Journal articles: 'Cantilever loading'

1

Yuan, Yan Hui, He Jun Du, Xin Xia, and Yoke Rung Wong. "Modeling, Fabrication and Characterization of Piezoelectric ZnO-Based Micro-Sensors and Micro-Actuators." Applied Mechanics and Materials 444-445 (October 2013): 1636–43. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.1636.

Full text

Abstract:

In this study, capabilities of zinc oxide (ZnO) thin films in sensing and actuating were investigated using micromachined micro-cantilevers. A heterogeneous piezoelectric cantilever was modeled to study its response under voltage and/or external mechanical loading. A ZnO thin-film micro-cantilever was designed based on the developed theoretical model. Simulated tip deflections of the micro-cantilever were on the nanometer level under typical electrical and mechanical input. A prototype was fabricated with microfabrication techniques. The ZnO thin film was sputtered at room temperature and demonstrated good compatibility with common chemicals and processes in micromachining. The fabricated micro-cantilever was experimentally characterized for its actuating and sensing performance. For actuator characterization tip deflection of the micro-cantilever was detected by a laser Doppler vibrometer, while for sensor characterization the micro-cantilever was calibrated as an acceleration sensor using a reference accelerometer. The experimental resonant frequency, actuating and sensing sensitivities agreed well the design specifications.

APA, Harvard, Vancouver, ISO, and other styles

2

Liu, C. C., S. C. Yang, and C. K. Chen. "Nonlinear Dynamic Analysis of Micro Cantilever Beam Under Electrostatic Loading." Journal of Mechanics 28, no. 1 (March 2012): 63–70. http://dx.doi.org/10.1017/jmech.2012.6.

Full text

Abstract:

ABSTRACTA hybrid differential transformation / finite difference scheme is used to analyze the complex nonlinear behavior of an electrostatically-actuated micro cantilever beam which high aspect ratios (length/width). The validity of the proposed method is confirmed by comparing the numerical results obtained for the tip displacement and pull-in voltage of the cantilever beam with the analytical and experimental results presented in the literature. The hybrid scheme is then applied to analyze both the steady-state and the dynamic deflection behavior of the cantilever beam as a function of the applied voltage. Overall, the results confirm that the hybrid method provides an accurate and computationally-efficient means of analyzing the complex nonlinear behavior of both the current micro cantilever beam system and other micro-scale electrostatically-actuated structures.

APA, Harvard, Vancouver, ISO, and other styles

3

Xiang, Min, and Cong Juan Yang. "Analysis of Eccentric Load Causing Torsion Effects of Variable Cross-Section Continuous Box Girder during Cantilevered Casting." Advanced Materials Research 446-449 (January 2012): 1194–98. http://dx.doi.org/10.4028/www.scientific.net/amr.446-449.1194.

Full text

Abstract:

The construction with hanging basket eccentric loading was studied for the cantilever casting of a 32m +48 m +32 m continuous box girder. The calculation of center deflecting angles of cantilever box girders with variable cross-section due to pure torsion was derived, and correspondingly a program was developed to calculate this formula. An analysis model of cantilever casting continuous beam bridge with hanging basket eccentric loading was established based on finite elements software, and the shear stress, the longitudinal normal stress and the combined stress of different section were analyzed under different construction process. The torsional effect due to hanging basket eccentric loading was studied and the results are helpful to guide the construction in practice.

APA, Harvard, Vancouver, ISO, and other styles

4

Liu, Wenguang, and Mark E. Barkey. "Prediction on Remaining Life of a V-Notched Beam by Measured Modal Frequency." Shock and Vibration 2019 (January 3, 2019): 1–10. http://dx.doi.org/10.1155/2019/7351386.

Full text

Abstract:

A prediction method for the remaining life of a V-notched beam using measured modal frequencies is proposed in this article. The main purpose is to provide a new monitoring method of crack growth for a cantilever beam. At first, the fatigue crack growth characteristic and the change law of modal frequencies of a V-notched cantilever beam under cyclic loading were studied by experiments. Subsequently, the relation of modal frequencies and crack growth were analyzed. Thereafter, the decrease ratio of the first modal frequency was employed to reflect the crack damage so as to set up the relation of the modal frequency and the crack damage, and the evolution model between the crack damage and the cyclic loading numbers were set up. A prediction method for crack growth life was proposed for a cantilever beam based on the decrease ratio of the first modal frequency in the end. The remaining life of a V-notched cantilever beam can be obtained using the proposed method with a given endured loading cycles and the corresponding measured modal frequency. Results indicate that the remaining fatigue life of the V-notched cantilever beam is related to the decrease ratio of the modal frequency, and the predicted remaining life is in good agreement with the measured remaining life as the crack depth extends to a certain value.

APA, Harvard, Vancouver, ISO, and other styles

5

Mumcu, Emre, Hakan Bilhan, and Ali Cekici. "Marginal Bone Loss Around Implants Supporting Fixed Restorations." Journal of Oral Implantology 37, no. 5 (October 1, 2011): 549–58. http://dx.doi.org/10.1563/aaid-joi-d-10-00018.

Full text

Abstract:

A key criterion of success following dental implants is the marginal bone level. Long-term clinical and radiographic evaluation is necessary to test the results of in vitro studies investigating how cantilevering of restorations or implant size affect bone level changes around implants. There is no consensus on the effect of several variables such as age, gender, implant size, and cantilever prostheses on marginal bone levels around fixed dentures supported by dental implants. Patients who received cemented, fixed restorations supported by implants and who were examined in routine recall sessions 6, 12, 24, and 36 months after loading were included in the study group. Comparative bone level measurements were obtained from images of radiographs at ×20 magnification using the CorelDraw 11.0 software program. Statistical analysis was performed using the Student t test and 1-way analysis of variance. In the 36-month observation period, there were no incidences of implant failure, excessive bone loss around implants, or peri-implant inflammation. One hundred twenty-six implants in 36 patients were evaluated, and the effect of several factors on marginal bone loss (MBL) during the 36 months after loading was analyzed statistically. There was no significant relationship between MBL and implant length or diameter, whereas age, gender, and cantilevers affected bone loss rates. MBL was elevated in older and female patients as well as in patients who received cantilevers. In cases of limiting anatomic conditions, short and/or narrow implants should be preferred over cantilever extensions.

