Deformation Of Beam Research Articles

Inelastic finite deformation beam modeling, simulation, and validation of additively manufactured lattice structures

Inelastic finite deformation beam modeling, simulation, and validation of additively manufactured lattice structures

Aeroelastic stability analysis of rotor blade with complex three-dimensional design

A rotor dynamic analysis method for the complex three-dimensional design blade was developed and applied to analyzing its aeroelastic stability. Based on the medium-size deformation beam theory and Hamilton principle, the joint transfer matrix was used in the blade kinematic and the deformation compatibility principle was used in the assembled finite element matrix to develop the complex three-dimensional rotor structural dynamics model. The BO105 rotor was used to validate this method and the aeroelastic characteristic of the complex three-dimensional rotor was analyzed in detail. The results showed that the negative structural coupling of flap-torsion was appeared with tip sweep, and the 1/rev torsion modal frequency was decreased, and the 1/rev torsion modal damping ratio was maximally decreased about 90%. The positive structural coupling of lag-torsion was appeared with tip droop, the 2/rev lag modal frequency was decreased, the 1/rev torsion modal damping ratio was maximally decreased about 62%. The torsion stability was sharply decreased with tip sweep and droop design.

Research on a rotary piezoelectric wind energy harvester with bilateral excitation.

This paper describes a rotary piezoelectric wind energy harvester with bilateral excitation (B-RPWEH) that improves power generation performance. The power generating unit in the current piezoelectric cantilever wind energy harvester was primarily subjected to a periodic force in a single direction. The B-RPWEH adopted a reasonable bilateral magnet arrangement, thus avoiding the drawbacks of limited piezoelectric cantilever beam deformation and unstable power generation due to unidirectional excitation force. The factors affecting the power generation were theoretically analyzed, and the natural frequency and excitation force of the piezoelectric cantilever have been simulated and analyzed. A comprehensive experimental research method was used to investigate the output performance. The B-RPWEH reaches a maximum output voltage of 20.48Vpp when the piezoelectric sheet is fixed at an angle of 30°, the Savonius turbine number is 3, and the magnet diameter is 8mm. By adjusting the fixed angle of the piezoelectric sheet, the number of Savonius wind turbine blades, and the magnet diameter, the maximum voltage is increased by 52.38%, 4.49%, and 245.95%, respectively. The output power is 24.5 mW with an external resistor of 8 kΩ, and the normalized power density is 153.14 × 10-3 mW/mm3, capable of powering light-emitting diodes (LEDs). This structure can drive wireless networks or low-power electronics.

Simulations of interaction between flow and a thin elastic beam using CIP-based model with adaptive mesh

The simulation of interaction between flow and the elastic structure is a complicated fluid-solid interaction problem, involving the structure's large deformation and fluid interface variation. In this paper, an adaptive CIP (constrained interpolation profile)-based numerical model has been presented to simulate this problem. In this CIP-based model, the constrained interpolation profile method, a high-order finite difference method, is employed as the base flow solver and THINC/SW (Tangent of Hyperbola for Interface Capturing with Slope Weighting) method, a volume of fluid method, is applied to capture the flow interface. IBM (immersed boundary method) method is used to treat the fluid-solid interface. The body deformation is calculated by coupled FDM-FEM (finite difference method and finite element method) method. Adaptive mesh is generated by Afivo (Adaptive Finite Volume quadtree/Octree mesh) framework. The cases of flow past a square and water entry of a symmetric solid wedge are carried out to validate the reliability of the flow solver in this present model. Cantilever beam deformation case is used to validate the accuracy of the solid solver in the present model. Then cases of a thin elastic beam in sloshing tank and dam-break flow are carried out by using this model. After that, the case of regular wave past a membrane breakwater is studied. Our numerical results are compared with previous experimental and numerical studies, and good agreements are obtained. It is demonstrated that this present numerical model has good applicability to simulate the interaction between flow and a thin elastic beam.

Data-driven computing for nonlinear problems of composite structures based on sub-domain search technique

The distance-minimizing data-driven algorithm brings new insight in computing nonlinear problems of composite structures, where the calculation is directly carried out by finding the material data that closest to equilibrium constraints. However, it is challenging to efficiently find the desired material data in a tremendous database. Towards this end, a sub-domain search technique is proposed to construct a sub-database with adaptive size for each computational step, which enables to significantly speed up the data search process in the data-driven algorithm. The databases of the composite materials are collected by the offline homogenization over the representative volume element. Several examples, including the nonlinear geometric behavior of sandwich beam, the internal instability of fiber reinforced composite plate and the large deformation of composite beam, are performed to validate the reliability and efficiency of the proposed technique. The results show that compared with the classical multiscale finite element method, the data-driven method with the sub-domain search technique is able to predict the nonlinear behaviors of composite structures with good accuracy and efficiency.

