Bending of piezoelectric beams with the flexoelectric effect under applied load at any position

2018 ◽  
Vol 32 (30) ◽  
pp. 1850372 ◽  
Author(s):  
J. Zhang ◽  
X.-F. Li
Keyword(s):  
Bending Moment ◽  
Elastic Behavior ◽  
Concentrated Force ◽  
Electric Voltage ◽  
Simply Supported ◽  
Flexoelectric Effect ◽  
Linear Piezoelectricity ◽  
Clamped Beams ◽  
Transverse Deflection ◽  
Bending Response

Flexoelectricity describes the coupling between polarization and strain gradients and presents a strong size dependence at nanoscale. In the current work, based on the extended linear piezoelectricity theory with flexoelectricity, we study bending of piezoelectric beams with consideration of flexoelectric effect. When a concentrated force at any position and electric voltage is exerted, the expression for bending deflection of simply-supported and clamped beams is derived. The obtained results show that flexoelectric effect can cause a softer elastic behavior of simply-supported and clamped beams. Sensitivity analysis of the transverse deflection and bending moment is made for two typical boundary conditions. Flexoelectric effect has a more significant effect on the bending response of a piezoelectric beam with smaller thickness.

scholarly journals Dynamic Large Deflection Response of RC Beams under Low-Speed Impact Loading

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Lu Guo ◽  
Renwei Mao ◽  
Zhifang Liu ◽  
Shiqiang Li ◽  
Guiying Wu ◽  
...  
Keyword(s):  
Impact Energy ◽  
Impact Loading ◽  
Large Deflection ◽  
Bending Moment ◽  
Theoretical Models ◽  
Rc Beams ◽  
Low Speed ◽  
Simply Supported ◽  
Analytical Formulas ◽  
Clamped Beams

The dynamic large deflection response of RC beams under low-speed impact loading at their midspan is investigated in this paper. Two simple methods such as extended Hamilton’s principle and equivalent static hypothesis are used to establish the theoretical models for both simply supported and fully clamped RC beams; analytical formulas for the maximum midspan deflection-input impact energy are obtained. The “equal area” method based on the deflection history of beams is only used during these derivations to determine the plastic bending moment and the stress distribution of the structure. Then, finite element simulations are carried out to verify the validity of the proposed predictions. It is shown that the maximum deflections for both simply supported and fully clamped beams are almost proportional with respect to the input impact energy, which agrees well with both simulations and other experimental results. Also, the boundary condition has more effect on the deflection response of the RC beams which is relatively longer.

scholarly journals A Locking-Free DPG Scheme for Timoshenko Beams

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Thomas Führer ◽  
Carlos García Vera ◽  
Norbert Heuer
Keyword(s):  
Bending Moment ◽  
Bernoulli Model ◽  
Timoshenko Beams ◽  
Test Functions ◽  
Optimal Test ◽  
Galerkin Scheme ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Beam Bending ◽  
Transverse Deflection

AbstractWe develop a discontinuous Petrov–Galerkin scheme with optimal test functions (DPG method) for the Timoshenko beam bending model with various boundary conditions, combining clamped, simply supported, and free ends. Our scheme approximates the transverse deflection and bending moment. It converges quasi-optimally in {L_{2}} and is locking free. In particular, it behaves well (converges quasi-optimally) in the limit case of the Euler–Bernoulli model. Several numerical results illustrate the performance of our method.

Post-Buckling Behaviour of Simply-Supported Cross-Ply Rectangular Plates

1976 ◽  
Vol 27 (4) ◽  
pp. 309-316 ◽  
Author(s):  
M K Prabhakara
Keyword(s):  
Large Deflection ◽  
Bending Moment ◽  
Double Series ◽  
Biaxial Compression ◽  
Rectangular Plates ◽  
Sine Series ◽  
Simply Supported ◽  
Unsymmetric Laminates ◽  
Post Buckling ◽  
Transverse Deflection

SummaryAn analysis is presented for the post-buckling behaviour of simply-supported, laminated cross-ply rectangular plates subjected to biaxial compression. The solution to von Kármán-type large deflection equations of the plate is expressed as a double sine series for the transverse deflection and a double series of clamped-clamped beam functions for the force function. All the boundary conditions, including those involving the normal bending moment at the edges, are satisfied exactly. The series solution is found to converge rapidly. Using only the first few terms in the series, numerical results for square graphite-epoxy unsymmetric laminates under uniaxial compression is presented graphically.

scholarly journals Influence of stirrup spacing on shear resistance and deformation of reinforced concrete beams

2018 ◽  
Vol 7 (1) ◽  
pp. 126
Author(s):  
Latha M S ◽  
Revanasiddappa M ◽  
Naveen Kumar B M
Keyword(s):  
Concrete Beam ◽  
Concrete Beams ◽  
Bending Moment ◽  
Maximum Load ◽  
Reinforced Concrete Beams ◽  
Test Results ◽  
Cement Concrete ◽  
Simply Supported ◽  
Reinforced Cement ◽  
Flexural Reinforcement

An experimental investigation was carried out to study shear carrying capacity and ultimate flexural moment of reinforced cement concrete beam. Two series of simply supported beams were prepared by varying diameter and spacing of shear and flexural reinforcement. Beams of cross section 230 mm X 300 mm and length of 2000 mm. During testing, maximum load, first crack load, deflection of beams were recorded. Test results indicated that decreasing shear spacing and decreasing its diameter resulted in decrease in deflection of beam and increase in bending moment and shear force of beam.