APA, Harvard, Vancouver, ISO, and other styles

6

Peng, Long Fan, and Zhi Da Li. "Analysis on the Deflection of Cantilever Construction Based on Viscoelasticity." Advanced Materials Research 1030-1032 (September 2014): 1078–81. http://dx.doi.org/10.4028/www.scientific.net/amr.1030-1032.1078.

Full text

Abstract:

The creep of concrete in the construction process of deformation influential, especially in the cantilever pouring construction, short age of concrete, creep effect more apparent. Meaning for cantilever construction of Bridges, creep analysis must be properly considered section at different time of loading values and the concrete ages of different segments. In this paper, based on the viscoelastic problem of cantilever construction of concrete creep analysis method, analyzes the deflection of cantilever construction process of a rigid-frame bridge, and compared with the actual measured value.

APA, Harvard, Vancouver, ISO, and other styles

7

Bilinska, Malgorzata, and Michel Dalstra. "The Effect of Symmetric and Asymmetric Loading of Frontal Segment with Two Curved Cantilevers: An In Vitro Study." Dentistry Journal 10, no. 4 (March 29, 2022): 52. http://dx.doi.org/10.3390/dj10040052.

Full text

Abstract:

Cantilevers generate statically determined force systems. The frontal segment loading with symmetric and asymmetric cantilevers in a three-piece intrusion base arch can be used to correct midline asymmetry. Three types of 0.017″ × 0.025″ beta-titanium cantilevers: tip-back (TB), deep curve (DC), utility arch (UA) were tested on typodonts simulating intrusion of the maxillary anterior segment. Typodonts with symmetric and asymmetric cantilevers were scanned with intraoral scanner (3Shape, TRIOS, Copenhagen, Denmark) before (T0) and after (T1) the experiment, scans were superimposed using Mimics software (Materialise, Leuven, Belgium). Data were analysed with qualitative analysis. All cantilevers generated vertical and horizontal forces. For symmetric design, the DC and TB displayed intrusive force with retrusive component, UA intrusion and protrusion. The asymmetric cantilevers produced transverse displacement of anterior segment. DC created lateral, UA medial force, the anterior segment displacement was consistent with the used configuration. The movement of an anterior segment with TB is smaller compared to DC and UA. Symmetric cantilevers configurations can achieve simultaneous intrusion and retrusion or protrusion of the anterior segment. The asymmetric design with transversal force can clinically aid the correction of midline discrepancies. The effect of the cantilever configuration on delivered force direction was confirmed.

APA, Harvard, Vancouver, ISO, and other styles

8

PRABAKAR, K., J. JAYAPANDIAN, A. K. TYAGI, C. S. SUNDAR, and BALDEV RAJ. "SENSITIVIY OF A NANOCANTILEVER-BASED MASS SENSOR." Nano 05, no. 01 (February 2010): 25–30. http://dx.doi.org/10.1142/s1793292010001834.

Full text

Abstract:

In the present work, mass and position sensitivity of a nanocantilever is simulated using finite element analysis. Changes in resonant frequency of various modes of a polysilicon cantilever, with a gold coating of different thickness, area, and spatial distribution is simulated. It is found that for a uniform increase in gold coating thickness, torsional mode gives an order higher mass sensitivity than vertical bending and lateral bending modes. In other cases, sensitivity is highly dependent on the position of the coating and is explained on the basis of flexural rigidity. Apart from this, simulations were performed for a point mass (gold cube) loading at various positions along the length and width axis of the cantilever. Further, for localized mass loading, cantilever was tailored for enhanced sensitivity. It is found that by introducing a step discontinuity in thickness of the cantilever, the mass sensitivity increases by two orders of magnitude and it depends on the position of step from free end, step thickness, and step width.

APA, Harvard, Vancouver, ISO, and other styles

9

Tuan Nam, Tran. "ANALYSIS OF A CANTILEVER COLUMN SUBJECTED TO CYCLIC LOADING." JOURNAL OF TECHNOLOGY & INNOVATION 1, no. 2 (March 3, 2020): 38–39. http://dx.doi.org/10.26480/jtin.02.2021.38.39.

Full text

Abstract:

In a seismic incident, the structural steel columns are commonly damaged with local buckling formulation at either the top or bottom ends. This study analyzes and simulates the hysteretic behavior of a hollow square steel column under cyclic loading by adopting the fiber-element approach. This method discretizes the hinge zone into a series of fibers and considers buckling behavior of those fibers along the column wall. The analytical result was achieved in good agreement with the component test.

APA, Harvard, Vancouver, ISO, and other styles

10

El-Sayem, Mohamed G., Mohamed S. A. Saafan, and Abd El-Rahim K. Dessouk. "Modelling Of Steel Cantilever With Gfrp Under Cyclic Loading." International Journal of Civil Engineering 6, no. 5 (May 25, 2019): 23–29. http://dx.doi.org/10.14445/23488352/ijce-v6i5p105.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

DongSheng, Li, Guo XingLin, and Li HongNan. "Random loading identification of a plastic glass cantilever beam." IFAC Proceedings Volumes 36, no. 16 (September 2003): 1173–77. http://dx.doi.org/10.1016/s1474-6670(17)34918-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Lee, Joon, and Byoung Lee. "Elastica of Non-Prismatic and Nonlinear Elastic Cantilever Beams under Combined Loading." Applied Sciences 9, no. 5 (March 1, 2019): 877. http://dx.doi.org/10.3390/app9050877.

Full text

Abstract:

This study presents the elastica of non-prismatic cantilever beams with rectangular cross-sections that are subjected to combined loading. The considered beams are nonlinearly elastic and obey Ludwick’s constitutive law. The combined loading system used in this study provides uniform loading, tip point loading, and tip couple loading individually or in combination. This loading system can create a total of seven loading cases that have not been covered in the literature. Ordinary differential equations governing the large deformed shapes of the elastica of the beams are derived and solved numerically. The effects of beam parameters on elastica behavior, including tip responses and strains and stresses loaded onto the cross-sections, were studied. It was observed that the exponential constant of the mechanical properties is very sensitive to elastica behavior. The results also demonstrate that the stresses near the neutral axis are larger with a larger exponential constant.