Vibration characteristics of arbitrary thick sandwich beam with metal foam core resting on elastic medium

An analysis is performed in this research to obtain the natural frequencies and mode shapes of a thick sandwich beam with metal foam core. Different types of foams are considered for the sandwich beam where distribution of pores is a functionally graded patterns. The governing equations of the sandwich beam are established by means of a shear and normal deformable thick beam model. This theory considers the thickness stretching and admits the nonuniform through-the-thickness shear strain. The governing equations of the sandwich beam are established which are four in number by means of the Hamilton principle. The established equations are solved for the case of thick sandwich beams resting on elastic foundation via the Navier solution method. Results of this study are first compared with the available data in the open literature and after that novel results are given to explore the effects of different parameters on the vibration characteristics of the sandwich beam. It is shown that porosity of the core is an important factor on vibration characteristics of sandwich beam with metal foam core.

Variable compression panel thickness for concrete members under bending and torsion: Experimental study

An experimental study was conducted on the behaviour of eight reinforced and prestressed concrete beams subjected to combined action of bending and torsion. The beams were heavily reinforced in the longitudinal direction so that the height of the concrete compression zone under pure bending would be much larger than the concrete diagonal strut thickness under pure torsion and measurements were done so that behaviour of this compressive zone could be observed. The amount of the reinforcement was designed close to the over-reinforcement limits, as would happen if the cross-section dimensions of an actual structure would be minimized in the design. The ultimate resistances and beam deformations were compared against the results of a plasticity-based space truss model where the panel on the compressive side of the cross-section had variable thickness in order to account for the resultant force demands of both the bending and torsion. Most heavily reinforced beams failed in a brittle manner due to the ineffectiveness of diagonally cracked concrete to resist the high normal stresses arising from the bending. The proposed model gave better predictions than the classical model where the panel thickness was constant, and the results showed the significance of concrete strength reduction factor contribution in ultimate resistance of concrete members under combined bending and torsion.

Experimental and Numerical Investigation of the Anti-Overturning Theory of Single-Column Pier Bridges

In recent years, overturning accidents at single-pier bridges have occurred frequently, resulting in significant property losses and safety accidents. Overturning accidents show that there are still many hidden dangers in the design, operation, and management of existing single-pier bridges. Therefore, this paper takes the K503 + 647.4 separated overpass of the Hegang–Dalian Expressway as the research object and carries out an onsite anti-overturning stability test of a single-column pier bridge. Through loading under various working conditions, the displacement changes of each support are measured, and the reaction changes of the supports are calculated. In the process of simulating the field test using the finite element program ANSYS, a rigid model based on ideal support and an elastic model considering beam deformation are established, and the accuracy of the elastic model is verified by comparison with the field-measured data. Furthermore, a series of parameters, such as the bridge side-span ratio, bridge span number, bearing spacing, loading position, and torsional rigidity, are varied, and finite element simulation is carried out on the basis of the elastic model. Through comparison of the results, a relationship between the parameters of the single-pier bridge and the anti-overturning ability is obtained, which provides a theoretical basis for anti-overturning design research and the effective reinforcement of single-pier bridges.

Free vibrations of Timoshenko nanoscale beams based on a hybrid integral strain- and stress-driven nonlocal model

Several non-classical elasticity theories are used for considering the size-dependent behavior of structures at small scales. The nonlocal theory is widely used to reflect the softening behavior of material at small scales, and theories like the strain gradient theory are employed to reflect the hardening behavior. In this article, the most general form of integral strain- and stress-driven nonlocal models with two nonlocal parameters is developed which is able to consider both hardening and softening influences simultaneously. To this end, it is considered that the stress field at the entire points of the domain is a function of strain field of the entire points of the domain. The free vibration problem of first-order shear deformable beams is solved herein. The integral form of governing equations and associated boundary conditions are obtained first, and then directly solved in a numerical approach. Through developing an efficient matrix formulation and using differential and integral matrix operators, the discretized governing equations are obtained. The simultaneous effects of strain- and stress-driven nonlocal parameters on the natural frequencies of fully clamped, fully simply-supported, and clamped-free nanobeams are investigated. The results indicate that the paradox related to the behavior of clamped-free nanobeams is resolved using the presented integral nonlocal formulation. Also, it is revealed that it is possible to find some specific values of nonlocal parameters at which the prediction of hybrid nonlocal model coincides with that of classical elasticity theory.

