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The surface-enhanced Raman scattering (SERS) technique provides outstanding molecular fingerprint identification and high sensitivity of analytes. Herein, colloidal sphere-shaped gold nanoparticles (Au-NPs) trapped in concentric rings of the Bessel beam generated from the optical fiber-based negative axicon has been reported as a SERS substrate. With the trapping of Au-NPs, the SERS ability of colloidal Au-NPs improved, and the average enhancement factor (AEF) of the rhodamine-6G (R6G) and 4-aminothiophenol (4-ATP) molecules can reach up to the order of 107. Control experiments were also carried out with the trapping of Au-NPs by Gaussian beam illumination, without any illumination of the light and with the trapping of Au-NPs by the Bessel beam illumination on a silver (Ag)-coated silicon (Si) substrate with a self-assembled monolayer (SAM) of 4-ATP. Theoretical studies were also carried out using the finite element method (FEM) to identify the hotspots generated in the gaps formed between the Au-NPs, leading to an enhancement in the SERS signal of the molecules, and the results were consistent with the experimentally determined AEFs. The obtained results demonstrate that the proposed SERS technique is stable. This study has significant potential applications in clinical diagnosis, food safety, environment safety, chemical sensing, and biosensing. [ABSTRACT FROM AUTHOR]

This study investigates acoustic radiation forces on spherical objects generated by Bessel beams in a viscous fluid. Radiation forces on elastic spheres and shells of different materials are examined using viscid expression with the thermoviscous correction included, and the results are then compared with numerical simulations based on the finite element method. The Stokes drag force for zero-order Bessel waves was theoretically derived, and in turn, a practical example of negative radiation forces is proposed and investigated together with the gravity, the buoyancy, and the drag force from acoustic streaming. It is found that the negative pulling force exists even including the positive forces from the other sources; however, the parameter regions for pulling forces are reduced especially for small objects. This work helps the further study of particle manipulations by acoustic Bessel beams in viscous fluids and also guides the experimental realization of acoustic tractor beams. [ABSTRACT FROM AUTHOR]

We propose an inverse problem of determining the mechanical and variable-order parameters of the Euler–Bernoulli beam on viscoelastic foundation. For this goal, we develop a fully-discrete Hermite finite element scheme for this model and analyze the corresponding error estimates. The Levenberg–Marquardt method is then applied to determine the multiple parameters. Extensive numerical experiments are performed under practical settings to demonstrate the behavior of the proposed model and the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

By applying two elastically supporting styles, the elastic supports beam (ESB) and elastic foundation beam (EFB) are proposed to simulate the underwater submerged floating tunnel (SFT) under hinged boundaries. Their equivalence is investigated through the frequencies/modes and forced responses caused by equidistant moving loads. The ESB model is built by regarding each tether as an elastic support and using the novel isolating/assembling technique between beam-segments and global tube, and the order of characteristic matrix for any number of intermediate elastic supports is reduced to 4 × 4. Then, the stiffness of all elastic supports and the uniformity/non-uniformity are well considered in the ESB model. The governing equations of the EFB model with a uniform linear elastic support are also given. The newly discovered results, which are verified by the finite element method (FEM), indicate the merging phenomena appear in the frequency spectrum in the ESB model. The equivalence holds for some uniform cases in the ESB model based on the peak values of responses by using the stiffness relationship and a correction coefficient, whereas the equivalence does not exist for the uneven case of elastic supports. [ABSTRACT FROM AUTHOR]

A method of experimental study of forced bending vibrations of unfixed spans of continuous thin‐walled structural element fixed on rigid support elements of finite dimensions has been developed using instrumental means for registration of vibration acceleration amplitudes. The technique is realized on beams with different types of their fixing under the loading of one of the beam section with an external force that varies in time according to a harmonic law. Experimental dependences of amplitude values of vibration accelerations in specific points of certain spans of the beam on the frequency of external load have been obtained. These results indicate the passage of vibrations through the fixed sections due to the transformation of bending vibration modes of the loaded section into longitudinal transverse‐shift vibrations of the fixed sections during the transition across the boundary from the unfixed section to the fixed one (from the fixed to the unfixed section). For the theoretical study of the described phenomenon a transformational model of the flat beam deformation is constructed on the basis of the refined Timoshenko model with additional account of the deformability of the section with fixation to a rigid support element of finite length on one of its face surfaces. The corresponding equations of motion of the unfixed and fixed sections are derived. The corresponding kinematic and force conditions of their conjugation are formulated. On their basis, analytical solutions of two specific problems are found in the linear approximation. One‐dimensional finite elements for modeling the dynamic response of continuous beam of the considered class are also constructed. Numerical experiments have been carried out for a flat beam made of aluminum alloys D16AT, AMg‐6 and unidirectional fiber reinforced plastic. The presence of a significant transformation of the stress‐strain state parameters of the considered beams at the transition across the boundary from unfixed to fixed sections and a significant increase in the level of transverse tangential stresses on the fixed section of the beam in the vicinity of the interface of the unfixed section with the fixed one have been revealed. [ABSTRACT FROM AUTHOR]

In this work, a corotational finite element formulation is suggested for spatial beams with geometrically nonlinear behavior subjected to static loads. We returned to the three successive rotation angle procedure, mainly the Tait-Bryan angles. By carefully defining the trigonometric rules for all rotation angles, the singularity problem, that had limited the use of these angles, is avoided. Three different types of coordinate systems are used: a fixed global coordinate system that stays fixed throughout the analysis, a fixed local coordinate system that is fixed and precisely attached to each element, and a corotational local frame for each element that moves and rotates together with the element throughout the analysis. The rigid body motion can easily be separated from the overall deformation since the deformation is always tiny relative to the corotational frame. An incremental-iterative method is used for the solution based upon the Newton-Raphson method. Different examples are solved to demonstrate the practicality, correctness, and accuracy of the proposed method. The solutions converge at a relatively quick rate. [ABSTRACT FROM AUTHOR]