APA, Harvard, Vancouver, ISO, and other styles

13

Pachkawade, Vinayak. "Precise Design of Micro-Cantilever Sensor for Biomedical Application." Sensor Letters 18, no. 12 (December 1, 2020): 900–904. http://dx.doi.org/10.1166/sl.2020.4305.

Full text

Abstract:

This research evaluates the impact of mass loading/perturbations on the characteristics of a micro-size cantilever bio-mass sensor. Design techniques are proposed through the application of the commercial, finite element modelling, and simulation package, i.e., COMSOL multiphysics. A finite element model and resulting simulations are provided for both the static and dynamic operation of a bio-mass sensor. In static mode, the obtained result provides the structural stress, strain, and displacement of a sensor against several mass loading conditions (point, edge, and boundary). In dynamic mode, shifts in the resonant frequencies of the sensor as a function of mass loading are obtained, which is another viable output of the biosensor. The proposed design and modelling techniques offer a guide in the rapid design and development of precise and efficient biomedical instrumentations and/or products.

APA, Harvard, Vancouver, ISO, and other styles

14

Tri Des Wantoro, Alfian, Ikhwanul Qiram, and Anas Mukhtar. "Pengaruh Beban Tersebar dan Terpusat Terhadap Lendutan (Cantilever) Batang Besi." V-MAC (Virtual of Mechanical Engineering Article) 5, no. 2 (November 17, 2020): 27–29. http://dx.doi.org/10.36526/v-mac.v5i2.1040.

Full text

Abstract:

In development planning in the mechanical industry or civil engineering construction, it is very common to use the properties of the iron rod material which can deflect or what is known as a cantilever. The factors that affect the size of the force exerted on the stem are directly proportional to the amount of deflection that occurs. In other words, the greater the load experienced by the rod, the greater the deflection. Deflection of rods plays an important role, especially in building construction, wherein certain parts such as the shaft, deflection is very undesirable. Because of deflection, the work of the shaft or construction will be abnormal so that it can cause damage to the construction or other parts. This study aims to find out how much deflection of cantilevered rods using metal plate material when given a distributed and concentrated load. Based on the data obtained from the research process, the results in this study indicate that there is an effect of slackening distance on the iron plate with 3 variations in loading. The results showed that the loading rate affected changes in the angle of deflection of the iron plate in every variation of the number of plates used. The greatest effect occurred in the plate variation size of 0.8 mm with a loading level of 3 kg, namely 3.64 x 10-5 and the smallest effect on plate variations was 1.8 mm with a loading rate of 3 kg, which was 0. The results showed that the loading rate was spread across 3 plate variations. with a load of 3 kg spread over 3 points with a distance of 15 cm from point 1 to point 3. The biggest deflection effect occurs in plate variations of 0.8 mm which is 3.64x10-5 and the smallest effect on plate variations is 1.8 mm with the same load of 0.

APA, Harvard, Vancouver, ISO, and other styles

15

King, William P., and Kenneth E. Goodson. "Thermomechanical Formation of Nanoscale Polymer Indents With a Heated Silicon Tip." Journal of Heat Transfer 129, no. 11 (January 15, 2007): 1600–1604. http://dx.doi.org/10.1115/1.2764088.

Full text

Abstract:

In thermomechanical data storage, a heated atomic force microscope cantilever tip is in contact with and scans over a polymer film. Heating in the cantilever and cantilever tip induces local deformation of the polymer near the tip, with indents as small as 22nm. This paper reports a simple modeling approach for predicting heat and mass transfer in the cantilever tip and polymer with the goal of predicting indent formation conditions. The model accounts for subcontinuum conduction in the cantilever tip and for the time- and temperature-dependent mechanical properties of the polymer. Simulations predict steady state and transient indent formation, and the results compare well with data. For loading forces 30–200nN and a tip radius of 20nm, a cantilever temperature of 200°C is required to form an indent at steady state. For heating pulses as short as 5μs, the cantilever temperature required for bit formation is as high as 500°C. By quantifying the conditions required for indent formation, this work may improve the operation of heated probes for thermomechanical data storage.

APA, Harvard, Vancouver, ISO, and other styles

16

Zuev, D. M., and K. G. Okhotkin. "Modified formulas for maximum deflection of a cantilever under transverse loading." Spacecrafts & Technologies 4, no. 1 (2020): 28–35. http://dx.doi.org/10.26732/j.st.2020.1.04.

Full text

Abstract:

Modern problems of aerospace industry require consideration of rods experiencing large deflections. The example of such a problem is development of large scale deployable umbrellatype antennas where rods are structural elements. Development of modern analytic methods in the field of solid mechanics allows to model rod bend shapes and to find expressions for maximum deflection. In addition, the analytic methods make it possible to find a full system of solution branches and all possible equilibrium shapes without significant time-consuming for numerical simulations. Wherein relatively simple methods for determining bending shapes in case of large deflections have significant importance for applied use. Namely, they can be used for preliminary design of complex rod constructions. The paper presents the method for obtaining of modified analytic formulas that enable to determine large deflections of a thin elastic cantilever under transverse loading. The method uses a rod’s arc-length saving condition which is important for applied use. The modified formulas allow to achieve accuracy comparable with exact nonlinear solutions given in terms of elliptic integrals and functions. That fact expands the loading range where the linear theory can be used. The authors considered the following cases: concentrated transverse loading on the free end and combined loading (uniformly distributed loading and concentrated transverse loading on the free end). The comparison with experimental data proved accuracy of the proposed method. In addition, the authors obtained approximate formulas based on the modified formulas. The approximate formulas can be use for engineering applications.

APA, Harvard, Vancouver, ISO, and other styles

17

Virgin, L. N. "Free Vibrations of Imperfect Cantilever Bars under Self-Weight Loading." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 201, no. 5 (September 1987): 345–47. http://dx.doi.org/10.1243/pime_proc_1987_201_133_02.

Full text

Abstract:

This brief study examines the relationship between the natural frequency of small oscillations and the length of vertical cantilever struts in a gravitational field. The analysis uses a Rayleigh approach and includes post-buckled equilibrium states and emphasizes the influence of initial imperfections.