Monolithically integrated triaxial high-performance micro accelerometers with position-independent pure axial stressed piezoresistive beams

With the increasing demand for multidirectional vibration measurements, traditional triaxial accelerometers cannot achieve vibration measurements with high sensitivity, high natural frequency, and low cross-sensitivity simultaneously. Moreover, for piezoresistive accelerometers, achieving pure axial deformation of the piezoresistive beam can greatly improve performance, but it requires the piezoresistive beam to be located in a specific position, which inevitably makes the design more complex and limits the performance improvement. Here, a monolithically integrated triaxial high-performance accelerometer with pure axial stress piezoresistive beams was designed, fabricated, and tested. By controlling synchronous displacements at both piezoresistive beam ends, the pure axial stress states of the piezoresistive beams could be easily achieved with position independence without tedious calculations. The measurement unit for the z-axis acceleration was innovatively designed as an interlocking proof mass structure to ensure a full Wheatstone bridge for sensitivity improvement. The pure axial stress state of the piezoresistive beams and low cross-sensitivity of all three units were verified by the finite element method (FEM). The triaxial accelerometer was fabricated and tested. Results showing extremely high sensitivities (x axis: 2.43 mV/g/5 V; y axis: 2.44 mv/g/5 V; z axis: 2.41 mV/g/5 V (without amplification by signal conditioning circuit)) and high natural frequencies (x/y axes: 11.4 kHz; z-axis: 13.2 kHz) were obtained. The approach of this paper makes it simple to design and obtain high-performance piezoresistive accelerometers.

Wave propagation in a porous functionally graded curved viscoelastic nano-size beam

In this paper, wave propagation analysis of a viscoelastic system of curved nanobeams made of porous functionally graded materials (P-FGM) is studied, for the first time. The displacement fields for the curved nanobeam are obtained via a higher-order shear deformation beam theory which contains curvilinear axial, rotation, transverse, and thickness stretching effects, while size effects are considered using nonlocal strain gradient theory. The effective material properties for P-FGMs are expressed by modified model of power-law variation which is connected with cosine functions to estimate the effect of porosity and Kelvin–Voigt viscoelastic model for estimating viscoelastic behavior on mechanics of nanostructures. The Hamilton’s principle is applied to find governing equations of motion of the viscoelastic curved nanobeam. The state space method and a set of mathematical series are developed to find response. The Influence of porosity value and types of distributions, viscosity coefficient, power-law index, geometry, and opening angle (related to curvature radius) on phase velocity of curved viscoelastic nanobeams is investigated.

A novel steel bulkhead based on the method of prefabrication and assembly and its first application to the Yuliangzhou immersed tunnel

Temporary bulkheads installed at the end of each tunnel element are indispensable for immersed tunnel elements to be watertight and float. Currently, welded steel bulkheads and cast-in-place concrete bulkheads have been applied in the installation of most immersed tunnels; however, these bulkheads have many inherent drawbacks. For example, existing cast-in-place concrete bulkheads are bulky and cannot be recycled after demolition. In addition, existing welded steel bulkheads, which cannot be fully reused, are installed and dismantled with a large number of on-site welding operations. Relying on the Yuliangzhou Immersed Tunnel in China, a novel steel bulkhead based on the method of prefabrication and assembly, namely, a piece-assembled steel bulkhead, was developed to address the abovementioned problems. The structural components of the new steel bulkhead applied to realize full recycling mainly include steel bulkhead panels, ethylene-propylene-diene-monomer (EPDM) sealing gaskets, steel bearings, and steel connecting bolts. The water tightness function of the new bulkhead was achieved through the compression deformation of the designed EPDM sealing gaskets inside the assembly seams, which were designed as multihole structures to save manufacturing material. Nonlinear finite element simulations were conducted to investigate the gasketed seam mechanical and sealant behavior. It was concluded that the control threshold value of gasketed seam compression displacement needed to satisfy the design requirement for a 250 kPa waterproof capacity could be taken as 15 mm, while that for seam offset displacement was set to 40 mm. To achieve the fast and efficient construction of the new steel bulkhead, a strategy of symmetrically installing and removing steel bulkhead panels piece by piece at one carriageway bore was proposed, and an automatic installation trolley that adjusts the bulkhead panel position in three directions was designed and developed. Finally, the on-site monitoring of the assembly seam displacements and the stress and deformation of the H-shaped steel beam verified that the new steel bulkhead was in a safe state and displayed good watertightness. This bulkhead was successfully applied in the Yuliangzhou Immersed Tunnel project, and this test application supports the use of these technologies in immersed tunnel construction.