Large Deflections of a Simply Supported Beam Subjected to Moment at One End

1984 ◽  
Vol 51 (3) ◽  
pp. 519-525 ◽  
Author(s):  
P. Seide
Keyword(s):  
Linear Theory ◽  
Bending Moment ◽  
Critical Value ◽  
The Other ◽  
Large Deflections ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Elastica Theory ◽  
Angle Of Rotation

The large deflections of a simply supported beam, one end of which is free to move horizontally while the other is subjected to a moment, are investigated by means of inextensional elastica theory. The linear theory is found to be valid for relatively large angles of rotation of the loaded end. The beam becomes transitionally unstable, however, at a critical value of the bending moment parameter MIL/EI equal to 5.284. If the angle of rotation is controlled, the beam is found to become unstable when the rotation is 222.65 deg.

Free Vibration of Thin-Walled Open Section Beams With Unconstrained Damping Treatment

1981 ◽  
Vol 48 (1) ◽  
pp. 169-173 ◽  
Author(s):  
S. Narayanan ◽  
J. P. Verma ◽  
A. K. Mallik
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Numerical Results ◽  
Simply Supported ◽  
Clamped Beams ◽  
Thin Walled ◽  
Open Cross Section

Free-vibration characteristics of a thin-walled, open cross-section beam, with unconstrained damping layers at the flanges, are investigated. Both uncoupled transverse vibration and the coupled bending-torsion oscillations, of a beam of a top-hat section, are considered. Numerical results are presented for natural frequencies and modal loss factors of simply supported and clamped-clamped beams.

Bending of a Uniformly Loaded Rectangular Plate With Two Adjacent Edges Clamped and the Others Either Simply Supported or Free

1952 ◽  
Vol 19 (4) ◽  
pp. 451-460
Author(s):  
M. K. Huang ◽  
H. D. Conway
Keyword(s):  
Rectangular Plate ◽  
Bending Moment ◽  
Simply Supported

Abstract The distribution of deflection and bending moment in a uniformly loaded rectangular plate having two adjacent edges clamped and the others either simply supported or free, are obtained by a method of superposition. Numerical values are given for square plates and, in one case, the results are compared with those obtained by another method.

Three-Dimensional Numerical Analyses of Pile Response due to Braceded Excavation-Induced Lateral Soil Movement

2014 ◽  
Vol 580-583 ◽  
pp. 524-531 ◽  
Author(s):  
Lin Li ◽  
Xiao Xin Hu ◽  
Guang Hui Dong ◽  
Ju Liu
Keyword(s):  
Lateral Displacement ◽  
Three Dimensional ◽  
Bending Moment ◽  
Elastic Behavior ◽  
Pile Head ◽  
Soil Pressure ◽  
Soil Movement ◽  
Standard Problem ◽  
Modified Cam Clay ◽  
Pile Response

Using the explicit finite difference code FLAC3D, the behavior of pile adjacent to braced excavation is investigated. The Modified-cam clay constitutive model was employed to model the non-linear stress-strain soil behavior, and the pile was assumed to have linear elastic behavior. The interface model incorporated in FLAC3D code was used to simulate the soil/pile contact, The built-in 'fish' language was used to calculate the data demanded. The pile response such as pile deflection, bending moment and lateral soil pressure were studied, and it is shown that the pile response is different from that caused by the excavations which are unstructted. In "standard" problem, the effect of different pile head constraints on the pile response was investigated, the effect of lateral displacement of the wall, distance from the excavation face, pile stiffness, pile length and axial load on the pile response are also investigated when the pile head is constrained from deflection. The research finding was compared with other published case history and reasonably good agreement was found between them.

Free Vibration of Bistable Clamped–Clamped Beams: Modeling and Experiment

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Xiaolei Song ◽  
Haijun Liu
Keyword(s):  
Analytical Model ◽  
Natural Frequencies ◽  
Classical Problem ◽  
Mode Shapes ◽  
Wide Range ◽  
Fundamental Understanding ◽  
Clamped Beams ◽  
Transverse Deflection ◽  
Symmetric And Antisymmetric Modes ◽  
Good Agreement

Abstract Bistable clamped–clamped beams have been used in a wide range of applications such as switches, resonators, energy harvesting, and vibration reduction. Most studies on this classic buckling problem focus on obtaining either the static configuration and the required critical axial load or the natural frequencies and mode shapes of postbuckling vibrations analytically. In this article, we present our study including analytical modeling and experimental method on bistable clamped–clamped beams, aiming to understand the detailed snap-through process and the ensuing vibration. In the analytical model, by decomposing the transverse deflection into static buckling configuration and linear vibration, we obtain the natural frequencies and mode shapes for the buckled beam and investigate the effects of static deflection on the symmetric and antisymmetric modes. An experimental design using noncontact methods is implemented to directly measure the response of the whole beam in the snap-through process and the sound generated by the vibrating beam. The measurements are characterized in both time and frequency domain and found to be in good agreement with the analytical model. The study presented in this article enhances the fundamental understanding of the classical problem of bistable clamped–clamped beams.

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