APA, Harvard, Vancouver, ISO, and other styles

18

Scavuzzo, Rudolph J. "Effect of Loading on Stress Intensification Factors." Journal of Pressure Vessel Technology 128, no. 1 (October 7, 2005): 33–38. http://dx.doi.org/10.1115/1.2148420.

Full text

Abstract:

The basic objective of this investigation is to determine the effect of loading on the stress intensification factors of Markl’s fatigue evaluation method for metal piping. Markl’s method is based on the fatigue testing of 4 in. schedule 40 carbon steel cantilever piping. Subsequent testing using a four-point loading showed that the S-N data were different from that predicted by the procedure and equation developed by Markl. Markl’s method is based on determining the elastic-plastic forces in a piping system by multiplying the elastic system stiffness by the actual deflection. In this manner a fictitious force is calculated to determine piping stresses assuming the elastic beam bending equation, Mc/I, applies even in partially plastic pipes. Previous analytical work on this topic by Rodabaugh and Scavuzzo (“Fatigue of Butt Welded Pipe and the Effect of Testing Methods–Report 2: Effect of Testing Methods on Stress Intensification Factors,” Welding Research Bulletin 433, July 1998) showed that these measured differences should occur between cantilever and four-point tests using Markl’s method. The basic assumption in this analytical comparison is that strain-cycle correlations lead to the correct prediction of fatigue life. Using the measured alternating strain, both types of test geometries lead to the same prediction of fatigue life using these strain-cycle correlations. In this study, the same analytical assumptions used by Rodabaugh and Scavuzzo (above) are applied to a pipe where the load is varied from a four-point loading through its extremes. Loads were varied from a cantilever to an end moment by changing the dimensions of four-point loading. Also, the shape of a bilinear stress-strain curve was varied from a perfectly plastic material to various degrees of work hardening by increasing the tangent modulus in the plastic regime. The results of the study indicate that Markl’s method is conservative by predicting too short a fatigue life for four-point loading for a given stress. As indicated by this study, the differences can be very large in the low-cycle regime for a perfectly plastic material and for a four-point loading approaching an end moment. Thus, piping could be over designed with unnecessary conservatism using the current ASME Code method based on stress intensification factors.

APA, Harvard, Vancouver, ISO, and other styles

19

LAKSHMOJI, K., K. PRABAKAR, ATUL KUMAR, J. JAYAPANDIAN, and A. K. TYAGI. "ENHANCING THE MASS SENSITIVITY OF NANOCANTILEVER." International Journal of Nanoscience 11, no. 01 (February 2012): 1250002. http://dx.doi.org/10.1142/s0219581x12500020.

Full text

Abstract:

In the present work, dynamic frequency analysis of different nanostructures like nanobelt, nanotube etc., which can be attached to a conventional micro cantilever, is performed for estimating the mass sensitivity using finite element analysis. It is found that compared to rectangular bar and cylinder shape, tube shape gives higher sensitivity and is explained on the basis of distribution of effective mass. In the case of nanocantilever, it is found that by introducing a step discontinuity along the length of the cantilever, mass sensitivity can be enhanced. It is also proved that mass sensitivity is highly dependent on the position of mass loading in cantilever based mass sensors.

APA, Harvard, Vancouver, ISO, and other styles

20

Li, Xi De, and Zhao Zhang. "Probe-Type Microforce Sensor for Mirco/Nano Experimental Mechanics." Advanced Materials Research 33-37 (March 2008): 943–48. http://dx.doi.org/10.4028/www.scientific.net/amr.33-37.943.

Full text

Abstract:

In recent years with the development of MEMS and NEMS, various micro and nano scale experiments are required. In general, the smaller the sample, the smaller the force is in the measurement. But it is difficult to load and measure such small force. We developed a probe-type loading and force sensor system to measure micro/nano samples. The system employs a semiconductor strain gauge of a cantilever type sensor and a micro manipulator. A highly sensitive, stable sensing cantilever beam made of single crystal silicon is ion implanted to form the P-type resistor (strain sensor). A tungsten probe with 100 nm radius of curvature was attached to the end of the cantilever as the micro loading tip. We constructed the measurement system and investigated its properties, such as linearity, dynamic response and stability. We also employed microspeckle interferometry to calibrate the force sensor. In preliminary experiments, we successfully obtained the force resolution 0.7 μN and applied our probe-type microforce sensor to calibrate an atomic force microscope (AFM) probe beam and test a single silkworm filament.

APA, Harvard, Vancouver, ISO, and other styles

21

Saseendran, Vishnu, Leif A. Carlsson, and Christian Berggreen. "Shear and foundation effects on crack root rotation and mode-mixity in moment- and force-loaded single cantilever beam sandwich specimen." Journal of Composite Materials 52, no. 18 (January 8, 2018): 2537–47. http://dx.doi.org/10.1177/0021998317749714.

Full text

Abstract:

Foundation effects play a crucial role in sandwich fracture specimens with a soft core. Accurate estimation of deformation characteristics at the crack front is vital in understanding compliance, energy release rate and mode-mixity in fracture test specimens. Beam on elastic foundation analysis of moment- and force-loaded single cantilever beam sandwich fracture specimens is presented here. In addition, finite element analysis of the single cantilever beam specimen is conducted to determine displacements, rotations, energy release rate and mode-mixity. Based on finite element analysis, a foundation modulus is proposed that closely agrees with the numerical compliance and energy release rate results for all cases considered. An analytical expression for crack root rotation of the loaded upper face sheet provides consistent results for both loading configurations. For the force-loaded single cantilever beam specimen (in contrast to the moment-loaded case), it was found that the crack length normalized energy release rate and the mode-mixity phase angle increase strongly as the crack length decreases, a result of increased dominance of shear loading.

APA, Harvard, Vancouver, ISO, and other styles

22

Kitamura, Shigeru. "Influence of Loading to Cantilever Pontic on Post-and-cores." Annals of Japan Prosthodontic Society 1, no. 3 (2009): 284–93. http://dx.doi.org/10.2186/ajps.1.284.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Salem, Abdelwahhab N., Omar Y. Ezzeldine, and Mohamed I. Amer. "Seismic loading on cantilever retaining walls: Full-scale dynamic analysis." Soil Dynamics and Earthquake Engineering 130 (March 2020): 105962. http://dx.doi.org/10.1016/j.soildyn.2019.105962.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Chandrashekhara, K. "Analysis of Long Cantilever Cylindrical Shell Subjected to Wind Loading." Journal of Engineering Mechanics 115, no. 9 (September 1989): 2101–5. http://dx.doi.org/10.1061/(asce)0733-9399(1989)115:9(2101).