Modeling a Viscoelastic Support Considering Its Mass-Inertial Characteristics During Non-Stationary Vibrations of the Beam

Non-stationary loading of a mechanical system consisting of a hinged beam and additional support installed in the beam span was studied using a model of the beam deformation based on the Timoshenko hypothesis with considering rotatory inertia and shear. The system of partial differential equations describing the beam deformation was solved by expanding the unknown functions in the Fourier series with subsequent application of the integral Laplace transform. The additional support was assumed to be realistic rather than rigid. Thus it has linearly elastic, viscous, and inertial components. This means that the effect of a part of the support vibrating with the beam was considered such that their displacements coincide. The beam and additional support reaction were replaced by an unknown concentrated external force applied to the beam. This unknown reaction was assumed to be time-dependent. The time law was determined by solving the first kind of Volterra integral equation. The methodology of deriving the integral equation for the unknown reaction was explained. Analytic formulae and results of computations for specific numerical parameters were given. The impact of the mass value on the additional viscoelastic support reaction and the beam deflection at arbitrary points were determined. The research results of this paper can be helpful for engineers in designing multi-span bridges.

Filtering approaches of AE data in damage severity assessment of highly emissive concrete structures under loading

The application of the AE technique in the field of civil engineering requires overcoming various issues related to several factors such as structure complexity, material nonhomogeneity, signal attenuation, environmental noise. In this concern, multivariate statistical analysis was successfully applied to manage AE data and discriminate relevant features related to main damage mechanisms in concrete. Principal component analysis (PCA) and artificial neural networks (ANN) were applied with promising results. However, a fundamental limitation of these numerical methods is that they are not user-friendly and their application requires suitable scientific expertise. In such a context, the development of an easy de-noising protocol, able to simplify the AE data analysis for damage structure assessment and failure prediction, is a fundamental improvement toward the applicability of this technology on real-scale concrete structures. In the present paper, the analysis of AE data collected during loading and unloading cycles up to the failure on a real scale post-tensioned concrete beam is reported. Different denoising approaches were adopted to remove a large incoherent AE population originating from the friction of hydraulic actuator steel plate on concrete surface and friction on beam supports during loading/unloading steps. Filtered data were then synchronized with the beam deformation and crack width opening. De-noising algorithms have then been validated by structure damage severity assessment using statistical indexes such as calm ratio, load ratio, severity, and historical index. The procedure was tested with interesting results on PT concrete beams characterized by different pre-existing damages on steel tendons. EWGAE 35, Ljubljana, Slovenia, 13th – 16th Sep. www.ewg

Stiffness and strength evaluation of prestressed timber beam with unbonded steel Strand and reinforced concrete Beam‐Column joint

AbstractThe deformation behavior of prestressed timber beams after a gap opens at the beam‐column interface is evaluated in this study using the compressive stress distribution along the beam length. The correlation between moment at the beam end and beam deformation is studied for three types of specimens. The evaluation results indicate that the prediction is in good agreement with the experimental results up to the proportional limit of the material. In addition, the bending ultimate strength calculated using the compressive stress distribution at the beam end, which is obtained from the compressive stress–strain relationship, is also verified with the values of moments in the experiment. Finally, an alternative elastic element model with a quadrilinear rigid‐plastic spring at the element end was proposed.

Experimental Study on the Flexural Ductility of BFRP Bar Concrete Beams With Bamboo Fiber and Steel Wire Mesh

In order to study the influence of bamboo fiber and steel wire mesh on the flexural ductility of Basalt Fiber Reinforced Polymer（BFRP）bars concrete beams, seven BFRP bars concrete beams reinforced with bamboo fiber and steel wire mesh were tested with the bamboo fiber length (0mm, 30mm, 45mm) and the steel wire mesh layout range (none, 1/2 maximum bending moment point layout, full beam segment layout) as variables. The flexural failure test of 7 basalt fiber reinforced concrete beams reinforced by bamboo fiber and steel wire mesh was carried out, and the initial crack load, crack development, ultimate load and deformation were detected. The effects of fiber length and layout range of wire mesh on the crack resistance and deformation resistance of specimens are analyzed by the test data. With the help of functional model, the equivalent yield points of the seven test beams were obtained, and the ductility coefficients of the specimens were calculated. The results show that the addition of bamboo fiber and steel wire mesh increases the cracking load of BFRP bars concrete beams by 12% ~ 68%, reduces the crack distribution spacing and length development speed, reduces the deformation of test beams under the same load, and increases the ductility coefficient by 1.58% ~ 31.75%.

