally graded (FG) beams reinforced by three-dimensional graphene foams (3D-GFs) restrained by elastic supports. The graphene foams are considered as graded variation in the thickness direction according to four different porosity distributions. The width and height of the non-uniform beams vary in the longitudinal direction in accordance with the power-law principle, and the multi-span beams consist of two types of optional beams. The governing equations of buckling behavior are derived based on the Timoshenko beam theory and the principle of virtual displacements, and solved by the discrete singular convolution (DSC) method. The purpose of this paper is to obtain the critical buckling load of FG 3D-GFs reinforced beams under the consideration of variable cross-section and multi-span beams with 2–4 spans. The effect of porosity coefficients, slenderness ratio, and spring constants on the buckling characteristic also are studied. The results suggest that the taper ratio of beams and the configuration of multi-span beams lead to remarkable changes in the critical buckling load of beams.

Evaluation of ultimate bearing capacity of large-scale perforated beams with variable cross-section: Experimental verification and numerical simulation

In order to meet the requirements of outfitting layout and light weight, circular or elliptical holes need to be opened on the web of the hull beam. Excessive opening will lead to stress concentration and reduce the bearing capacity of the beam. For the super-standard openings, the general strengthening method cannot guarantee the ultimate bearing capacity of the beam, and locally increasing the web to form a variable cross-section beam can compensate for the lost bearing capacity. In the present paper, the three-point bending load tests of variable cross-section opening beams and equal cross-section beams are carried out. Combined with the results of nonlinear finite element analysis, the ultimate bearing capacity and failure mode of transverse bending are compared, and it is verified that the ultimate bearing capacity of beams with variable cross-section openings is better than that of beams with equal cross-section. By changing the cross-section size and optimizing the transition form, the variable cross-section perforated beam is further improved and optimized to enhance the ultimate strength.

A nested genetic algorithm strategy for an optimal seismic design of frames

AbstractAn innovative strategy for an optimal design of planar frames able to resist seismic excitations is proposed. The optimal design is performed considering the cross sections of beams and columns as design variables. The procedure is based on genetic algorithms (GA) that are performed according to a nested structure suitable to be implemented in parallel on several computing devices. In particular, this bi-level optimization involves two nested genetic algorithms. The first external one seeks the size of the structural elements of the frame which corresponds to the most performing solution associated with the highest value of an appropriate fitness function. The latter function takes into account, among other considerations, the seismic safety factor and the failure mode that are calculated by means of the second internal algorithm. The proposed procedure aims at representing a prompt performance-based design procedure which observes earthquake engineering principles, that is displacement capacity and energy dissipation, although based on a limit analysis, thus avoiding the need of performing cumbersome nonlinear analyses. The details of the proposed procedure are provided and applications to the seismic design of two frames of different size are described.

Enhancement of Doppler spectroscopy to transverse direction by using optical vortex

Tunable diode laser absorption spectroscopy (TDLAS) is a valuable method for measuring particle flow velocities in plasma. However, conventional TDLAS using a plane-wave beam is sensitive only to the laser propagation direction. This limitation is particularly unfavorable for the observation of the particle transportation perpendicularly incident on the material in the plasma–material interaction. In this paper, we show for the first time that flow measurements perpendicular to the beam direction are possible by replacing the probe beam with an optical vortex beam. Because an optical vortex has a helical wavefront, particles moving in its field experience an azimuthal Doppler shift in addition to the translational Doppler shift. Assuming a uniform gas flow across the optical vortex, the azimuthal Doppler shift of the absorption spectrum observed in the beam cross-section varies sinusoidally in the azimuthal direction. The transverse flow velocity is derived from the amplitude of this sinusoidal variation. At transverse velocities above 70 m/s, the measurement errors are found to be less than 15%, with a mean absolute percentage error of less than 8%.