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Jumel, Julien, Michal K. Budzik, and Martin E. R. Shanahan. "Process zone in the Single Cantilever Beam under transverse loading." Theoretical and Applied Fracture Mechanics 56, no. 1 (August 2011): 7–12. http://dx.doi.org/10.1016/j.tafmec.2011.09.006.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Kurniawan, Cyrilus Winatama, and Mahen Mahendran. "Elastic lateral buckling of cantilever Litesteel Beams under transverse loading." International Journal of Steel Structures 11, no. 4 (December 2011): 395–407. http://dx.doi.org/10.1007/s13296-011-4001-z.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Yazdani Sarvestani, Hamidreza, Suong V. Hoa, and Mehdi Hojjati. "Stress analysis of thick orthotropic cantilever tubes under transverse loading." Advanced Composite Materials 26, no. 4 (June 10, 2016): 335–62. http://dx.doi.org/10.1080/09243046.2016.1190992.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Xiang-sheng, Cheng. "On buckling of cantilever rectangular plates under symmetrical edge loading." Applied Mathematics and Mechanics 11, no. 4 (April 1990): 377–83. http://dx.doi.org/10.1007/bf02015121.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

England, A. H., and T. G. Rogers. "Loading and unloading of an elastic-plastic fibre-reinforced cantilever." Mechanics Research Communications 19, no. 4 (July 1992): 333–40. http://dx.doi.org/10.1016/0093-6413(92)90052-c.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Du, Binyang, Mark R. VanLandingham, Qingling Zhang, and Tianbai He. "Direct measurement of plowing friction and wear of a polymer thin film using the atomic force microscope." Journal of Materials Research 16, no. 5 (May 2001): 1487–92. http://dx.doi.org/10.1557/jmr.2001.0207.

Full text

Abstract:

Nanometer-scale plowing friction and wear of a polycarbonate thin film were directly measured using an atomic force microscope (AFM) with nanoscratching capabilities. During the nanoscratch tests, lateral forces caused discrepancies between the maximum forces for the initial loading prior to the scratch and the unloading after the scratch. In the case of a nanoscratch test performed parallel to the cantilever probe axis, the plowing friction added another component to the moment acting at the cantilevered end compared to the case of nanoindentation, resulting in an increased deflection of the cantilever. Using free-body diagrams for the cases of nanoindentation and nanoscratch testing, the AFM force curves were analyzed to determine the plowing friction during nanoscratch testing. From the results of this analysis, the plowing friction was found to be proportional to the applied contact force, and the coefficient of plowing friction was measured to be 0.56 ± 0.02. Also, by the combination of nanoscratch and nanoindentation testing, the energetic wear rate of the polycarbonate thin film was measured to be 0.94 ± 0.05 mm3/(N m).

APA, Harvard, Vancouver, ISO, and other styles

31

Aalami, MR, and TN Chakherlou. "Investigating the effects of loading system on the fracture behavior of DCB specimens considering T-stress." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 235, no. 12 (October 4, 2021): 2654–65. http://dx.doi.org/10.1177/14644207211030963.

Full text

Abstract:

Double cantilever beam specimen is a standard specimen for assessment of mode I failure and separation in adhesively bonded joints and also composite materials. Among the several load introduction systems, the piano hinges and end loading blocks are more common. It has been accepted that the fracture toughness results of the two cases are different, but the effect of the loading system on the load-displacement data and fracture mechanisms is not entirely known yet. Therefore, in this study, the two loading concepts are compared both by precise finite element simulations and experimental tests. The adhesive layer is modeled with its own material properties, and the failure of adhesive is investigated by known LEFM procedures. The results reveal that the load block makes the double cantilever beam specimen stiffer and exhibit more non-linear behavior. Moreover, double cantilever beam with the load block system fails in higher loads and lower crack opening displacements compared with the same specimen loaded by the hinges. To study the effect of loading arrangement in more details and including the softening phase, cohesive zone model was utilized. A correction for strain energy release rate based on the parameter T was proposed, and the role of the T-stress on the traction-separation law of the cohesive zone model and the load-displacement behavior were investigated. It was concluded that the T-stress as a crack tip constraint parameter can successfully justify the difference between the two cases. Applying the correction to the traction-separation law of CZM proves the validity of proposed correction in justifying the experimental results.

APA, Harvard, Vancouver, ISO, and other styles

32

Aalami, MR, and TN Chakherlou. "Investigating the effects of loading system on the fracture behavior of DCB specimens considering T-stress." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 235, no. 12 (October 4, 2021): 2654–65. http://dx.doi.org/10.1177/14644207211030963.

Full text

Abstract:

Double cantilever beam specimen is a standard specimen for assessment of mode I failure and separation in adhesively bonded joints and also composite materials. Among the several load introduction systems, the piano hinges and end loading blocks are more common. It has been accepted that the fracture toughness results of the two cases are different, but the effect of the loading system on the load-displacement data and fracture mechanisms is not entirely known yet. Therefore, in this study, the two loading concepts are compared both by precise finite element simulations and experimental tests. The adhesive layer is modeled with its own material properties, and the failure of adhesive is investigated by known LEFM procedures. The results reveal that the load block makes the double cantilever beam specimen stiffer and exhibit more non-linear behavior. Moreover, double cantilever beam with the load block system fails in higher loads and lower crack opening displacements compared with the same specimen loaded by the hinges. To study the effect of loading arrangement in more details and including the softening phase, cohesive zone model was utilized. A correction for strain energy release rate based on the parameter T was proposed, and the role of the T-stress on the traction-separation law of the cohesive zone model and the load-displacement behavior were investigated. It was concluded that the T-stress as a crack tip constraint parameter can successfully justify the difference between the two cases. Applying the correction to the traction-separation law of CZM proves the validity of proposed correction in justifying the experimental results.