This study introduces a novel framework for local resonant systems to low bandgap frequencies without greatly increasing spatial penalties in grid structures. The proposed double-spiral resonator (DSR) consists of a pair of spiral spring-like structures and a rigid plate acting as the "mass" of the oscillating system, which can serve as an effective mechanical filter. A rapid and accurate calculation based on the stiffness matrix method is proposed to precisely predict the fundamental resonant frequency of the resonator. Periodic installation of these resonators in a grid-like beam structure can lead to the formation of a new type of metastructure that possesses negative effective properties. Investigations on the bandgap characteristics of the proposed metastructure are conducted using the finite element method. It is found that a low-frequency resonant-type bandgap is present in such a structure. Changing the thickness of the central mass or the number of parasitic beam segments enables the manipulation of the bandgap location. The validity of the analytical results is evaluated via comparison with the finite element results and experimental measurements. By using multiple resonators with similar resonance frequencies, the attenuation bandwidth can be effectively broadened. The physics behind wave attenuation can be realized by introducing a negative effective mass density. The results demonstrate that the proposed structure exhibiting unique dynamic characteristics can successfully attenuate undesired structural vibrations at low frequencies. It may be concluded that this DSR can be used as an alternative to current vibration filtering systems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the lateral deflection of a simply supported periodic stepped beam under uniform load by using an analytical method. This study considers each element of the biperiodic stepped beam as a Euler–Bernoulli beam. By using the local coordinates alongside with the boundary and continuity conditions, the different coefficients for each element caused by the jump of the bending rigidity are calculated. The continuous deflection problem of the multi-stepped repetitive beam is formulated as a linear first-order difference equation with second member. With these coefficients, the deflection at mid-span of the biperiodic beam is analytically found in exact form. This deflection is satisfactory compared to the results of a finite element model based on beam discretization techniques using Hermitian cubic shape functions. The normalized deflection at mid span converges non-monotonically towards the homogenization beam model based on equivalent homogenized stiffness. [ABSTRACT FROM AUTHOR]

An analytical wave propagation approach is developed in this paper for the free and forced vibration of a system of multiple elastically connected beams for the first time. The beams of the system are continuously joined by a massless, linear, elastic layer which can be regarded as continuous spring. The coupled partial differential equations governing the vibration of the multi-beam system are established and decoupled by using a technic developed based on matrix theory. For the decoupled equations, a general "vibration" state is introduced into the symplectic dual system. By solving the symplectic eigenproblem and utilizing the wave propagation theory, the general "vibration" state can be analytically described in symplectic space. By using these analytical expressions and satisfying the physical boundary conditions of the system, the natural frequencies, mode shapes and forced responses can be obtained analytically and explicitly. In the numerical examples, free and forced transverse vibration of the two- and three-beam system with various combinations of boundary conditions are considered. The effectiveness of the present method is validated by comparing the present results with the analytical results from the literature and the results calculated by the finite element method. [ABSTRACT FROM AUTHOR]

This article presents large deflection data for prismatic (unvarying cross section across length) and non-prismatic (tapered, i.e. varying cross section across length) cantilever beams subjected to concentrated tip loads using the finite element method for different taper ratios. The approximate nonlinear solution is derived from the perspective of a polynomial function. The tapered beams that correlate to the nonprismatic cantilever beams have different widths, depths, and diameters. Using the aforementioned large displacement data that have been analysed, a very simple approach is used to evaluate the large amplitude first mode frequency for the cantilever beam with (nonprismatic) tapered and without (prismatic) tapered. The current approach can be used effectively to find accurate results with far less computer capacity as compared to other methods available in the literature. The difference between the current findings and the bibliographic data is shown. The major goal of this work is to contribute to the simple description of polynomial functions for large amplitude first mode free vibration frequency problems with and without tapered beams in terms load parameter(𝜆) versus tip slope (𝛼)and tip amplitude(𝑎/𝐿). Large amplitude first mode frequency (𝛺) increases with tip slope(𝛼). This indicates that the prismatic and non-prismatic cantilever beams exhibit hardening type nonlinearity. At a particular tip slope(𝛼), the diameter taper shows higher frequency than other tapered beams and uniform beams. According to current studies, it can be restricted to a lower range of tip slope(𝛼)or amplitude(𝑎/𝐿). [ABSTRACT FROM AUTHOR]

This paper investigates nonlinear free and flexural analysis of hyperelastic beams. The constitutive relations of the hyperelastic beam were derived using the neo-Hookean strain energy function and Timoshenko beam theory. Also, the nonlinear governing equations and nonlinear natural boundary conditions were derived using Hamilton's principle. The meshless collocation method based on the multiquadric radial basis function (MQ-RBF) was utilized to discretize the nonlinear governing equations. Also, the arc-length algorithm was used to solve the nonlinear system of equations. To validate the results of the meshless method, different boundary conditions (clamped–clamped, simply supported–simply supported, clamped–simply supported, and clamped-free) were examined, and the results obtained from the meshless method were compared with those of the finite element method in Abaqus finite element software. The results show that the maximum and minimum differences between meshless and finite element methods occur in clamped and free-boundary conditions, respectively. The results also show that the meshless method based on the MQ-RBF has good accuracy compared to the finite element method for bending and free vibration analysis of hyperelastic beams. [ABSTRACT FROM AUTHOR]