Analysis of Dynamic Characteristics of Tristable Exponential Section of Piezoelectric Energy Harvester

Variable-cross-section beams have better mass and strength distribution compared with constant cross-section beams, which can optimize the harvesting power of piezoelectric vibration energy harvesters, which are widely used in self-supplied and low-power electronic devices, providing more convenience and innovation for the development of micromechanical intelligence and portable mobile devices. This paper proposes a piezoelectric energy harvester with a tristable-exponential-decay cross section, which optimizes the strain distribution of the cantilever beam through exponential decay changes to improve the harvesting efficiency of the harvester in low-frequency environments. First, the nonlinear magnetic force is obtained based on the magnetic dipole, and the dynamic model is established by using the Euler–Bernoulli beam theory and Lagrangian equation. The influence of the structural parameters of the harvester on the system dynamics and output characteristics is analyzed in the two dimensions of time and frequency, and the influence of the exponential decay coefficient on the system dynamic response and output power is deeply studied. The research shows that the exponential decay section can reduce the first natural frequency of the cantilever beam; by changing the amplitude, frequency, d and dg of the excitation acceleration, the switching of the monostable, tristable and bistable states of the system can be realized. With a decrease in the exponential decay coefficient, under a low-frequency excitation of 0–7 Hz, the output power of the cantilever beam per unit volume is significantly improved, and under a 4 Hz low-frequency excitation, the acquisition output power per unit volume of the cantilever beam is increased by 7 times, thus realizing low-frequency, high-efficiency energy harvesting.

ALE-ANCF circular cross-section beam element and its application on the dynamic analysis of cable-driven mechanism

ALE-ANCF circular cross-section beam element and its application on the dynamic analysis of cable-driven mechanism

Two-stage multi-objective optimization of reinforced concrete buildings based on non-dominated sorting genetic algorithm (NSGA-III)

The colossal environmental footprint of the construction industry is a paramount ecological concern, especially in the wake of climate change threats and natural resources depletion. The present study performs a novel two-stage optimization approach for the design of reinforced concrete (RC) frame buildings to minimize the water footprint (WF) and cost, based on non-dominated sorting genetic algorithm (NSGA-III). The first stage includes multi-objective optimization (MOO) with respect to the cost and capacity of cross-sections of RC beam and column elements for any possible combination of design variables using section-based database schema (SBDBS). The second stage is MOO based on NSGA-III to minimize the volumes of reinforcing steel and concrete in RC structure considering the optimal sections generated by SBDBS as a pre-determined list for elements. Four structural archetypes consisting of 4, 8, 12, and 16-story frames were considered in the design optimization problems. The main objective of this optimization is to calculate the cost and WF of RC structures for various unit cost and WF of materials, and as a result, identify the optimal design of RC structures. The result of this optimization framework allows the decision maker to identify the optimal RC structural design for any cost or WF condition by performing a sensitivity analysis, without need for additional structural analysis or optimization. The proposed approach further allows the decision maker to consider the uncertainty of WF and cost of materials that emanate from regional or spatiotemporal variables. The results show that the shape of the optimal design Pareto front (PF) is more related to the values of unit WF of materials than the costs. To highlight the advantages of the proposed procedure, probabilistic sensitivity analysis and decision-making strategy were performed and pertinent conclusions were drawn.

Methodology to predict mechanical properties of PA-12 lattice structures manufactured by powder bed fusion

Topology optimization for weight reduction of additive manufacturing parts is commonly achieved throughout the creation of lattice structures, typically generated with beams of small size cross-section. In order to carry out accurate simulations of these lattice structures, knowing the mechanical behavior of pillars is required. In this paper, a methodology for determining the mechanical properties of small size pillars printed in PA-12 material, using polymer powder bed fusion (PBF) and in particular the Selective Laser Sintering (SLS) technology, is presented. The effect of defects originated during the manufacturing process on the macroscopic mechanical properties is studied and the mechanisms which influence these properties are analyzed. A methodology for the determination of these properties is proposed, based on a successive correction of the printed nominal diameters according to two approaches; one due to the outer skin of unmelted material and the other due to internal melting defects. Once the material properties are determined, as a function of the cross-section of the lattice pillars, the numerical simulation of lattice-type structures has been carried out and the degree of adjustment of the proposed methodology has been experimentally verified, obtaining good results. This validation provides a reliable method for the simulation of the macroscopic behavior of lattice-type structures with reduced sizes, taking into account the intrinsic defects generated during the printing process.