APA, Harvard, Vancouver, ISO, and other styles

33

Machado, Raissa Micaella Marcello, Luciana de Rezende Pinto, Otacílio Luiz Chagas Júnior, and Fernanda Faot. "Semirigid Cantilever Extension System for Splinting Implants: A Clinical Report." Case Reports in Dentistry 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/192974.

Full text

Abstract:

In mandibular edentulous patients, treatment based on immediate loading with rigid splinting in the mandible is well accepted; however, it is cost and time dependent, which sometimes limits this type of rehabilitation. To overcome these problems, the technique of immediate loading using a semirigid splinting extension system has been developed. Its advantages include low cost, technical feasibility, and reduced clinic time. This clinical report presents the applicability and the predictability of semirigid splinting of implants in the mandibular arch of an edentulous patient using adistal extension bar prosthesis system.

APA, Harvard, Vancouver, ISO, and other styles

34

Catapano, Santo, Mattia Ferrari, Nicola Mobilio, Marco Montanari, Massimo Corsalini, and Francesco Grande. "Comparative Analysis of the Stability of Prosthetic Screws under Cyclic Loading in Implant Prosthodontics: An In Vitro Study." Applied Sciences 11, no. 2 (January 11, 2021): 622. http://dx.doi.org/10.3390/app11020622.

Full text

Abstract:

Background: To compare the loss of preload in absence of loading and after a fixed number of cyclic loadings on 7-mm distal cantilever in two different connection systems using all-on-four prosthetic model. Methods: Two equal models of an edentulous mandible rehabilitated with all-on-four technique with two types of abutment system (MUA and OT-Bridge) supporting a hybrid prosthesis, were used. Initial torque values of the prosthetic fixing screw, after ten minutes from initial screw tightening and after 400,000 repeated loadings were registered using a mechanical torque gauge. Differences between initial and final torque values were reported for each anchoring system and the two systems were finally compared. Results: No statistically significant differences regarding the loss of preload between MUA and OT-Bridge system were found after 400,000 cyclic loadings; however, in MUA system it was found between anterior and posterior implant screws. A significant difference in preload loss was found only for MUA system comparing the initial screw torque to that measured after 10 min from the tightening in absence of cyclic loadings. Conclusions: Within the limits of the present study, MUA and OT-Bridge may be considered reliable prosthetic anchoring systems able to tolerate repeated cyclic occlusal loads on distal cantilever in all-on-four rehabilitation model without any significant loss of preload in screw tightening.

APA, Harvard, Vancouver, ISO, and other styles

35

Catapano, Santo, Mattia Ferrari, Nicola Mobilio, Marco Montanari, Massimo Corsalini, and Francesco Grande. "Comparative Analysis of the Stability of Prosthetic Screws under Cyclic Loading in Implant Prosthodontics: An In Vitro Study." Applied Sciences 11, no. 2 (January 11, 2021): 622. http://dx.doi.org/10.3390/app11020622.

Full text

Abstract:

Background: To compare the loss of preload in absence of loading and after a fixed number of cyclic loadings on 7-mm distal cantilever in two different connection systems using all-on-four prosthetic model. Methods: Two equal models of an edentulous mandible rehabilitated with all-on-four technique with two types of abutment system (MUA and OT-Bridge) supporting a hybrid prosthesis, were used. Initial torque values of the prosthetic fixing screw, after ten minutes from initial screw tightening and after 400,000 repeated loadings were registered using a mechanical torque gauge. Differences between initial and final torque values were reported for each anchoring system and the two systems were finally compared. Results: No statistically significant differences regarding the loss of preload between MUA and OT-Bridge system were found after 400,000 cyclic loadings; however, in MUA system it was found between anterior and posterior implant screws. A significant difference in preload loss was found only for MUA system comparing the initial screw torque to that measured after 10 min from the tightening in absence of cyclic loadings. Conclusions: Within the limits of the present study, MUA and OT-Bridge may be considered reliable prosthetic anchoring systems able to tolerate repeated cyclic occlusal loads on distal cantilever in all-on-four rehabilitation model without any significant loss of preload in screw tightening.

APA, Harvard, Vancouver, ISO, and other styles

36

Koryagin, Sergey I., Nikolay L. Velikanov, and Oleg V. Sharkov. "Experimental Research of Crack Resistance of Composite Materials." Key Engineering Materials 736 (June 2017): 8–11. http://dx.doi.org/10.4028/www.scientific.net/kem.736.8.

Full text

Abstract:

An adhesive composition is used as a binder in many composite materials. Crack resistance of an adhesive composition is the most important characteristic determining the bearing capacity of composite materials. To date, a significant number of methodological recommendations and standards have been developed for estimation of adhesive compositions bearing capacity in different types of loading forces exertions which, with certain assumptions, can be used to assess their crack resistance. Known testing procedure for crack resistance of adhesive composition was selected as a basic one. It includes a bending load in the form of loadings acting perpendicular to cantilever beams which is applied to the double-cantilever sample. Therewith a sample response and a corresponding change in length of the resulting crack in the adhesive compound layer are being recorded. This is followed by a determination of the specific energy of crack propagation which provides information about the value of crack resistance.

APA, Harvard, Vancouver, ISO, and other styles

37

Glagolev, V. V., L. V. Glagolev, and A. A. Markin. "Energy product in a crack-like defect model under loading of mode II type." PNRPU Mechanics Bulletin, no. 4 (December 15, 2019): 48–58. http://dx.doi.org/10.15593/perm.mech/2019.4.05.

Full text

Abstract:

The loading of a crack-like defect in mode II is considered. In contrast to the classical representation of a crack in the form of a mathematical cut, the proposed model defines a crack in the form of a physical cut with a characteristic linear size. The mental continuation of a physical cut in a solid forms an interaction layer. It is significant that the stress-strain state of the layer does not introduce a singularity to the crack model. The product of the increment of the specific free energy in the face square element of the layer by the linear size determines its energy product. The object of the study is a double-cantilever sample, and the subject of study is the energy product in the face element of the interaction layer. The external load of the cantilevers leads to their horizontal antisymmetric displacements, which form uniform shear deformations in the interaction layer. From the equilibrium conditions of the cantilevers in the variation form, taking into account the hypothesis of axial deformation homogeneity and their reduction, a system of differential equations is obtained, which relates the stress state in the layer and the cantilevers. The solution of the characteristic equation of the system is investigated for various ratios of layer thickness and cantilevers. It is shown that when the relationship is less than a certain value, depending on the Poisson's ratio, real roots take place. In the framework of the real roots of the characteristic equation, an analytical solution of the problem is obtained. Subject to the neglect of compression cantilevers found a simplified solution. The deformations in the layer are determined taking into account the compression of the consoles and without it. The analysis of the dependence of the energy product on the relationship of the thickness of the layer and cantilevers. It is shown that with a thickness ratio of 10-6 or less, the energy product practically does not change its value. Accounting for the compression of cantilevers gives a difference in the values of the energy product of the order of 20 % in relation to the simplified solution of the problem.