The expressions of the axial and transverse acoustic radiation forces of a rigid sphere arbitrarily positioned in a zero-order Mathieu beam are derived in this paper. The expansion coefficients of the off-axis zero-order Mathieu beam are obtained using the addition theorem of the Bessel functions, and numerical experiments are conducted to verify the theory. The three-dimensional acoustic radiation forces on a rigid sphere are studied when the beam is set at different ellipticity parameters, half-cone angles, and offsets of the incident wave relative to the particle center. Simulation results show that the axial acoustic radiation forces of the rigid sphere are always positive, but the transverse forces vary with the positions of the particle and the beam parameters. Also, by changing the frequency, half-cone angle, and offset of the zero-order Mathieu beam, the value and direction of the transverse forces can be adjusted, which has applications in controlling the rigid sphere to be close to or away from the beam axis. Furthermore, the finite element model is set up to verify the theoretical model, and the results obtained by the two methods are in good agreement. This work may contribute to a better understanding of the underlying mechanisms of the particle manipulation with different acoustic beams. [ABSTRACT FROM AUTHOR]

In order to suppress the vibration of a class of multi-coupling flexible beams, a three-coupling flexible beam experimental device is constructed. The vibration characteristics and active vibration control algorithms of three coupled flexible beams are studied. Due to the complex residual vibration of multi-coupled flexible beam structure, which shows the interaction between beams and close frequency characteristics, the dynamic model of coupled flexible beam structure is established by finite element method (FEM) and its theoretical modal analysis is carried out. Furthermore, the parameters of the experimental system are identified, and the close modal frequencies and damping ratios of the actual system are obtained. The characteristics of close modal vibration are verified. A reinforcement learning (RL) vibration controller based on proximal policy optimization (PPO) algorithm is designed. The algorithm mainly includes actor neural network and critic neural network, which are used to approximate the control strategy and evaluate state respectively. Based on theoretical modeling and experimental identification correction model, the agent learns offline, and then transfers the learned policy parameters to the experimental system for vibration control experiments. The experimental results demonstrate that the designed RL controller can effectively suppress the residual vibration of three coupled flexible beams. [ABSTRACT FROM AUTHOR]

The finite element method (FEM) is used to investigate the free and forced vibration characteristics of functionally graded graphene-nanoplatelet-reinforced composite (FG-GPLRC) beams. The weight fraction of graphene nanoplatelets (GPLs) is assumed to vary continuously along the beam thickness according to a linear, parabolic, or uniform pattern. For the FG-GPLRC beam, the modified Halpin–Tsai micromechanics model is used to calculate the effective Young's modulus, and the rule of mixture is used to determine the effective Poisson's ratio and mass density. Based on the principle of virtual work under the assumptions of the Euler–Bernoulli beam theory, finite element formulations are derived to analyze the free and forced vibration characteristics of FG-GPLRC beams. A two-node beam element with six degrees of freedom is adopted to discretize the beam, and the corresponding stiffness matrix and mass matrix containing information on the variation of material properties can be derived. On this basis, the natural frequencies and the response amplitudes under external forces are calculated by the FEM. The performance of the proposed FEM is assessed, with some numerical results obtained by layering method and available in published literature. The comparison results show that the proposed FEM is capable of analyzing an FG-GPLRC beam. A detailed parametric investigation is carried out to study the effects of GPL weight fraction, distribution pattern, and dimensions on the free and forced vibration responses of the beam. Numerical results show that the above-mentioned effects play an important role with respect to the vibration behaviors of the beam. [ABSTRACT FROM AUTHOR]

The dynamic characteristics of a hub-functionally graded material beam undergoing large overall motions are studied. The deformation field of the flexible beam is described by using the assumed mode method (AMM), the finite element method (FEM) and the point interpolation method (PIM). Assuming that the physical parameters of functionally graded materials follow certain kind of power law gradient distribution and vary along the thickness direction. The longitudinal deformation and transversal deformation of the beam are both considered, and the nonlinear coupling term which is known as the longitudinal shortening caused by transversal deformation is also taken into account. The rigid-flexible coupling dynamics equations of the system described by three different discrete methods which have a uniform form are derived via employing Lagrange's equations of the second kind. The validity of the point interpolation method established in this paper is verified by comparing with the numerical simulation results of the assumed mode method and the finite element method. On this basis, the influence of the functional gradient distribution rules on the dynamic characteristics of flexible beams undergoing large overall motions is discussed. The results show that the assumed mode method cannot deal with large deformation problem. Remaining other physical parameters of functionally graded materials beam unchanged, the maximum displacement of the beam increases with the increase of functionally graded materials index. The natural frequency of transverse bending of beam increases with the increase of rotational speed, when rotational speed is constant, the natural frequency will decrease with the increase of functional gradient index. [ABSTRACT FROM AUTHOR]

This paper presents an analytical transfer matrix modeling framework for the forced vibration of a bending-torsional-warping coupling Euler-Bernoulli thin-walled beam carrying an arbitrary number of three degree-of-freedom (DOF) spring-damper-mass (SDM) subsystems. The thin-walled beam is divided into a series of distinct sub-beams whose ends are connected to the SDM subsystems. The transfer matrix for each sub-beam is developed based on the exact shape functions of the bending-torsional-warping coupling Euler-Bernoulli theory. Each SDM system is modelled by a set of effective springs based on the dynamic condensation method. The governing matrix equation is formulated based on the compatibility conditions of the placement and the force at the common interfaces of two adjacent sub-beams. Then, a closed-form expression for the frequency response function of the thin-walled beam system is proposed. The results computed by the proposed method achieve good agreement with those obtained by the conventional finite-element method, which shows the accuracy and reliability of the proposed method. The effects of the system parameters on the vibration transmission and vibration isolation properties of the thin-walled beam system are studied. The presented method can simultaneously consider arbitrary number of SDM subsystems and boundary conditions. Furthermore, none of the associated matrices are larger than 12 × 12, which provides a significant computational advantage. [ABSTRACT FROM AUTHOR]

In this paper, a semi-analytical method for solving circular curved beams is proposed to study the free vibration of in-plane circular curved beams in both undamaged and damaged configurations. The crack damage of the structure is represented by the cross-sectional reduction of the damaged element. Based on the discrete circular curved beam model, the coupling stiffness matrices of shear, compression and bending are derived. Combined with the lumped mass matrix and the dynamic characteristic equation of the multi-degree-of-freedom system, the frequencies and modes of the damaged and undamaged structures are calculated. The results are compared with the finite element method, and the good consistency between them is verified. [ABSTRACT FROM AUTHOR]

The investigation of curved structures has attracted more and more attention, and the mainstream research focuses on the characteristics of curved beams subject to transverse loads, while sometimes axial loads are inevitable in engineering practice. Hence, this work aims to investigate the nonlinear vibrations of a curved beam subject to axial loads by developing appropriate modeling and solving methods. In this work, a nonlinear dynamic model of a hinged–hinged slightly curved beam (SCB) with sinusoidal shape subject to axial loads is first established, and the modal hypothesis method is subsequently used to obtain natural frequencies and mode shapes of the SCB subject to axial loads. Thereafter, a procedure to calculate the forced vibration responses of the SCB subject to axial loads is proposed by successively using the Galerkin truncation method, harmonic balance method and pseudo arc-length method. Finally, case studies are carried out to validate the above modeling and solving methods of the SCB subject to axial loads and explore its nonlinear dynamic characteristics. On the one hand, the effectiveness and accuracy of the proposed modeling and solving methods are verified by comparing with the results of finite element analysis. On the other hand, the results of the case studies demonstrate that the initial curvature, axial force, external excitation amplitude and initial configuration of the SCB can significantly affect its nonlinear dynamic characteristics. [ABSTRACT FROM AUTHOR]

Cold-formed steel (CFS) structural members retain their preferred position in the lightweight construction industry, which is due to their significant advantages. The optimization of these CSF elements will make it possible to construct buildings at very competitive prices, having in addition an increased load capacity, and thus obtaining a stable and economical construction. The main objective of this research being the evaluation of the effectiveness of these new sections in (CSF) and the estimation of the remarkable instabilities as well as the failure modes. This article deals with an experimental study on the behavior of CSF beams of delta and bi-delta shape, solicited by four-point bending loads. These cross section shapes are often used in floors as main and secondary beams. The properties of this type of sections are most often based on the method involving the effective width designated by the Eurocode 3 standard. A nonlinear analysis by finite elements (FE) using the ABAQUS calculation program is carried out, thus making it possible to compare the experimental results with the numerical ones as well as those which are given by the theory proposed by Eurocode 3. Finally, the results obtained essentially showed that the failure modes of the delta and bi-delta beams corresponded to the buckling modes local. [ABSTRACT FROM AUTHOR]

This paper presents a beam theory for analyzing the static response of slightly curved three-layer beams with interlayer slip. Since the beams are supposed to be immovably supported, membrane stresses develop even at moderately large deflections and the response becomes geometrically nonlinear. The theory is based on a layerwise application of the Euler–Bernoulli theory and a linear elastic constitutive law for the interlaminar displacements. In three application examples, the accuracy of this theory is shown by comparing the results of this theory with the outcomes of a more complex finite element analysis assuming a plane stress state. These application examples demonstrate the effect of a small initial deflection on the nonlinear response of the considered layered structural members. [ABSTRACT FROM AUTHOR]

In this paper, the expansion coefficients of the off-axial Gaussian beam are obtained using the localized approximation and the translational addition theorem for spherical wave function. The three-dimensional acoustic radiation force of a sphere positioned in an off-axial Gaussian beam is derived. The axial acoustic radiation force of a rigid sphere is computed to verify the derived expressions. The effect of the position of a polystyrene sphere in an off-axial Gaussian beam on the transverse and axial acoustic radiation forces is studied to explore the changing law of particle acoustic manipulation using a Gaussian beam. The calculated results show that the axial force repels the polystyrene particle away from the center of the beam. However, for the transverse force, there is a negative acoustic radiation force at some positions, which is related to the position of the polystyrene sphere in the Gaussian beam, and the negative transverse forces usually pull the polystyrene particle toward the beam axis. In addition, the numerical simulations based on the finite element method are presented to validate the analytical theory, and the comparison results are in good agreement with each other. The study may provide a theoretical basis for the development of single-beam acoustic tweezers using a Gaussian beam. [ABSTRACT FROM AUTHOR]

A piezoelectric metamaterial beam composed of metamaterials and piezoelectric energy harvesting is proposed to realize the dual-functional characteristics of vibration reduction and power generation simultaneously. Based on the theoretical derivation of the electrical domain and the structural domain, the transfer matrix of the piezoelectric metamaterial beam is constructed using the charge accurate integration method and the transfer matrix method. The energy band structure of the infinite periodical model and the vibration transmission of the finite periodical model are analyzed numerically to illustrate the low frequency bandgaps of the piezoelectric metamaterial beam. An external load circuit for energy harvesting is introduced, and its influence on the vibration characteristics of the original system is analyzed. On this basis, Kirchhoff's law is used to derive accurate analytical solutions for the output voltage and output power of each piezoelectric oscillator, and the relationship between the local resonance bandgap and band-edge effect and the power generation performance of the piezoelectric metamaterial beam is investigated in detail. Finally, the theoretical analysis results are verified by finite element simulation analysis. It is shown that the introduction of an external load circuit for energy harvesting results in the vanishing of the dense resonant frequency range at the lower band edge of the local resonance bandgap and the modal peaks near the upper and lower band edges are effectively suppressed, consequently expanding the range of the bandgap. In addition, an excellent power generation performance is observed in the local resonant bandgap and the passband of the upper and lower band edges. [ABSTRACT FROM AUTHOR]

Ensuring the accuracy of an analytical solution is important in modeling real engineering structures. For determining the stress-deformation condition of a thin-walled beam structure in bending, inadequately, the simple beam formula can only provide uniform average stress-deformation distribution at specific cross-sectional elevations. The recently developed analytical solution for determining stress-deformation conditions with consideration of the shear lag effect of a prismatic thin-walled box beam subjected to transverse load causing bending using classical quadratic deplanation function did not provide an accurate but rather a good estimate when compared with finite element analysis results. In this paper, the objective of the study was to see if the accuracy can be improved. The same Vlasov's method was used. The method was developed using Calculus of Variations based on a Stress-form stationary condition complementary energy which included the shear lag effect. All calculations were computerized using the software MAPLE 18 which assisted in getting quick results (especially for preliminary design studies) for various geometries, material properties, and loading conditions. Several deplanation functions were introduced. Two variants of the quadratic functions, i.e. x²y³ and x²y, and the quartic functions, i.e. x4y³ and x4y were used to find the best match against empirical data and FEA (finite element analysis) results. The finding was that the quartic variant of the deplanation functions provided improved matching with experimental data as well as FEA results. Noteworthy to point out that the characteristic of the functions with quartic-x or x4 of having almost flat variation in the center part enhances matching with the experimental data. Moreover, the characteristic of the function with cubic-y or y³ of having steeper slopes enhances matching with the FEM results at the edge. [ABSTRACT FROM AUTHOR]

A crack or any kind of damage induces a sharp discontinuity in the rotational displacement curve in a structure under load. However, if the beam is not loaded sufficiently or crack depth is very small, the discontinuity may not be possible to identify through conventional methods. This study proposes a non-destructive approach to reveal the presence of a crack in structural components based on the measurement of very small discontinuity in rotational displacement by employing a piezoelectric sensor (PZT). An analytical model of a statically loaded cracked beam with PZT attached to the beam is developed for various boundary conditions. The solution is obtained through Ritz approximation. Rotational displacements at different points along the length of the beam are determined. Subsequently, a finite element analysis on ABAQUS platform is carried out for comparison. The results obtained from these analyses are validated with the experimental data published in open literature. Two distinct techniques are employed to monitor the damage in slender and short length beams. the efficacy of the technique in the detection of small cracks in structure is established. It is also shown that the presence of multiple cracks in beams having various boundary conditions can be monitored by a single non-destructive investigation following the method. [ABSTRACT FROM AUTHOR]

In this article, a nonlinear structural formulation that uses a new dimensionless set of generalized displacements is proposed for solving geometrically nonlinear beam problems, being validated by several applications given in literature where a cantilever beam is likely to undergo large displacements. By this approach, useful simplifications and insights are achievable in the analysis process, as the system matrices becoming linear and the reduction of required interpolation continuity degree. The formulation is firstly developed—in a Lagrangian perspective—and the equilibrium equations are then derived using Hamilton's principle. In the sequence, using finite element method, it is substantiated by comparison to examples given in literature in static, dynamic, and finally in an application where piezoelectric effects intervene, in order to assess its multiframework capabilities and deliver a convenient approach whereby beams constituted of smart or conventional materials can be efficiently studied. [ABSTRACT FROM AUTHOR]

In this study, the geometrically nonlinear behaviour caused by large displacements and rotations in the cross sections of thin-walled composite beams subjected to axial loading is investigated. Newton–Raphson scheme and an arc length method are used in the solution of nonlinear equations by finite element method to determine the mechanical effect. The Carrera-Unified formulation (CUF) is used to solve nonlinear, low or high order kinematic refined structure theories for finite beam elements. In the study, displacement area and stress distributions of composite structures with different angles and functionally graded (FG) structures are presented for Lagrange polynomial expansions. The results show the accuracy and computational efficiency of the method used and give confidence for new research. [ABSTRACT FROM AUTHOR]

Developing particle-in-cell (PIC) methods using finite element basis sets, and without auxiliary divergence cleaning methods, was a long-standing problem until recently. It was shown that if consistent spatial basis functions are used, one can indeed create a methodology that was charge conserving, albeit using a leapfrog time stepping method. While this is a significant advance, leapfrog schemes are only conditionally stable and time step sizes are closely tied to the underlying mesh. Ideally, to take full advantage of advances in finite element methods (FEMs), one needs a charge conserving PIC methodology that is agnostic to the time stepping method. This is the principal contribution of this paper. In what follows, we shall develop this methodology, prove that both charge and Gauss' laws are discretely satisfied at every time step, provide the necessary details to implement this methodology for both the wave equation FEM and Maxwell solver FEM, and finally demonstrate its efficacy on a suite of test problems. The method will be demonstrated by single particle evolution, non-neutral beams with space-charge, and adiabatic expansion of a neutral plasma, where the Debye length has been resolved, and real mass ratios are used. [ABSTRACT FROM AUTHOR]

Tunable stiffness mechanisms can increase the noninvasiveness and stability of organ manipulation in laparoscopic liver resection. We have developed an organ-grasping device using beam-shaped tunable stiffness mechanism. Increasing the change ratio of stiffness will improve the performance of the device by offering high flexibility when adhering to the liver surface and high rigidity during the manipulation of the liver; however, optimal design of the beam has not been investigated. In this study, we investigate the wavy structure shape of the device that enhances the change in the ratio of stiffness. To increase the stiffness in a high-stiffness state, we used principal stress lines in the device to design the edge curve of the wavy shape material in the beams. We also investigated the arrangement of the wavy shape to decrease the stiffness in a low-stiffness state. Simulation using finite element method showed that the change ratio of stiffness was improved up to 13.0 by the new wavy shape arranged with the uniformly thick bottom of the waves. [ABSTRACT FROM AUTHOR]

• A nonlinear formulation for large deformation of elastic curved beams is developed. • The incompressibility constraint is exactly satisfied. • The formulation models moderately thick as well as thin hyperelastic beams. • A Total Lagrangian FE formulation is developed to solve the nonlinear equations. • The element based on the present formulation does not suffer from shear locking. The aim of this contribution is to develop a nonlinear formulation for modelling the large deformation of elastic curved beams made of fully incompressible hyperelastic materials. The basic idea is to apply the incompressibility constraint besides the plane stress assumption in the directions perpendicular to the centreline of the beam. Accordingly, a system of three nonlinear algebraic equations for the hydrostatic pressure as well as normal strain components in the beam cross section are obtained. By solving the system of equations, either analytically or numerically, it is possible to propose constitutive equations for the force and moment resultants present in the formulation. The main advantage of this strategy is that it allows for using three-dimensional incompressible constitutive equations. Due to highly nonlinear nature of the differential equations, a Total Lagrangian finite element formulation is developed. Performance and accuracy of the formulation are investigated through several numerical examples. [ABSTRACT FROM AUTHOR]

A sequentially coupled shape and topology optimization framework is presented in which the outer geometry and the internal topological layout of beam-type structures are optimized simultaneously. The outer geometry of the beam-type structures is parametrically described by non-uniform rational B-splines (NURBS), which guarantees a highly accurate description of the structural shape and enable an efficient control of the design domain with only a few control points. The computational efficiency of the coupled optimization approach is assured by applying a gradient-based optimization algorithm, for which the sensitivities are derived in closed form. The formulation of the coupled optimization approach is tailored toward 2.5D and full 3D representations of beam structures used in engineering applications. The 2.5D beam model, which has been taken from the literature, uses standard beam elements to simulate the beam response in the longitudinal direction, whereby the cross-sectional properties of the beam elements are calculated from additional 2D finite element method (FEM) analyses. A comparison study of a cantilever beam problem subjected to pure shape optimization and pure topology optimization illustrates that the 2.5D and 3D beam models lead to similar shape and topology designs, but that the 2.5D beam model has a significantly higher computational efficiency. Specifically, the computational times for the 2.5D model are about a factor 70 (shape optimization) and 1.4 (topology optimization) lower than for the 3D model, which indicates that in the coupled optimization approach the optimization of the shape provides the largest contribution to the higher computational efficiency of the 2.5D model. The coupled shape and topology optimization analysis subsequently performed on the 2.5D cantilever beam model demonstrates that the specific order at which the alternating shape and topology optimization increments are performed in the staggered update procedure turns out to have some influence on the computational speed and the value of the minimal compliance computed. Despite these differences, the final beam structures following from the different staggered update procedures illustrate how shape and topology can be efficiently optimized in an integrated, coupled fashion. [ABSTRACT FROM AUTHOR]

Twist beam rear suspension systems are frequently used in front wheel drive cars owing to their compactness, lightweight and cost-efficiency. Since the kinematic behavior of twist beam rear suspension systems are determined by the elastic properties of the twist beam, the twist beam is the most critical component of this suspension system. In the study, a simplified optimization model is presented to offer designers the most suitable beam structure in the early stage of the vehicle system development. With the optimization model, designers will be able to obtain the most suitable twist beam structure in a very short time. Opposite wheel travel analysis based on finite element modeling of twist beam is conducted to examine the kinematic performance of the twist beam rear suspension. The cross-section, position and direction of the twist beam are the most important parameters affecting the performance of the twist beam rear suspension system. In this study, optimization studies with 25 design variables including variable cross-sections, twist beam position and twist beam orientation are performed. Nine different optimization studies are carried out to investigate the effects of design variables better. In optimization studies carried out with the genetic algorithm, the objective and constraint functions are obtained with the moving least squares meta-modeling method. In the study, toe angle, camber angle and roll steer are decided as constraints, and mass as the objective function. With the optimization models, lightweight designs up to 25% have been obtained according to the initial design. It is validated that the proposed simplified model and analysis of twist beam rear suspension with connecting bushing is a quite efficient approach in terms of accuracy and to speed up the optimum design process. [ABSTRACT FROM AUTHOR]

This paper adopts both explicit and implicit finite element methods in a specialist package LS-DYNA to investigate the nonlinear, dynamic response of a long span shell roof structure when subjected to blast loading. Parametric studies have been carried out on blast loaded laminated glass plates with reference to experimental results obtained by European researchers. A case study that has been chosen is a light rail station in The Netherlands called The Erasmusline. Following the detonation of 15 kg TNT charge, explicit analysis showed breakage surrounding the rigid supports along the edge beam where modal vibrations are restrained. An implicit analysis has confirmed the resonances in global eigen-frequencies where most blast damage is localized around the roof canopy hence producing cracking and potential glass detachment from the panels without full structural demolition. This insight from this study will inform structural engineers about the potential modes of failure and preventative strategies to minimize further secondary losses of life or assets from a terrorist attack. [ABSTRACT FROM AUTHOR]

This paper gives the analytical investigation of six reinforced concrete deep beams reinforced with horizontal and vertical web reinforcement. Reinforced concrete deep beams analysis is a complex problem where there is no exact solution. The effect of reinforcement distribution has been studied and compared to experimental investigation and various codes such as ACI 318 and IS 456. A new formula is proposed to define shear strength of deep beams. The codal equations are too traditional for predicting the shear strength of RC deep beams, so an improved and simplified equation was proposed using nonlinear finite element method by ABAQUS. The FE results are compared with experimental results in terms of ultimate loads, displacements, tension stress damage. The proposed shear strength equation predicts 80% of the experimental data in the range of 66-110% of measured shear strength. FE model results accurately predicted. The stress contours suggested high stresses in the path of cracks and low stresses in the uncracked regions. [ABSTRACT FROM AUTHOR]

In this paper, we derive the meso-scale equations of motion for particle reinforced Timoshenko beam from corresponding micro-scale equations by letting the scale parameter denoting the ratio of the particle radius and beam thickness decrease to zero. The beam is cantilevered at one end and is subject to a normal pressure of constant magnitude at the other end. The displacement field and the stress-strain state of the beam are determined for a decreasing sequence of values of the scale parameter to establish the convergence of solutions numerically using the finite element analysis. [ABSTRACT FROM AUTHOR]

The purpose of the work was analytical research and computer modeling of the influence of shape and size of console beams of elastic plates in non-base configurations for the cam of the automatic half-hose machine under the conditions of flexibility, strength, and minimization of sizes. The scientific novelty of the work lies in the further development of the theory and methodology of designing the elements of knitting systems of the automatic half-hose machines based on regimes of loading, limitations in strength and dimensions, as well as requirements of the technological process. In order to increase the flexibility of the elastic plate, the symmetrical introduction of two console beams of trapezoidal shape was proposed. The influence exerted by the coefficient of the shape of console beams and their lengths on the magnitudes of deflections and stresses was analyzed, which allows making grounded and flexible decisions regarding the dimensions of the root and the end sections of the beams at the preliminary stage of design. The mathematical support was presented mainly in an explicit form, which simplified the analysis of the influence of controlled dimensions of the elastic plates on their flexibility and strength, as well as contributes to the comprehensive approach to the development of cams of different constructions with elastic plates and allows improving the quality and efficiency of design solutions of cams. The beam bending theory and the finite element method based on Code_Aster shared software were used. The model of the plate was represented by an ordered grid of finite nodal elements of the same size, without the use of elongated and flat elements. According to the results of simulation experiments, the distributions of deformations and stresses on the surface of the elastic plate of the cam were obtained, depending on its shape and size, which confirmed the validity of calculated recommendations. [ABSTRACT FROM AUTHOR]

In this study free vibration behavior of a stepped beam on an elastic foundation is considered. The vibration of uniform beams on an elastic foundation has been previously studied extensively and various solutions are available in the literature. However, the problem considered in current study appears not to have been widely covered in the literature and analytical solutions are strictly limited. To this aim, semi-analytical solutions are obtained first by using Adomian decomposition method, then finite element solutions are computed via structural finite element analysis software (SAP 2000). The free vibration analysis of stepped beam considering the combinations of different support conditions at each end are performed employing semi-analytical and finite element methods. The findings of the analysis are compared and discussed in detail. [ABSTRACT FROM AUTHOR]

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• Self-adjoint positive-definite fractional-order nonlocal elastic model established. • Paradoxical nonlocal interactions addressed by the fractional-order continuum model. • Ritz finite element model for the fractional-order BVP developed. • Singularities in the kernel of fractional derivative circumvented. • Validation and convergence tests of the fractional-Finite Element Model accomplished. We present the analytical formulation and the finite element solution of a fractional-order nonlocal continuum model of a Euler-Bernoulli beam. Employing consistent definitions for the fractional-order kinematic relations, the governing equations and the associated boundary conditions are derived based on variational principles. Remarkably, the fractional-order nonlocal model gives rise to a self-adjoint and positive-definite system accepting a unique solution. Further, owing to the difficulty in obtaining analytical solutions to this boundary value problem, a finite element model for the fractional-order governing equations is presented. Following a thorough validation with benchmark problems, the fractional finite element model (f-FEM) is used to study the nonlocal response of a Euler-Bernoulli beam subjected to various loading and boundary conditions. The fractional-order positive definite system will be used here to address some paradoxical results obtained for nonlocal beams through classical integral approaches to nonlocal elasticity. Although presented in the context of a 1D Euler-Bernoulli beam, the f-FEM formulation is very general and could be extended to the solution of any general fractional-order boundary value problem. [ABSTRACT FROM AUTHOR]

This study proposes a time-domain spectral finite element (SFE) method for simulating the second harmonic generation (SHG) of nonlinear guided wave due to material, geometric and contact nonlinearities in beams. The time-domain SFE method is developed based on the Mindlin–Hermann rod and Timoshenko beam theory. The material and geometric nonlinearities are modeled by adapting the constitutive relation between stress and strain using a second-order approximation. The contact nonlinearity induced by breathing crack is simulated by bilinear crack mechanism. The material and geometric nonlinearities of the SFE model are validated analytically and the contact nonlinearity is verified numerically using three-dimensional (3D) finite element (FE) simulation. There is good agreement between the analytical, numerical and SFE results, demonstrating the accuracy of the proposed method. Numerical case studies are conducted to investigate the influence of number of cycles and amplitude of the excitation signal on the SHG and its performance in damage detection. The results show that the amplitude of the SHG increases with the numbers of cycles and amplitude of the excitation signal. The amplitudes of the SHG due to material and geometric nonlinearities are also compared with the contact nonlinearity when a breathing crack exists in the beam. It shows that the material and geometric nonlinearities have much less contribution to the SHG than the contact nonlinearity. In addition, the SHG can accurately determine the crack location without using the reference data. Overall, the findings of this study help further advance the use of SHG for damage detection. [ABSTRACT FROM AUTHOR]

The paper is devoted to simply supported beams under three-point bending. Their mechanical properties symmetrically vary in the depth direction. The individual shear deformation theory for beams of such features is proposed. Based on the principle of stationary total potential energy the differential equations of equilibrium are obtained. The system of the equations is analytically solved, and the shear coefficients and deflections of example beams are calculated. The solution is compared with other analytical results obtained with the use of another deformation function. Moreover, the bending problem of these beams is also numerically studied using the finite element method. Results of analytical and numerical studies are presented in Figures and Tables. [ABSTRACT FROM AUTHOR]

The paper presents a comparative analysis of the behaviour of a composite beam, consisting of a precast element with indented surface and new concrete layer, subjected to 4-point bending. The results obtained from the virtual model of the beam created using the finite element method (Abaqus/CEA 2019 software) were compared with the laboratory test results obtained with use of the digital image correlation (DIC) method for identifying the crack pattern. The virtual model of composite beam was calibrated by the choice of interface parameters ensuring that the value of load resulting in delamination between concrete layers was close to that value obtained in the laboratory tests. The comparative analysis showed that the pattern of bending and shear cracks and the pattern of interface crack obtained with the finite element method reflect the laboratory test results properly. It can be assumed that the crack between concrete layers is related to the appearance and propagation of shear cracks. On the basis of FEM analysis it can be concluded that the phenomena identified as "shear friction" and "dowel action" are significantly activated after the interface cracking. [ABSTRACT FROM AUTHOR]

The influence of various crack inclination angles on the mode shape, rotational stiffness at the cracked cross section and the stiffness of the cracked cantilever beam was investigated. Finite element analysis for different scenarios of inclined cracked cantilever beam has been performed to obtain frequencies and zero frequency deflections. Rotational spring is considered as a simulation of the cracked section and based on zero frequency deflection; rotational spring stiffness and stiffness of cracked beam are analytically calculated. Also, the first three mode shapes of bending vibration and harmonic response are extracted and studied. The investigation of results revealed that the effect of inclined crack with ϕ = 40°, ϕ = 55° and ϕ = 120°, respectively, is much, moderate and minimum severe, respectively, on the cracked cantilever beam. [ABSTRACT FROM AUTHOR]

In this paper, a new dynamic model for the vibration analysis of an inwardoriented rotating cantilever beam with extra distributed mass was presented. The derived differential equation of motion was solved using the meshless methods of generalizedMultiquadric Radial Basis Function (RBF) and the eigenfrequencies of the system were determined. The same problem was also modeled using the finite element method and the results were compared to validate the accuracy of the proposed model. Later, the effect of the partially distributed mass amount and location on the eigenfrequencies was studied for various beam lengths. The results showed that the eigenfrequency at a constant rotational speed mostly decreased unless the mass was located at the free end of the beam. The location of the mass had a greater effect on the first eigenfrequency compared to the second and third eigenfrequencies. A joint dimensionless eigenfrequency was found at a specific rotational speed regardless of the distributed mass. Nearly constant dimensionless eigenfrequencies could be obtained for a wide range of rotational speeds by adjusting the distributed mass. [ABSTRACT FROM AUTHOR]

The paper presents simple computational algorithms for analyzing the lateral-torsional buckling of prismatic beams with rectangular cross-sections under bending action due to uniform and nonuniform loads by the Adomian decomposition method (ADM) and variational iteration method (VIM). Unlike the numerical techniques that lead to a discretization process, the proposed method allows us to derive the solution in terms of an analytical function for the problem considered. Although the governing equations of the problem appear as a system of two coupled variable coefficient ordinary differential equations, they reduce to a single equation for rectangular beams. The buckling loads for different loading conditions are computed, with the results for the simple beam compared with previous available results by the differential transformation method (DTM), variational iteration method (VIM) and finite element method (FEM) based on coupled governing equations. The results clearly show the efficiency and advantage of the present technique over those based on the coupled governing equations using the DTM and VIM in view of the number of terms required to obtain the convergent solution. [ABSTRACT FROM AUTHOR]

The effect of the cellular core on the stress intensity factor at the tip of a crack in the adhesive layer of a five-layer sandwich composite beam is investigated. A Nomex sheet is used to model the cellular core with honeycomb, square, and triangular cells. The mechanical properties of these cells are obtained by the finite element analysis supported by theoretical two- and three-dimensional equations. Based on the deduced properties, the load-displacement curve is generated for a sandwich beam under mode I fracture. The numerical findings are validated against available experimental data. It is shown that the lowest values of the stress intensity factor are observed for a core with a honeycomb structure as compared to the other two cell shapes used in this study, which are composed of equilateral triangles or squares. An increase in the wall thickness of the cells leads to an increase in the stress intensity factor. [ABSTRACT FROM AUTHOR]