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Showing papers on "Beam (structure) published in 2022"


Journal ArticleDOI
TL;DR: In this paper , a dual-polarized vortex beam generator based on metasurface and metagrating (MG) is proposed, where the phase is modulated through moving the position of meta-atoms instead of varying the geometrical parameters or rotating the unit cells.
Abstract: Traditional methods of generating vortex beams based on metasurfaces consist mainly in modulating propagation phase or geometric phase. Here, by introducing detour phase, we propose the construction of dual-polarized vortex beam generators in the form of metasurface and metagrating (MG). The phase is modulated through moving the position of meta-atoms instead of varying the geometrical parameters or rotating the unit cells. To use detour phase, two kinds of unit cells are designed to achieve specific diffraction order. Each unit can arbitrarily and independently adjust the operation frequency and diffraction angle of transverse electric (TE) and transverse magnetic (TM) polarizations. Two vortex beam generators are designed and fabricated with different topological charges carried by orthogonal polarizations. To demonstrate the ability to independently manipulate, two polarizations of the generator based on MG are designed in different frequency bands. Both the simulation and experimental results validate the proposed method, showing great potential for polarization division multiplexing in orbital angular momentum (OAM) communication systems.

77 citations


Journal ArticleDOI
TL;DR: In this article , the impacts of different proportions of tension reinforcement and waste lathe scraps on the failure and bending behavior of reinforced concrete beams (RCBs) are clearly detected considering empirical tests.
Abstract: In this study, the impacts of different proportions of tension reinforcement and waste lathe scraps on the failure and bending behavior of reinforced concrete beams (RCBs) are clearly detected considering empirical tests. Firstly, material strength and consistency test and then ½ scaled beam test have been carried out. For this purpose, a total of 12 specimens were produced in the laboratory and then tested to examine the failure mechanism under flexure. Two variables have been selected in creating text matrix. These are the longitudinal tension reinforcement ratio in beams (three different level) and volumetric ratio of waste lathe scraps (four different level: 0%, 1%, 2% and 3%). The produced simply supported beams were subjected to a two-point bending test. To prevent shear failure, sufficient stirrups have been used. Thus, a change in the bending behavior was observed during each test. With the addition of 1%, 2% and 3% waste lathe scraps, compressive strength escalated by 11.2%, 21.7% and 32.5%, respectively, compared to concrete without waste. According to slump test results, as the waste lathe scraps proportion in the concrete mixture is increased, the concrete consistency diminishes. Apart from the material tests, the following results were obtained from the tests performed on the beams. It is detected that with the addition of lathe waste, the mechanical features of beams improved. It is observed that different proportions of tension reinforcement and waste lathe scraps had different failure and bending impacts on the RCBs. While there was no significant change in stiffness and strength, ductility increased considerably with the addition of lathe waste.

51 citations


Journal ArticleDOI
TL;DR: In this article , the caesium conditioning procedure and the corresponding beam performances during the first operation of SPIDER with caesIUM were described. But the results obtained in this first investigation provided key indications on the operation of the largest existing sources of accelerated negative hydrogen-like ions.
Abstract: The negative-ion based neutral beam injector for heating and current drive of the ITER plasma (ITER HNB) is under development, at present focusing on the optimization of the full-scale plasma source in the SPIDER test stand. The production of H− or D− ions in the ion source is based on the low work function surfaces obtained by caesium evaporation. This paper describes the caesium conditioning procedure and the corresponding beam performances during the first operation of SPIDER with caesium. Technical solutions to overcome present limitations of the test stand are described. The influence of source parameters on the caesium effectiveness was investigated in short beam pulse operation; with total radio-frequency (RF) power of 400 kW and filling pressure below 0.4 Pa, and a limited number of extraction apertures, a negative ion current density of about 200 A m−2 was extracted in hydrogen, with beam energy lower than 60 keV. Beam optics and beam uniformity were assessed thanks to the acceleration of isolated ion beamlets. A possible procedure to accelerate a uniform beam was demonstrated at low RF power. The results obtained in this first investigation provided key indications on the operation of one of the largest existing sources of accelerated negative hydrogen-like ions.

49 citations


Journal ArticleDOI
TL;DR: In this paper , a data-driven model based on 2D convolutional neural network (CNN) is established, where model inputs contain the beam width, beam height, stirrup width and stirrup height.

48 citations


Journal ArticleDOI
TL;DR: In this article , the authors studied the crack and flexural behavior of reinforced concrete beams with various bottom ash ratios (BARs) considered as fine aggregate in an experimental and numerical investigation.
Abstract: In this research, it is studied the crack and flexural behavior of reinforced concrete beams with various bottom ash ratios (BARs) considered as fine aggregate in an experimental and numerical investigation. For experimental purposes, different concrete series are considered varying aggregate sizes ranging from 0 to 25 mm. To supplement concrete, bottom ash is put to use in conjunction with material from 0–5 mm in size aggregate particles as replacement for fine aggregates with ratios of 25%, 50%, 75%, and 100%. Experiments were done to investigate the behavior of the beams and how flexural and fracture behaviors are represented. 75% BARs gave optimum results in terms of displacement capacity. Increasing BAR to 100% decrease deflection capacity of the beam. Also, ANSYS software is used to build 3D finite element models (FEMs) of beams to compare with experiment data. Experimental and 3D numerical tests show exceptionally tight flexural and fracture behaviors. Following this, a computer-generated structure is made by running SAP 2000, and the strength of the beams is then utilised in an RC structural model. Every stage of the building’s construction is thoroughly assessed utilizing multiple types of seismic testing, employing the SAP2000 program, with the resulting analysis providing significant findings on how the seismic force of 75% BAR affects horizontal displacement of each floor. The results showed that the weight of the structure dramatically decreases as the number of columns and RCBs are raised while also increasing the number of BARs. Moreover, the magnitude of earthquake and BAR have a significant effect on the horizontal displacement behavior of reinforced concrete structures. The strength of the concrete structure varies between close- and far-fault earthquakes, and for close-fault earthquakes, concrete strength is stronger than for far-fault earthquakes. This brings us to the second disadvantage of BAR which is the 75% strain produces a severe displacement of reinforced concrete structures. Besides, it was seen that the simulations and experiments yield tiny cracks with very identical configurations.

48 citations


Journal ArticleDOI
TL;DR: In this paper , the authors evaluate the effectiveness of using ultra-high performance fiber reinforced concrete (UHPFRC) as a strengthening technique to improve the shear strength of RC beams.

45 citations


Journal ArticleDOI
TL;DR: In this article, the buckling problem of nonhomogeneous microbeams with a variable cross-section is analyzed, and the Rayleigh-Ritz numerical solution method is used to solve the eigenvalue problem for various conditions.
Abstract: In the present study, the buckling problem of nonhomogeneous microbeams with a variable cross-section is analyzed. The microcolumn considered in this study is made of functionally graded materials in the longitudinal direction and the cross-section of the microcolumn varies continuously throughout the axial direction. The Bernoulli–Euler beam theory in conjunction with modified strain gradient theory are employed to model the structure by considering the size effect. The Rayleigh–Ritz numerical solution method is used to solve the eigenvalue problem for various conditions. The influences of changes in the cross-section and Young’s modulus, size dependency, and non-classical boundary conditions are examined in detail. It is observed that the size effect becomes more pronounced for smaller sizes and differences between the classical and non-classical buckling loads increase by increasing the taper ratios.

43 citations


Journal ArticleDOI
TL;DR: In this article , the authors proposed a general method to perfectly control diffraction patterns based on a multi-beam PGM, which can be used to design multiple-beam antennas and that has significance in wireless communication applications.
Abstract: Phase-gradient metasurfaces (PGMs) constitute an efficient platform for deflection of a beam in a desired direction. According to the generalized Snell's law, the direction of the reflected/refracted wave can be tuned by the spatial phase function provided by the PGMs. However, most studies on PGM focus only on a single diffraction order, that is, the incident wave can be reflected or refracted to a single target direction. Even in the case of multiple beams pointing in different directions, the beams are still in the same order mode, and the energy carried by different beams cannot be controlled. In addition, the energy ratio of multiple beams is generally uncontrollable. Here, we propose a general method to perfectly control diffraction patterns based on a multi-beam PGM. An analytical solution for arbitrarily controlling diffraction beams is derived through which the generation and energy distribution in high-order diffraction beams can be achieved. Three metasurfaces with different diffraction orders and energy ratios are designed and fabricated to demonstrate the proposed method. The efficiencies of diffraction for the desired channels are close to 100%. The simulated and measured far-field patterns are in good agreement with theoretical predictions, validating the proposed method that provides a new way to design multi-beam antennas and that has significance in wireless communication applications.

43 citations


Journal ArticleDOI
TL;DR: In this paper, the authors analyzed the dispersion characteristics of flexural waves in a functionally graded (FG) porous nanobeam and established integro-differential constitutive laws of the stress resultant fields with equivalent differential relations equipped with non-standard boundary conditions.

39 citations


Journal ArticleDOI
TL;DR: In this article , an on-beam quartzenhanced photoacoustic spectroscopy (QEPAS) sensor based on a custom quartz tuning fork (QTF) acting as a photo-acoustic transducer, was realized and tested.

37 citations


Journal ArticleDOI
TL;DR: In this paper , the behavior of reinforced concrete beams with circular openings and the failure types resulting from strengthening these beams with CFRP are parametrically investigated and the ultimate load capacity, ductility, stiffness, energy dissipation capacity and failure modes of the beams were determined.

Journal ArticleDOI
TL;DR: In this paper , the authors investigated the properties of traditional reinforced-concrete beam with recycled steel wires (RSWT) obtained from the waste tires and found that there was an effective increase in the compressive and tensile strength of concrete with the increase of fiber content.
Abstract: In parallel with the increase in vehicle sales worldwide, waste tires are becoming an increasing problem. The storage and disposal of these waste tires are critical environmental problems. Re-using these wastes in different areas instead of being disposed of is vital in preventing environmental pollution and creating new low-cost products. From this motivation, this paper investigates the properties of traditional reinforced-concrete beam with recycled steel wires (RSWT) obtained from the waste tires. RSWT were added to reinforced-concrete beam between 1% and 3% by weight with an increment of 1%. In total, 9 cubes, 12 cylinders and 12 reinforced-concrete beams were cast and tested to obtain the compressive, splitting tensile and flexural strengths, respectively. RSWT added to the concrete by 1%, 2% and 3% increased the compressive strength by 17.2%, 30.8% and 46.4%, respectively, compared to the reference concrete. In split tensile strength, 14.4%, 25.1% and 36.7% increases were observed, respectively. This showed that there was an effective increase in the compressive and tensile strength of concrete with the increase of fiber content. Although the effect of fiber content in samples with high stirrup spacing (27 cm) provides significant benefit in improving the beam behavior, the effect of fibers was more limited as the stirrup spacing decreased (20 cm and 16 cm). An approximation of over 91% was obtained between the analytical calculations and the experimental results. This shows that the analytical calculations given in the standards can be used for new experimental studies.


Journal ArticleDOI
TL;DR: In this article , the authors analyzed the dispersion characteristics of flexural waves in a functionally graded (FG) porous nanobeam and established integro-differential constitutive laws of the stress resultant fields with equivalent differential relations equipped with non-standard boundary conditions.

Journal ArticleDOI
TL;DR: In this paper, the authors evaluated the effects of loading regimes on the behavior of reinforced concrete (RC) frames under a middle column removal scenario, two series of half-scale RC beam-column subassemblages were tested in two loading regimes.

Journal ArticleDOI
TL;DR: In this article , the authors evaluated the effects of loading regimes on the behavior of reinforced concrete (RC) frames under a middle column removal scenario, two series of half-scale RC beam-column subassemblages were tested in two loading regimes.

Journal ArticleDOI
TL;DR: In this article , a parallel-coupled quasi-zero stiffness (QZS) vibration isolator for an axially loaded beam, with the goal of enhancing the effectiveness of low-frequency isolation, is presented.
Abstract: Traditional vibration isolation of satellite instruments has an inherent limitation—that low-frequency vibration suppression leads to structural instability. This paper explores a parallel-coupled quasi-zero stiffness (QZS) vibration isolator for an axially loaded beam, with the goal of enhancing the effectiveness of low-frequency isolation. A QZS contains two magnetic rings, which contribute negative stiffness, and one spiral spring, with positive stiffness, a combination that has high static stiffness to resolve the structural instability. The frequency response functions (FRFs) of power flow are used to measure the effectiveness of vibration isolation. The magnetic stiffness of the magnetic rings is calculated using the principle of equivalent magnetic charge. The heights, radii, and gap of the magnetic rings affect its stiffness. The parallel-coupled QZS vibration isolator of an axially loaded beam is modeled using an energy method. Based on the Galerkin truncation, harmonic balance analysis, and arc-length continuation, an approach is proposed to analyze the FRFs of power flow for the parallel-coupled QZS vibration isolation of an axially loaded beam. Numerical results support the analytical results. Both analytical and numerical results show that the power reduction of axially loaded beams with a parallel-coupled quasi-zero vibration isolation system is more significantly suppressed at low frequencies.


Journal ArticleDOI
TL;DR: In this article , a numerical model based on the application of cohesive elements was developed to characterize the fracture process of a reinforced concrete beam strengthened with fiber-reinforced polymer (FRP) in detail.
Abstract: This study presents a numerical model to characterize the fracture process of a reinforced concrete (RC) beam strengthened with fiber-reinforced polymer (FRP) in detail. A numerical model based on the application of cohesive elements was developed. Mixed-mode constitutive models were proposed to characterize the mechanical behavior of the FRP–concrete interface, the concrete potential fracture surfaces, and the rebar–concrete interface. The normal separation of the interface and its coupling effect on the shear behavior were considered in the constitutive model. In addition, the friction effect was explicitly considered in the constitutive model. Three different typical cases of FRP-strengthened RC from other experimental research were selected to validate the numerical model developed in this paper. Finally, the influence of different constitutive models on the simulation accuracy was analyzed.

Journal ArticleDOI
TL;DR: In this article , a multifunctional coding metasurface (MCMS) has been proposed to realize dual-circularly polarized beams and beam focusing with transmission and reflection, where the phase distribution of the circularly polarized four-beam is determined according to the convolution theorem of patterns and the phase compensation principle.
Abstract: In this paper, a multifunctional coding metasurface (MCMS) has been proposed to realize dual-circularly polarized beams and beam focusing with transmission and reflection. The phase of transmissive wave is controlled by rotating the elements, and the corresponding element, which consists of two quadrate voids etched on a single layer substrate, is designed for the metasurface with Pancharatnam-Berry (PB) phase. The phase distribution of the circularly polarized four-beam is determined according to the convolution theorem of patterns and the phase compensation principle. In order to validate the proposed metasurface, the multifunctional meta-device is fabricated and measured to illustrate the four-beam with left circular polarization in transmissive space and the right circularly polarized four-beam in reflective space by MCMS with x-polarized incidence. The experimental results heavily agree with the simulated data. The MCMS has potential applications in wireless communications due to its low profile, compact, and lightweight features.

Journal ArticleDOI
01 Sep 2022-Polymers
TL;DR: In this article , the effect of FRP composite wrapping on the flexure performance of reinforced concrete (RC) filled pultruded glass-FRP (GFRP) profile hybrid beams with damage analysis was investigated.
Abstract: The application of pultruded fiber reinforced polymer (FRP) composites in civil engineering is increasing as a high-performance structural element or reinforcing material for rehabilitation purposes. The advantageous aspects of the pultrusion production technique and the weaknesses arising from the 0° fiber orientation in the drawing direction should be considered. In this direction, it is thought that the structural performance of the profiles produced by the pultrusion technique can be increased with 90° windings by using different fiber types. This paper presents experimental studies on the effect of FRP composite wrapping on the flexure performance of reinforced concrete (RC) filled pultruded glass-FRP (GFRP) profile hybrid beams with damage analysis. The hybrid beams are wrapped fully and partially with Glass fiber reinforced polymer (GFRP) and carbon fiber reinforced polymer (CFRP) composites. Hybrid beam specimens with 0° to 90° fiber orientations were tested under three- and four-point bending loads. Based on the experimental load–displacement relationship results, initial stiffness, ductility, and energy dissipation capacity were compared. The experimental findings revealed that the maximum load-carrying capacities of beams produced with pultrude profiles increased by 24% with glass wrapping and 64.4% with carbon wrapping due to the change in the damages. A detailed damage analysis is provided. Similarly, significant increases were observed in structural performance ratios such as initial stiffness and ductility ratio.

Journal ArticleDOI
TL;DR: In this paper , an innovative replaceable fuse connection for beam members in moment resisting steel frames was proposed, where steel angles are designed as fuse elements for energy dissipation and post-earthquake replacement.

Journal ArticleDOI
TL;DR: In this article, a novel refined shear deformation beam theory is proposed and applied, for the first time, to investigate the bending behavior of functionally graded (FG) sandwich curved beam.

Journal ArticleDOI
TL;DR: In this paper , a novel machine learning model, eXtreme Gradient Boosting (XGBoost), was used for the purpose of evaluating the moment capacity of cold-formed steel (CFS) channel beams with edge-stiffened web holes subject to bending.
Abstract: A novel machine learning model, eXtreme Gradient Boosting (XGBoost), was used for the purpose of evaluating the moment capacity of cold-formed steel (CFS) channel beams with edge-stiffened web holes subject to bending. A total of 1620 data points were generated for training the XGBoost model, using an elasto-plastic finite element model which was validated against 12 sets of test data taken from the existing literature. The R2 score of XGBoost predictions for the moment capacity was around 99%. The performance of current design equations was evaluated through the comparison of their results against those obtained from the XGBoost model. The moment capacities obtained from the XGBoost testing dataset were also compared with that determined from the existing design equations for un-stiffened holes (USH) and edge-stiffened holes (ESH). The moment capacities determined from the current design equations for USH and ESH were found to be excessively conservative by 38.3%, and unconservative by 36.2% on average, respectively. Therefore, new design equations were proposed based on the results of parametric study using the XGBoost model. In the detailed parametric analysis, the effects of web depth, section thickness, and beam length on the moment capacity of channel beams (CFSCB) with ESH were considered. From the results of XGBoost outputs, the absolute percentage error of new design equations for that based on the strengths of unperforated CFSCB was 8.78%, and for that based on the strengths of CFSCB with USH, the absolute percentage error was 13.7%. Additionally, a reliability analysis was performed to evaluate the accuracy of the proposed equations that were used to predict the moment capacity of CFS channel beams with ESH subject to bending. The reliability indices of all the proposed equations were greater than 2.5 which can be reliable as per the guidelines of AISI.

Journal ArticleDOI
TL;DR: In this article , a reflective-type 1 bit metasurface element is designed by employing a multilayer structure composed of metallic back plate-LC-complementary split ring resonator (CSRR).
Abstract: Terahertz wave manipulations, especially the phase manipulations, through metasurfaces has attracted considerable interests. Here, we develop a terahertz beam steering device using the liquid-crystal (LC)-integrated programmable metasurface. Specifically, a reflective-type 1 bit metasurface element is designed by employing a multilayer structure composed of metallic back plate-LC-complementary split ring resonator (CSRR). Numerical simulations show that, at the optimized operation frequency of 0.675 THz, the developed metasurface element has a nearly 180° phase difference between unbiased and biased states with close reflection amplitudes. Furthermore, a one-dimensional programmable metasurface array with 32 independently controlled subarrays is designed and fabricated using the lithography technology. Both simulated and measured far-field scattering patterns of the metasurface certify the anomalous beam reflection and wide-angle beam steering performances. Nevertheless, the optimal frequency red shifts to 0.645 THz in the experiment. This work may advance the application of metasurfaces in terahertz beam manipulation devices.

Journal ArticleDOI
TL;DR: In this article , a finite element-based higher-order zigzag theory was used for bending and free vibration analysis of functionally graded carbon nanotube-reinforced (FG-CNTR) sandwich beams.
Abstract: In the present work, bending and free vibration analyses of functionally graded carbon nanotube-reinforced (FG-CNTR) sandwich beams are carried out using finite element-based higher-order zigzag theory. Face sheets are assumed to be made up of FG-CNTR composite, and the core is assumed to be made up of balsa wood (softcore). The present formulation also takes into account transverse normal stresses. The computational model incorporates transverse shear stress and transverse normal stress continuity condition at interfaces. Zero transverse shear stress condition at the bottom and top surfaces of the beam is also satisfied. The principle of minimum potential energy is employed for carrying out bending analysis, while Hamilton’s principle is adopted for free vibration analysis. The investigation is carried out for different gradation laws which govern the distribution of CNTs across the thickness of face sheets. The influence of the core’s thickness on stresses and displacements is also critically analyzed in the present work. It has been observed that the thickness of the core and CNT gradation law significantly affect the mechanical behavior of the sandwich FG-CNTRC beam.

Journal ArticleDOI
TL;DR: In this article, a finite element-based higher-order zigzag theory was used for bending and free vibration analysis of functionally graded carbon nanotube-reinforced (FG-CNTR) sandwich beams.
Abstract: In the present work, bending and free vibration analyses of functionally graded carbon nanotube-reinforced (FG-CNTR) sandwich beams are carried out using finite element-based higher-order zigzag theory. Face sheets are assumed to be made up of FG-CNTR composite, and the core is assumed to be made up of balsa wood (softcore). The present formulation also takes into account transverse normal stresses. The computational model incorporates transverse shear stress and transverse normal stress continuity condition at interfaces. Zero transverse shear stress condition at the bottom and top surfaces of the beam is also satisfied. The principle of minimum potential energy is employed for carrying out bending analysis, while Hamilton’s principle is adopted for free vibration analysis. The investigation is carried out for different gradation laws which govern the distribution of CNTs across the thickness of face sheets. The influence of the core’s thickness on stresses and displacements is also critically analyzed in the present work. It has been observed that the thickness of the core and CNT gradation law significantly affect the mechanical behavior of the sandwich FG-CNTRC beam.

Journal ArticleDOI
TL;DR: In this paper , the authors investigated the correlation between the vertical profile of beam intensity and the vertical profiles of plasma properties at the extraction region of the source, focusing on the influence of increasing cesium injection.
Abstract: Giant negative ion sources for neutral beam injectors deliver huge negative ion currents, thanks to their multi-beamlet configuration. As the single-beamlet optics defines the transmission losses along the beamline, the extraction of a similar current for all beamlets is extremely desirable, in order to facilitate the beam source operation (i.e., around perveance match). This Review investigates the correlation between the vertical profile of beam intensity and the vertical profiles of plasma properties at the extraction region of the source, focusing on the influence of increasing cesium injection. Only by the combined use of all available source diagnostics, described in this Review, can beam features on the scale of the non-uniformities be investigated with a sufficient space resolution. At RF power of 50 kW/driver, with intermediate bias currents and a filter field of 2.4 mT, it is found that the central part of the four vertical beam segments exhibits comparable plasma density and beamlet currents; at the edges of the central segments, both the beam and electron density appear to decrease (probably maintaining fixed electron-to-ion ratio); at the bottom of the source, an increase of cesium injection can compensate for the vertical drifts that cause a much higher presence of electrons and a lower amount of negative ions.

Journal ArticleDOI
01 Feb 2022
TL;DR: In this paper , the authors derived the interfacial energy release rate at the notch location for strengthened steel beams and derived the tendency prediction for fatigue life of interfacial debonding development for the strengthened steel beam with/without WDC exposure, based on Paris' law.
Abstract: Prestressed carbon fiber reinforced polymer (CFRP) strengthening is effective in suppressing crack propagation of steel beams. However, the fatigue behavior of notched steel beams with prestressed CFRP under a hygrothermal environment is not fully understood. Generally, notch machining on the steel beam is an ordinary method to simulate a fatigue defect for laboratory tests. In this study, the interfacial energy release rate at the notch location was first derived for strengthened steel beams. The theoretical results show that the interfacial energy release rate can be significantly reduced by prestressed CFRP strengthening, contributing to improving the interfacial fatigue performance. In addition, notched steel beams strengthened by prestressed CFRP (with a prestress level of 25% of tensile strength of CFRP plate) were exposed to wetting/drying cycles (WDCs) and then tested under fatigue loading. The experimental results show that prestressed CFRP strengthening increases the fatigue resistance of interfacial debonding initiation and failure 3.47 times and 7.83 times, respectively, which agrees with the tendency revealed by the theoretical results. In contrast, WDC exposure reduced the fatigue lives of interfacial debonding initiation and failure by 34.6% and 27.2%, respectively. An S–N curve based on the maximum principal interfacial stress at the notch location was proposed to predict the tendency of fatigue life of debonding initiation for strengthened steel beams. Moreover, the tendency prediction for fatigue life of interfacial debonding development for the strengthened steel beams with/without WDC exposure was developed based on Paris’ law.

Journal ArticleDOI
TL;DR: In this article , a novel refined shear deformation beam theory is proposed and applied, for the first time, to investigate the bending behavior of functionally graded (FG) sandwich curved beam.