APA, Harvard, Vancouver, ISO, and other styles

38

Mesquita, Luciane R., Sheila C. Rahal, Camilo Mesquita Neto, Washington T. Kano, Antônio C. Beato, Luís G. Faria, and Maíra S. Castilho. "Development and mechanical properties of a locking T-plate." Pesquisa Veterinária Brasileira 37, no. 5 (May 2017): 495–501. http://dx.doi.org/10.1590/s0100-736x2017000500012.

Full text

Abstract:

ABSTRACT: This study aimed to develop a locking T-plate and to evaluate its mechanical properties in synthetic models. A titanium 2.7mm T-plate was designed with a shaft containing three locked screw holes and one dynamic compression hole, and a head with two locked screw holes. Forty T-shaped polyurethane blocks, and 20 T-plates were used for mechanical testing. Six bone-plate constructs were tested to failure, three in axial compression and three in cantilever bending. Fourteen bone-plate constructs were tested for failure in fatigue, seven in axial compression and seven in cantilever bending. In static testing higher values of axial compression test than cantilever bending test were observed for all variables. In axial compression fatigue testing all bone-plate constructs withstood 1,000,000 cycles. Four bone-plate constructs failure occurred before 1,000,000 cycles in cantilever bending fatigue testing. In conclusion, the locking T-plate tested has mechanical properties that offer greatest resistance to fracture under axial loading than bending forces.

APA, Harvard, Vancouver, ISO, and other styles

39

Shan, Baoxiang, and Assimina A. Pelegri. "Assessment of the Fracture Behavior of an Asymmetrically Loaded Cantilever Composite Structure." Journal of Engineering Materials and Technology 125, no. 4 (September 22, 2003): 353–60. http://dx.doi.org/10.1115/1.1605108.

Full text

Abstract:

The complex fracture behavior of a cross-ply composite cantilever beam with artificially embedded delamination is investigated analytically, numerically, and experimentally. The analysis of the cantilever beam is divided into two geometric configurations: the global bending of the undelaminated cantilever, and the local buckling of the delaminated part. A finite element model developed in ANSYS is used to concurrently analyze the effects of contact zone and delamination in the aforementioned asymmetrically loaded structure. The obtained experimental data are correlated and compared with the findings of the FEM simulations. All numerical, analytical, and experimental results illustrate that the fracture behavior of the laminate cantilever beam is dominated by mode II, mainly due to the effect of a large contact zone. The latter is determined by geometric and loading parameters. The dominance of mode II over mode I, leads to the initiation and propagation of an interfacial crack rather than an intralayer one. Furthermore, experimental evidence indicates that crack kinking during propagation depends on the architecture of the specimens.

APA, Harvard, Vancouver, ISO, and other styles

40

Liu, L., H. Jiang, Y. Dong, L. Quan, and Y. Tong. "Study on Flexibility of Intracranial Vascular Stents Based on the Finite Element Method." Journal of Mechanics 35, no. 4 (August 28, 2018): 465–74. http://dx.doi.org/10.1017/jmech.2018.31.

Full text

Abstract:

ABSTRACTFlexibility is a particularly important biomechanical property for intracranial vascular stents. To study the flexibility of stent, the following work was carried out by using the finite element method: Four mechanical models were adopted to simulate the bending deformation of stents, and comparative studies were conducted about the distinction between cantilever beam and simply supported beam, as well as the distinction between moment-loading method and displacement-loading method. A complete process as implanting a stent including compressing, expanding and bending was also simulated, for analyzing the effects of compressing and expanding deformation on stent flexibility. At the same time, the effects of the arrangement and the number of bridges on stent flexibility were researched. The results show that: 1. A same flexibility index was obtained from cantilever beam model and simply supported beam model; displacement-loading method is better than moment-loading for simulating the bending deformation of stents. 2. The flexibility of stent with compressing and expanding deformation is lower than that in the initial form. 3. Crossly arranging the neighboring bridges in axial direction, can effectively improve the stent flexibility and reduce the flexibility difference in various bending directions; the bridge number, has proportional non-linear correlation with the stent rigidity as well as the maximum moment required for bending the stent.

APA, Harvard, Vancouver, ISO, and other styles

41

Zhang, Rui Jun, Min Li, Min Qin Zhang, and Xiao Wei Wang. "Structural Reliability Analysis of Loading Platform Cantilever under Multiple Failure Modes." Advanced Materials Research 102-104 (March 2010): 204–9. http://dx.doi.org/10.4028/www.scientific.net/amr.102-104.204.

Full text

Abstract:

Force behaviors of the loading platform of rotating stereo garages is analyzed, equations describing the load capacity and the deformation limit state are proposed for the key sections by applying the second-order moment into the reliability analysis of the main beam. Considering random parameters subject to normal distribution, a reliability model of the main beam of the loading platform is set up based on multiple failure modes and the reliability is analyzed and calculated by using second-order moment. Simulation results show that the reliability model is significant to guide designing on the reliability of rotating stereo garages and improves rotating stereo garages.