Finite Element and Vibration Frequency Analysis of Cracked Solid Beams: A Comparison of Iron, Steel, and Titanium Materials

Different solid materials are widely used in various constructions due to their availability and low cost. However, cracks or conversions in the structures can affect their stiffness and vibration signatures. This research aims to evaluate the load distribution, deformation, and the effects of the cracks on the natural frequencies and deformations of iron, steel, and titanium beams. A finite element‐based model and COMSOL Multiphysics software were employed to measure and compare the frequencies and strengths of the beams. The results showed that the frequencies increased with the load, and titanium beams had the highest frequencies and deflections, while steel beams had the highest stress resistance. This frequency analysis can help to detect very small cracks (less than 0.05 mm) in the beams. The study concluded that steel is the most suitable material for construction due to its elasticity, availability, and low cost.

Numerical modeling of inverted-U-shaped connectors to enhance the performance of composite beams

Steel and concrete are the most essential and frequently encountered building materials. These materials are used in combined structural systems, such as concrete cores surrounded by steel pipes, as well as composite structures with steel and concrete components. In numerous countries, the combination of concrete cores, steel frames, and composite slab construction has become the typical construction approach for multistory commercial buildings. The shear stud connector is one of the elements used in the construction of composite sections. The use of inverted-U-shaped reinforcement experimentally and numerically significantly improves punching shear resistance for post-tensioned slabs compared with slabs that use stud connectors. Other experimental and numerical studies using inverted-U-shaped reinforcement in post-tensioned beams indicate an enhancement in their shear strength. Recently, an experimental investigation was performed on composite beams to inspect the effect of mild and rigid shear stud connectors. The experimental and numerical results for the composite beams showed good correlation. The goal of this study was to numerically model the capacity and deformation of composite beams with inverted-U-shaped connectors of varying configuration and mechanical properties and compare the beam performance with composite beams using shear stud connectors.

Explicit design of framed tube high‐rise buildings via inverse problem approach

AbstractAn explicit design procedure of cross‐sections of framed tube high‐rise buildings via an inverse problem approach is presented. In the formulation, interstory drift ratios and net deformations of beams are prescribed. The derived expressions clearly express the three‐dimensional effect (tube effect) from the orthogonal frame. The expressions are helpful for the preliminary design because cross‐sections are rationally and rapidly provided for a set of target deformations without trial‐and‐error repetition. In the proposed design method, a 2×2‐bay basic model under a set of static horizontal loads is designed at first. Then, this 2×2‐bay model is transformed into a multi‐bay model. The second moments of cross‐section of the multi‐bay model can be obtained based on the equivalence of the responses of those two models in the case where the elongation of columns is neglected. In addition, assumptions of axial strains of columns are introduced to obtain the equivalent parameters of cross‐sections of the 2×2‐bay model. It is demonstrated through numerical examples that the proposed method has reasonable accuracy.

Dynamic finite element analysis of microbeams under a moving mass based on refined third-order shear deformation theory

The dynamic behavior of microbeams with rectangular cross section under action of a moving mass is studied in the present paper in the framework of a refined higher-order shear deformation beam theory. The modified couple stress theory (MCST) with only one additional scale parameter is adopted to describe the influence of the microsize effect on the dynamic response of the microbeams. A finite element formulation with ten degrees of freedom is formulated and used to establish the discretized equation of motion for the microbeams. The formulation, taking into account the influence of the inertial effect, the Coriolis and centrifugal forces resulted from the mass moving, is derived from the expressions of the elastic and kinetic energies of the microbeams. The accuracy and efficiency of the derived formulation are confirmed by comparing the result obtained in the present work with the published data. The dynamic response of the microbeams with simply supported ends, such as the curves for dimensionless mid-span deflection-moving time relationship, the dynamic magnification factors (DMFs) and the thickness distribution of stresses are assessed by using an implicit Newmark method. The obtained numerical results reveal that the material length scale parameter which is introduced in the MCST has an important role on the dynamic behavior of the microbeams, and the DMF obtained from the theory incoporating the MCST is considerably lower than that using the conventional beam theory. It is also shown that the amplitude of both the axial stress and shear stress is considerably decreased by the increase of the material length scale parameter. A numerical study is carried out to highlight the influence of various parameters such as the moving mass velocity and the the ratio of the total beam length to its height on the dynamic response of the microbeams.