Deformation Of Beam Research Articles

A brief study concerning rational type contraction via a digraph and deformation of an elastic beam

A brief study concerning rational type contraction via a digraph and deformation of an elastic beam

Nonlinear isogeometric analysis of axially functionally graded graphene platelet-reinforced composite curved beams

The linear and nonlinear isogeometric finite element models of an axially functionally graded graphene platelet-reinforced composite (AFG-GPLRC) curved beam are established within the framework of the third-order shear deformation beam theory (TSDT) and von-Kármán’s nonlinear geometric relation. The AFG-GPLRC curved beams can be seen as composite structures in which the graphene platelets (GPLs) are continuously distributed in the matrix along the length direction of the curved beam according to different patterns. The modified Halpin-Tsai parallel model and the rule of mixture are implemented to predict the effective Young’s modulus and mass density as well as Poisson’s ratio, respectively. Hamilton's principle, TSDT, and von-Kármán’s strain-displacement relation are combined to derive the governing partial differential equation of motion and corresponding boundary conditions. Furthermore, the Non-Uniform Rational B-splines (NURBS)-based isogeometric analysis (IGA) approach together with a direct iterative technique are utilized to solve the nonlinear governing equation. The accuracy and efficiency of the proposed IGA framework are confirmed by comparing corresponding numerical solutions with other available results. The parametric investigations, such as the curved beam’s geometric parameters, boundary conditions, and GPL’s distribution patterns, on the nonlinear bending and vibration responses of the AFG-GPLRC curved beams are carried out by some illustrative examples.

Wave propagation in beams with functionally graded porosity distribution under highly transient axial and transverse impacts

Recent advances in the manufacturing process provide a possibility of fabricating a new generation of porous materials denoted by functionally graded porous materials (FGPM). This paper aims to present a time domain analysis of wave propagation through the porous structures with functionally graded porosity distribution, which has not been completely studied before. For this purpose, the beams with different functionally graded porosity distributions subjected to both axial and transverse tip impact loads with a high-frequency content are investigated. The shear deformable cantilevered functionally graded porous beams with various porosity distributions through the beam thickness are studied. The governing differential equations are derived using the Hamiltonian principle based on the Timoshenko beam theory. A locking-free first-order shear deformable beam element is used to derive the finite element formulation of the equations. The Newmark time integration method is used to perform a time domain analysis of the equations of motion and to investigate the transient response of the beams. The axial and transverse wave propagation characteristics through functionally graded (FG) porous beams are found using time domain analysis of the results. Deflection and velocity time histories of the tip and each point of the beam, reflection time, and variation of support reactions are obtained. The influences of the porosity magnitude and porosity distribution on the wave propagation characteristics and overall time responses are investigated. The results reveal that porosity distribution has a significant effect on the wave amplitude, wave speed, and reflection from the boundary. Also, this study can help in a better understanding of porous structures' behavior subjected to high-transient impact loads in different engineering applications.

An electromagnetic vibration energy harvester with compact flexure guide for low frequency applications

This paper presents the design, modeling, fabrication, and characterization of a novel electromagnetic vibration energy harvester (EVEH) using a compact flexure guide structure and opposing permanent magnets. The flexure guide is a unique cylindrical structure, and can transfer force and motion by the deformation of elastic beams. It allows the single-degree-of-freedom motion characteristic, and eliminates the friction between the permanent magnets and the housing structure, which exists in mostly reported magnet-spring based vibration energy harvesters. The structure also greatly reduces the spacing between the coil and the permanent magnets, which considerably increases the magnetic flux linkage through the coil. Experimental results show that the EVEH prototype can generate an output voltage of 6.08 V and output power of 4.02 mW from 0.1 g acceleration at resonant (19.5 Hz), achieving a normalized power density of 3.28 mW cm − 3g − 2. In addition, the flexure guide can be directly fabricated by 3D printing, which greatly simplifies the harvester assembly compared to other EVEHs reported. In terms of the proposed EVEH, a self-powered sensor network is implemented to transfer the GPS data to some appointed terminals.

Experimental study on seismic performance of internal cruciform joints of grouting sleeve connection for modular integrated construction

Modular integrated construction (MiC) adopts room units that integrate maintenance structure, decoration and equipment pipelines in the factory-made modules, resulting in a lack of operating space for connecting modules at the construction site. In the previous research, the joints between modules are usually hinged or semi-rigid connections and partial strength joints. In this paper, a new type of joint with the grouting sleeve connection is proposed to connect modules horizontally and vertically, which is more convenient for construction and does not conflict with interior decoration. Six full-scale cruciform joints were tested to study the effect of axial compression ratio and different structural details. The test results presented the failure mode, stiffness, ductility, and energy dissipation of the specimens. The ultimate inter-story drift ratio is between 4.78 % rad and 5.96 % rad, which is larger than the requirement of 4 % rad in the special moment frame (SMF) system. The horizontal connection plate between modules can cooperate the deformation of left and right beams and columns, and significantly improve the lateral resistance of the joint. The vertical connection between modules did not slip or open and the grouting material is not broken. The inner and outer reinforced plates in the beam-to-column connection can transfer the tensile force of the beam flange well so the outer sleeve does not tear, and the wedge-shaped stiffener can inhibit the cracking of the beam-to-column connection. EC3 Part 1–8 was adopted to evaluate the stiffness characteristic of the proposed connection, indicating that the proposed joint can be classified as rigid joint for the non-sway frame. Finally, the theoretical ultimate resistance of the joint under the ideal failure mode is obtained, which is lower than the test results, indicating that the plastic development of the joint is sufficient and can be classified as full-strength joint.

The Effect of Torsional and Bending Stiffness on the Aerodynamic Performance of Flapping Wing

For large bird-like flapping wing aircraft, the fluid–structure coupling problem is very important. Through the passive torsional deformation of the wing, sufficient thrust is generated and propulsion efficiency is ensured. Moreover, spanwise bending deformation will affect lift and thrust. The flow field on the surface of the wing and the geometric nonlinearity caused by the large deformation of the wing should be considered during the design process. Existing research methods do not solve this problem accurately and efficiently. This paper provides a method to analyze the fluid–structure coupling problem of the flapping wing which adopts the three-dimensional unsteady panel method to solve the aerodynamic force, and adopts the linear beam element model combined with the corotational formulation method to consider the geometric nonlinear deformation of the wing beam. This article compares the performance of the flapping wing with different torsional and bending stiffness, and analyzes the airfoil surface pressure coefficients at different portions of the wing during the period. The results show that torsional stiffness has a large influence on the lift coefficient, thrust coefficient and propulsion efficiency. Meanwhile, the torsional stiffness of the wing beam and the initial geometric twist angle of the wing need to be well coordinated to achieve high efficiency. Moreover, appropriate bending stiffness of the wing is conducive to improving propulsion efficiency.

A triboelectric-piezoelectric hybrid nanogenerator for rotational energy harvesting based on bistable cantilever beam

This study presents a triboelectric-piezoelectric hybrid nanogenerator for harvesting rotational energy based on a bistable cantilever beam. The nonlinear bistable behavior effectively enhances the collision force with the triboelectric nanogeneration (TENG) boundary, enlarges the effective contact area of the triboelectric functional materials, and significantly increases the deformation of the piezoelectric cantilever beam, thereby improving the overall electrical output performance of the system. Excessive deformation of the piezoelectric cantilevers is effectively constrained by the TENG boundary, which prevents the degradation and failure of the piezoelectric material. A prototype is prepared and verified experimentally. The effects of key parameters on the output performance are systematically analyzed. According to the results on the overall electrical output of hybrid nanogenerator with and without bistable behavior, the hybrid nanogenerator with bistable behavior achieved an energy density of 29.04 W/m3 at a rotational speed of 450 r/min, which is 2.65 times higher than that of the hybrid nanogenerator without bistable behavior. In addition, the rotational speed range is broadened by more than 1.5 times, and the prototype can realize self-powered temperature monitoring and wireless transmission. Overall, the proposed rotational energy harvester with a magnetic coupling cantilever bistable behavior and TENG boundary mechanism offers a novel means to improve the electrical performance of energy harvesting systems for self-powered internet of things.

The theoretical and experimental buckling analysis of a nanocomposite beams reinforced by nanorods made of recycled materials

AbstractIn this article, the numerical and experimental results for buckling analysis of a nanocomposite beams reinforced by nanorods are studied and compared. The Chebyshev–Ritz method is used to calculate the buckling numerically and compare it with the buckling test. Epoxy resin, glass's fiber, and nanorods are used to make composites. These nanorods are made using recycled materials. Also, bending and tensile tests are used to obtain the properties of these composites. In addition, the effect of various parameters such as Young's modulus, temperature change, Poisson's ratio, and boundary conditions, the strain gradient parameter, and different shape function is investigated. The addition of nanorods increases the strength and stiffness of composites and increases the critical buckling load. Actually, the made nanorods are used as a reinforcement in matrix, thus in the made nanocomposites, fracture and buckling tests are done and the results indicate that the inclusion of nanorods (0.32%) increases the critical buckling load by 16.4%. A facile hydrothermal method to synthesis the nano rodes has a less cost with the other methods, thus by adding a small percentage of it to the composite, the stiffness of the structure increases. According to the results and the significant increase in Young's modulus and critical buckling load and the cost‐effectiveness of carbon nanorods (CNRs) made from recycled materials, these environmentally friendly reinforcements can be used in various industries such as machine body construction, automobile manufacturing, shipbuilding and construction of type's turbines.Highlights Using potato peels and hydrothermal methods, CNRs produced. These CNRs are useful, and production is cheap and no harm environmental. Buckling sample include of glass fiber, without and with CNRs and epoxy resin. Third order shear deformation beam theory and Chebyshev–Ritz are used Theoretical and experimental buckling critical load are compared.

Free vibration of functionally graded carbon nanotube-reinforced composite beam

The purpose of this paper is to investigate the free vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam. The carbon nanotubes (CNTs) are aligned and distributed in polymeric matrix with different patterns of reinforcement. The material properties of the FG-CNTRC beam are estimated by using the rule of mixture. The trigonometric shear deformation beam theory is employed to deal with the problem. The mathematical models provided in this paper are numerically validated by comparison with some available results. New results of free vibration analyses of FG-CNTRC beam are presented and discussed in detail. The effects of the length to thickness ratio and CNT volume fraction are taken into investigation.

On shear-dependent vibration of nano frames

In this study, the effect of shear deformation on the atomic size-dependent free vibration of nanoframes is investigated. The equations of motion of axial and bending vibrations are obtained via the variational algebra according to nonlocal elasticity theory. Axial and bending behaviors are expressed by using simple rod theory and first-order shear deformation beam theory, respectively. By combining the nonlocal finite element solutions for the equations of motion, an eigenvalue formulation for the free vibration of nanoframe is developed. In the presentation of numerical results, firstly, some comparison studies are carried out to show the accuracy of the present analysis. Then, the variations of nondimensional frequencies of three different nanoframe structures are investigated with respect to various parameters, and the results are discussed in detail. The focus of this study is to better understand the dynamic behavior of nanostructures that are within the scope of nano-electro-mechanical systems (NEMS) technology and can be modelled with discrete members.

GEODESIC MONITORING OF SHORT-TERM BRIDGE DEFORMATIONS IN RIVNE

The safe bridges functioning is a condition for long-term and accident-free operation of highways and railways. This work object is to study the short-term deformations of the bridge. The relevance of this problem is that the short-period component of deformations understudied, because its monitoring requires continuous observations of the bridge structure and requires the installation of stationary measurement stations. The very values of the deformations and their influence on the safe functioning of the structure remain little researched. A Leica TCR 1205 electronic reflection-free total station was used to study the short-term deformations of the bridge along Popovycha Street in Rivne. Eight cycles of observations were conducted during daylight hours from one station. The measurement results were processed as double exact measurements of homogeneous quantities. 
 The monitoring results indicate that the short-term deformations of the bridge beams are significant and can be recorded by geodetic methods. Spatial deformations of different points of the bridge in one cycle differ significantly from each other. The maximum deformation values obtained at the points turned towards the sun's rays. There are complex deformations of the beams, such as transverse bending and torsion, which significantly increases the forces in the structural elements of the bridge. Short-term deformations reach their maximum value at the period from 1 to 4 p.m., and then subside. The hypothesis that the main cause of short-term deformations is the heating of structures by solar rays seems reliable. Short-term deformation monitoring should be considered as an integral part of the bridge information system (BrIM).

The computational design of a fractal-inspired soft robotic

Soft robotics, with their application in biomedical fields like flexible surgical tools and wearable exo-suits, have revolutionized biomedical practices. To adapt to different scales of application scenarios, our research emphasizes fractal-inspired soft robotics, leveraging the unique scalable and reconfigurable properties of fractal structures. This study focuses on the computational design and simulation of these robots. Traditional modeling methods, apt for rigid robotic arms, falter for soft materials due to their extensive flexibility. We introduced a deep learning strategy with physics-informed neural network for accurate soft robot dynamics modeling. Unlike existing networks optimized for rigid systems, our approach integrates elastic beam theory and deformation laws into Lagrangian Dynamics, making it ideal for simulating fractal soft robotic arms. Compared to conventional finite element simulations and learning approaches, our method shows superior effectiveness. We also conducted simple simulation experiments to show that fractal soft arm is potentially suitable for medical procedures (such as dilating passages) and proved that this fractal-designed soft robotic arm exhibits good portability and adaptability to various scenarios, making it a promising candidate for guiding the design of future surgical robots.

A Novel Differential Quadrature Galerkin Method for Dynamic and Stability Behaviour of Bi-directional Functionally Graded Porous Micro Beams

The free vibration and buckling behaviours of 2D-FG porous microbeams are explored in this paper utilizing the Quasi-3D beam deformation theory based on the modified couple stress theory and a Differential Quadrature Galerkin Method (DQGM) systematically, as a combination of the Differential Quadrature Method (DQM) and the semi-analytical Galerkin method, which has used to reduce computational cost for problems in dynamics. The governing equations are obtained using the Lagrange’s principle. The mass and stiffness matrices are calculated using the weighting coefficient matrices given by the differential quadrature (DQ) and Gauss-Lobatto quadrature rules. The matrices are expressed in a similar form to that of the Differential Quadrature Method by introducing an interpolation basis on the element boundary of the Galerkin method. The sampling points are determined by the Gauss-Lobatto node method. The influence of the thickness-to-material length scale parameter (MLSP) on the nondimensional natural frequencies and nondimensional critical buckling loads of 2D-FG porous microbeams are investigated, along with the effects of the boundary condition, aspect ratio and gradient index. The results are validated with literature to establish the accuracy of the procedure described. This work will provide a numerical basis for the design of FG microstructures in the field of micromechanics. These results can be applied to the engineering design of porous FG microstructures.

Transformational deformation models of continuous thin‐walled structural elements with support elements of finite sizes: Theoretical foundations, computational, and physical experiments

AbstractA 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.

Exact solution of thermal postbuckling of porous piezoelectric nanobeams with surface effect

In this paper, the thermal postbuckling of porous piezoelectric nanobeams is analyzed using the first-order shear deformation beam theory based on the surface elasticity theory and "core-shell" model, where the surface effect is introduced by employing the surface energy model. The governing equations for thermal postbuckling of porous piezoelectric nanobeams were derived by the principle of minimum potential energy. It is found that surface effect increases the effective elastic modulus and dimensionless critical load and reduces the thermal postbuckling conformations, thermal postbuckling paths and amount of induced charge. Meanwhile, the reasonable pore distribution pattern can effectively improve the mechanical properties.

Shear and flexural deformations in flextegrity segmental beams inspired by Leonardo’s triangular masonry construction

In Tabula XCI verso of Codex Atlanticus, Leonardo da Vinci presents an ingenious masonry structure composed of segments in the shape of inverted triangles. These are assembled by contact in a chain to obtain a lintel or jack arch, where they are pressed together by the thrust of the end constraints. Drawing inspiration from Leonardo’s sketches, we show that, by connecting the segments in pair through elastic tendons, this system represents a new type of flextegrity beam. In a classical flextegrity, the contact surfaces of the segments are curved conjugate profiles, imposing a pure rolling motion along properly designed pitch lines: the consequent elongation of the tendon dictates the constitutive response as a function of the relative rotation of the segments. Here, the contact is through plane surfaces, so that the kinematics, besides the relative rotation, is characterized by segmental shearing. This system is theoretically analysed and a continuum model is derived as the length of the segments becomes small. Comparisons with experiments on three-dimensional-printed prototypes confirm the theoretical findings and highlight the possible competition between rotational and sliding types of deformation. Apart from the historical value, this type of construction can be used in innovative structures or metamaterials.

Weighing demonstration experiment based on light spot deflection method

The cantilever beam is a well-known mechanical model among science and engineering students. In general physics experiments, the light spot deflection method serves as an optical amplification technique for measuring small rotations. In this study, a method for measuring the angular deformation of a cantilever beam using the light spot deflection method is proposed and applied to weight measurement. Furthermore, we replaced the scaleplate in the traditional light spot deflection method with charge-coupled device (CCD). By employing the linear arrangement of CCD pixels and the digital speckle algorithm, the convenience and accuracy of the spot movement measurement have been greatly improved.

An Analytical Solution to Buckling of Thick Beams Based on a Cubic Polynomial Shear Deformation Beam Theory

An Analytical Solution to Buckling of Thick Beams Based on a Cubic Polynomial Shear Deformation Beam Theory

Martensitic Phase-Transforming Metamaterial: Concept and Model.

We successfully developed a mechanical metamaterial that displays martensitic transformation for the first time. This metamaterial has a bistable structure capable of transitioning between two stable configurations through shear deformation. The outer shape of the unit cell of this structure is a parallelogram, with its upper and lower sides forming the bases of two solid triangles. The vertices from these triangles within the parallelogram are linked by short beams, while the remaining vertices are linked by long beams. The elastic energy of the essential model of the metamaterial was formulated analytically. The energy barrier between these two stable configurations consists of the elastic strain energy due to the tensile deformation of the short beams, the compressive deformation of the long beams, and the bending deformation of the connecting hinges. One example of a novel metamaterial was additively manufactured via the materials extrusion (MEX) process of thermoplastic polyurethane. The metamaterial exhibited deformation behaviors characteristic of martensitic transformations. This mechanical metamaterial has the potential to obtain properties caused by martensitic transformation in actual materials, such as the shape memory effect and superelasticity.

Evaluations of J-integral of nuclear graphite combining experimental and numerical methods

Three-point bending tests were performed on centrally notched graphite beams to study the fracture properties of nuclear graphite. Electronic speckle pattern interferometry (ESPI) was used to measure the full-field deformation of graphite beams. In order to understand crack growth in graphite, numerical simulations were performed using a combination of ABAQUS software and the extended finite element method (XFEM). The numerical results were compared with the experimental results and good agreement was observed, confirming the validity of the numerical models. For evaluation of the J-integral, single specimen method is recommended; however, its geometric factor is uncertain and not easily determined. Thus, the load–displacement curves of beams with similar geometry and different notch depths were computed using the numerical simulations and a formula was proposed to obtain the geometric factor. Based on the ESPI results, the J-integral for crack extension was obtained by numerical computations using the measured full-field displacements as boundary conditions. Furthermore, the fracture resistance (R-curves) of the graphite was evaluated experimentally and compared with that calculated by way of the empirical formulas. The results indicated that energy dissipation rose rapidly to approximately 137 N/m before the peak load, and then increased gradually until reaching a plateau of approximately 209 N/m, when the fracture process zone was fully developed. Finally, the fracture parameters, including the critical crack opening displacements and J–integral at the fracture initiation of the graphite beams, were evaluated.