APA, Harvard, Vancouver, ISO, and other styles

42

Deng, Wenqin, Duo Liu, Zongqing Peng, and Jiandong Zhang. "Behavior of Cantilever Composite Girder Bridges with CSWs under Eccentric Loading." KSCE Journal of Civil Engineering 25, no. 10 (July 8, 2021): 3925–39. http://dx.doi.org/10.1007/s12205-021-2328-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Chaterjee, S., and G. Pohit. "Squeeze-Film Damping Characteristics of Cantilever Microresonators under Large Electrostatic Loading." Mechanics of Advanced Materials and Structures 19, no. 8 (December 2012): 613–24. http://dx.doi.org/10.1080/15376494.2011.572247.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Berry, A. G., and S. P. G. Madabhushi. "Modelling of waterfront cantilever sheet pile walls subjected to earthquake loading." Geomechanics and Geoengineering 2, no. 3 (August 20, 2007): 207–18. http://dx.doi.org/10.1080/17486020701493996.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Oguibe, Chuks N., and David C. Webb. "Large deflection analysis of multilayer cantilever beams subjected to impulse loading." Computers & Structures 78, no. 4 (December 2000): 537–47. http://dx.doi.org/10.1016/s0045-7949(00)00042-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Mohammed, Abbas, Khattab Saleem Abdul-Razzaq, Nildem Tayşi, and Awat FAQE. "Modelling of Bonded Post-Tensioned Concrete Cantilever Beams under Flexural Loading." Civil Engineering Journal 3, no. 7 (July 30, 2017): 463–79. http://dx.doi.org/10.28991/cej-2017-00000105.

Full text

Abstract:

Prestressing is widely used technic all over the world for constructions of buildings, bridges, towers, offshore structures etc. due to its efficiency and economy for achieving requirements of long span with small depth. It is used for flexural strengthening of reinforced concrete structures for improving cracking loads and decreasing deflections due to service loads. There are two methods for prestressing (pre-tensioning and post-tensioning). In this paper, a three-dimensional nonlinear Finite Element (FE) method is used to determine the behaviour of Post-Tensioned (PT) concrete cantilever beams with different tendon profiles. Numerical analyses ANSYS package program is used for analysis of beams. The results from FE analysis is verified by experimental reference test result and good agreement is achieved. This paper is focused on the effect of different tendon profiles on the flexural behaviour of Bonded Post Tensioned (BPT) reinforced concrete cantilever beams. Six models with different tendon profiles are investigated. These models are without tendons, two tendons at the bottom, middle, top, parabolic tendons with one draped point and two draped points. Failure loads, deflections, and load versus deflection relationships for all models are examined and it is seen that the beam with one draped tendon profile shows a highest performance.

APA, Harvard, Vancouver, ISO, and other styles

47

Navaee, S., and R. E. Elling. "Equilibrium Configurations of Cantilever Beams Subjected to Inclined End Loads." Journal of Applied Mechanics 59, no. 3 (September 1, 1992): 572–79. http://dx.doi.org/10.1115/1.2893762.

Full text

Abstract:

In this study, equilibrium configurations of a cantilever beam subjected to an end load with constant angle of inclination is investigated. It is shown analytically that if the beam is sufficiently flexible, there are multiple equilibrium solutions for a specific beam and loading condition. A method is also presented for the determination of these deflected configurations. The cantilever beam studied in this research is considered to be initially straight and prismatic in addition to being homogeneous, elastic, and isotropic. The procedure outlined in this paper is utilized to show that for each combination of load and beam parameters, there are certain number of equilibrium configurations for a cantilever beam. The ranges of these combinations, along with some examples of the deflected shapes of the beams, are provided for several load inclination angles.

APA, Harvard, Vancouver, ISO, and other styles

48

Wang, Xing Guo, Jun Hui Yue, Li Li, and Yu Zhou Zheng. "Behavior of Cantilever RC Beam Support Strengthened with Near-Surface-Mounted FRP Bars." Advanced Materials Research 243-249 (May 2011): 1762–66. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.1762.

Full text

Abstract:

Several parameters, including typical loads, deflection, strains of steel bar and fiber- reinforced-polymer(FRP) bar under different sustained loading, were studied. The yield load and ultimate load of cantilever beams strengthened with near-surface-mounted(NSM) FRP bars are improved by 6.0%~15.2% and 55.7%~64.5% compared with non-strengthened beams, respectively. For strengthened beams,sustained loading can weaken the reinforced effect.The flexural behaviors of mounted beams were influenced by the lateral groove .

APA, Harvard, Vancouver, ISO, and other styles

49

Rizov, Victor Iliev. "Influence of Loading History on Delamination in Multilayered Beam with Creep." Materials Science Forum 1046 (September 22, 2021): 23–28. http://dx.doi.org/10.4028/www.scientific.net/msf.1046.23.

Full text

Abstract:

The present paper deals with an analytical study of the time-dependent delamination in a multilayered inhomogeneous cantilever beam with considering of the loading history. The multilayered beam exhibits creep behaviour that is treated by using a non-linear stress-strain-time relationship. The material properties are continuously distributed along the thickness and length of the layers. The external loading is applied in steps in order to describe the loading history. The analysis reveals that during each step of the loading, the strain energy release rate increases with time. The influences of crack length and location on the time-dependent strain energy release rate are also investigated.

APA, Harvard, Vancouver, ISO, and other styles

50

Abu-Alshaikh, Ibrahim Mousa. "Closed-Form Solution of Large Deflected Cantilever Beam a gainst Follower Loading Using Complex Analysis." Modern Applied Science 11, no. 12 (November 20, 2017): 12. http://dx.doi.org/10.5539/mas.v11n12p12.

Full text

Abstract:

The literature reveals that the non-conservative deflection of an elastic cantilever beam caused by applying follower tip loading was investigated and solved by various numerical methods like: Runge Kutta, iterative shooting, finite element, finite difference, direct iterative and non-iterative numerical methods. This is due to the fact that the Euler–Bernoulli nonlinear differential equation governing the problem contains the “slope at the free end”, this slope however needs special numerical treatment. On the other hand, some of these methods fail to find numerical solutions for extremely large loading conditions. Hence, this paper is aimed to obtain a closed-form solution for solving the large deflection of a cantilever beam opposed to a concentrated point follower load at its free end. This closed-form solution when compared with other conventional numerical approaches is characterized by simplicity, stability and straightforwardness in getting the beam deflection and slopes even for extremely large loading conditions. The closed-form solution is obtained by applying complex analysis along with elliptic-integral approach. Very good results were obtained when the elastica of the beam compared with that of various numerical methods which are used in analyzing similar problem.

APA, Harvard, Vancouver, ISO, and other styles

Journal articles on the topic 'Cantilever loading'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles