Deflection Of Cantilever Beam Research Articles

An Elliptic Integral Solution to the Multiple Inflections Large Deflection Beams in Compliant Mechanisms

In this paper, a solution based on the elliptic integrals is proposed for solving multiples inflection points large deflection. Application of the Bernoulli Euler equations of compliant mechanisms with large deflection equation of beam is obtained ,there is no inflection point and inflection points in two cases respectively. The elliptic integral solution which is the most accurate method at present for analyzing large deflections of cantilever beams in compliant mechanisms.

Prediction on Deflection of Box-Core Sandwich Panels in Weak Direction

In a C-core sandwich panel, the shear stiffness of the sandwich panel in the weak direction is much smaller. The deflection of a C-core sandwich beam consists of two parts: flexural deformation and shear deformation. The flexural deformation of a C-core sandwich beam can be calculated simply from beam theory while the shear deformation is rela- tively difficult to calculate due to the mutual action between the facing plates and the C-core stiffener. Considering the contact between the flanges of the C-core and the facing plates, the shear deformation of a typical segment in a C-core sandwich panel is analyzed based on compatibility conditions. By using Castigliano's second theorem, the equation for calculating the deflection caused by shear action of a C-core sandwich panel under bending is obtained. The accuracy of the presented equations for calculating the deflection of a C-core sandwich cantilever beam and a C-core sandwich panel under three-point bending is then verified by comparing with finite element and experimental results reported in the corre- sponding reference. It is found that the predicted results from the presented equation agree quite well with finite element and experimental results, which shows the reliability and accuracy of the proposed equation.

Damage Assessment in a Cracked Fiber-Reinforced Cantilever Beam Using Wavelet-Kurtosis Techniques

In the last decades the use of composite materials has increased especially in light-weight structural applications, such as wind turbine blades. These structural components require reliable methods for damage assessment to avoid progressive or sudden and catastrophic failures. In this paper, a model of a fiber-reinforced composite cantilever beam with a bridged edge crack, representing an existing damage state, is considered. The composite matrix of the beam exhibits a linear-elastic behavior, whereas a fracture mechanics-based theoretical model incorporating the crack bridging forces in the fiber-reinforcement is used to describe the elastic-plastic response of the cracked beam section subjected to bending moment. This model is employed to simulate the nonlinear static deflection of cantilever beams with different crack locations and depths. Wavelet and kurtosis-based identification techniques are employed in the localization and calibration of this damage in presence of noise. The influence of the bridging effect of the fibers on the success of the damage assessment is discussed.

Study for the Measurement of Cantilever Beam Deflection by Using Digital Projection Speckle Correlation Method (DPSCM)

Digital Projection Speckle Correlation Method is a new technique of 3D morphology measurements based on Digital Speckle Correlation Method.In this paper,cantilever beam deflection concentrated load is measured well by DPSCM,which reflects effectiveness of the method.

Fabrication of a Wrinkled Surface on Poly(dimethylsiloxane) Using a Thermal Curing Process

We describe the fabrication of a spontaneous wrinkled surface on poly(dimethylsiloxane) (PDMS). The wrinkled surface on an elastic PDMS substrate was fabricated by thermally shrinking liquid PDMS coated on a cured PDMS layer during a simple thermal curing process. Optical and atomic force microscopy, deflections of PDMS cantilever beams on the wrinkled surface, and contact angles of water droplets on the wrinkled surface were used to quantitatively investigate the wrinkled patterns on the PDMS layer. The morphology of cells seeded on the fabricated wrinkled surface was observed.

Nonlinear Analysis of Leaf Springs of Functionally Graded Materials

Abstract The present study deals with the numerical analysis of large deflection of prismatic cantilever beams for various types of material properties with a transverse load at free end, to study the displacement response of leaf springs. Besides the free end displacement, the variation of stress, strain and the bending moment of the beam having variable material properties with the beam length are obtained by the technique of minimization of total potential energy. The mathematical formulation is based on a variational principle using Galerkin's assumed mode method. The displacement functions are approximated by linear combination of sets of orthogonal coordinate functions, developed through Gram-Schmidt scheme and substituted in the governing equilibrium equation. The final solution of the large displacement geometric nonlinear problem is obtained iteratively with the help of MATLAB computational simulation. It is observed that the free end displacements and the shortening of projected beam length are greatly affected by the variation in elasticity modulus value. The present computational method has been validated and some new results have been furnished. The influence of material gradation for various types of exponential and parabolic distribution is shown for three different types of loading.

Non-Uniform Leaf Springs with Geometric Nonlinearity

The present study deals with the analysis of large deflection of cantilever beams for various cross sections with a transverse load at free end. The aim of this analysis is to study the vertical and horizontal displacement behaviour of leaf springs which is traditionally modeled as cantilever beams of variable cross section. Besides the free end displacement, the variation of stress, strain and the bending moment of the beam are obtained by the technique of minimization of total potential energy principle. The displacement functions are approximated by linear combination of sets of orthogonal coordinate functions, developed through Gram-Schmidt scheme and substituted in the governing equilibrium equation. The final solution of the large displacement geometric nonlinear problem is obtained iteratively with the help of matlab computaional simulation. It is observed that the free end displacements and the maximum stress at fixed end are greatly affected by the geometry of the beam cross section. The present computational method has been validated and some new results have been furnished.

The influence of stiffness of implant-abutment connection on load-deflection ratios of a screw-retained stiff cantilever beam. 3-D measurements in vitro

The purpose of this in vitro study was to investigate the influence of degree of stiffness of implant-abutment connection of a Brånemark implant system on load- deflection ratios in three dimensions of the beam-end of a screw-retained stiff cantilever beam when subjected to vertically directed loads. Two different implant-abutment connections were tested; welded and screw-retained. One of the abutments (EsthetiCone 2.0; Nobel Biocare AB) was screwed with a torque force of 20 N cm and then laser welded around its entire periphery to one of two Brånemark implants (welded unit). This unit and the other implant were tightly screwed into each of two pre-threaded holes in a steel plate so that the implants became submerged in the plate. The remaining abutment was thereafter screwed to its implant with a torque force of 20 N cm (screw-retained unit). A cantilevered gold beam of 6 mm height and width comprising a gold cylinder (Nobel Biocare AB) was attached to each abutment with a slotted, flat headed, prosthetic gold screw (torque force 10 N cm). A force transducer, synchronized with a 3-D motion analysis system, was glued on the upper surface of each beam-end 19.4 mm from the implant, to register the loads transferred from a specially built loading device. The beam-ends were stepwise subjected to vertically directed loads from 14.9 to 40.3 N and the vertical and horizontal deflections of the beam-ends were registered with the 3-D motion analysis system. For load 14.9-40.3 N the vertical (z-axis) deflections of the beam-end were for the welded implant-abutment connection reduced with 18-46% compared with the screw-retained unit. After maximal loading (40.3 N) the horizontal counter-clockwise rotation of the beam around the screw joints (y-axis rotations) was reduced with 61% for the welded connection. The horizontal movements of the beam-end along the x-axis (x-axis deflections) were reduced with 49% at maximal loading. It was concluded that increased implant-abutment stiffness will substantially reduce both vertical and horizontal deflections of a screw-retained stiff cantilever beam subjected to vertically directed loads.

Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

This work studies large deflections of slen- der, non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed con- tinuous load and a concentrated load at the free end of the beam. The material of the cantilever is assumed to be non- linearly elastic. Different nonlinear relations between stress and strain in tensile and compressive domain are considered. The accuracy of numerical solutions is evaluated by com- paring them with results from previous studies and with a laboratory experiment.

Preliminary Investigation on Young's Modulus Measurement of Cantilever Beam by Integrating Nanoindenter with Optical System

Nanoindenter has been used to directly indent on the cantilever beam to measure Young’s modulus such that the substrate effects can be avoided. However, the deflections of cantilever beam are indirectly extracted from the displacement of nanoindenter and therefore their measurement results are easily influenced by local behaviors around the indentation. In this paper, to the authors’ best knowledge, this is the first time that the nanoindenter is integrated with an optical system to measure Young’s modulus of cantilever beam. The deflection of cantilever beam is directly measured from a specially designed optical system. The influences of substrate effects and local behaviors around indentation are simultaneously avoided from the proposed methodology.

Investigation of Tool Deflection of Solid Carbide End Mill in Cutting Process

Tool deflection is one of the important influencing factors for surface roughness and surface integrity of work piece in cutting process. The excessive deflection even causes seriously defects of work piece or failures of tool. This paper gives theory analysis and mathematic method to predict the tool deflection by means of the cantilever beam deflection theory. Based on modeling of 3-dimmsion milling force model, the finite element analysis has been performed for calculation of tool deflection. The experiment of tool deflection of solid end mill is performed to compare simulation and theory. Results show the correction and reliability of research method. It lays a foundation for fast calculation of tool deflection and optimization of milling parameters.

Bending Deformation Measurement of Bone Cantilever Using Image Correlation

Bone is an anisotropic inhomogeneous material, and its piezoelectric behavior is more complex than mineral piezoelectric materials such as quartz crystal or ceramics. This article aimed to understand the piezoelectric properties of bone by investigating its converse piezoelectric effect. Bending deformation of bone specimens subjected to an external electric field was observed. Displacements or deflections of bone cantilever beams were measured by a high resolution digital microscope combined with digital image correlation technique. In order to demonstrate the validity of the experiment, specimens made of non piezoelectric materials were also tested in the same experimental condition as bone. The results indicate that the bending deformation of the bone cantilever may come from the non uniform piezoelectric properties of bone, compared to an analytical solution.

Large Deflection of Cantilever Beam with Uniformly Distributed Load Using Homotopy Analysis Method

The large deflection behavior of prismatic cantilever beams subjected to uniformly distributed load is investigated. An approximate analytical solution is obtained using the homotopy analysis method (HAM). The solution is validated by the nonlinear shooting method. This reveals that the solution is accurate, efficient and convenient for cantilever beams with uniformly distributed loads.

Size effect in micro-scale cantilever beam bending

When the thickness of metallic cantilever beams reduces to the order of micron, a strong size effect of mechanical behavior has been found. In order to explain the size effect in a micro-cantilever beam, the couple-stress theory (Fleck and Hutchinson, J Mech Phys Solids 41:1825–1857, 1993) and the C-W strain gradient theory (Chen and Wang, Acta Mater 48:3997–4005, 2000) are used with the help of the Bernoulli–Euler beam model. The cantilever beam is considered as the linear elastic and rigid-plastic one, respectively. Analytical results of the cantilever beam deflection under strain gradient effects by applying these two kinds of theories are obtained, from which we find an explicit relationship between the intrinsic lengths introduced in the two kinds of theories. The theoretical results are further used to analyze the experimental observations, and predictions by both theories are further compared. The results in the present paper should be useful for the design of micro-cantilever beams in MEMS and NEMS.

Finding the optimal characteristic parameters for 3R pseudo-rigid-body model using an improved particle swarm optimizer

Compliant mechanisms have been used in many engineering areas where high precision and sensitivity are required. One of the major challenges of designing compliant mechanisms lies in understanding and analyzing the nonlinear deflections of flexible members. The pseudo-rigid-body model (PRBM) method, which simplifies the modeling of the nonlinear deflection by approximating it as motion of rigid links, has been accepted as one of the most important tools for synthesis and analysis of compliant mechanisms. In this paper, a review of various PRBMs is presented. The 3R PRBM whose characteristic parameters are independent of external loads is discussed in detail. For the purpose of finding the optimal set of the characteristic parameters for the 3R PRBM, a six-dimensional objective function is formulated by combining the approximation errors of both tip point and tip slope for the two extreme load cases, i.e., pure moment load and pure vertical force load. A particle swarm optimizer was employed to conduct a continuous search on the objective function. The resulting 3R PRBM with the optimized characteristic parameters shows better performance in predicting large deflections of cantilever beams over the original 3R PRBM.

A Deflection of Nano-Cantilevers Using Monotone Solution

In this paper, a monotone positive solution is studied for deflection of nano cantilever beams which is subject to electrostatic and intermolecular forces in a distributed model. A positive monotone solution base on Green's function in the form of a nonlinear iterative integral is introduced, to obtain a solution for deflection of nano cantilever beams. In order to determine the accuracy of presented method, the results are compared with numerical results of a boundary value method. The results show the monotone iterative solution is stable and converged to numerical results with a few iterations. The results of present work are useful to prove the stability and convergence of Green's function to deal with deflection of nano cantilever switches in future works and simplifications.

Fiber Bragg Grating Liquid Level Sensor with Double Pressure and Temperature Sensitivities

A fiber Bragg grating liquid level sensor is presented by using a transmission shaft connected to the center of corrugated diaphragm and the free end of cantilever beam. Under the action of liquid pressure, the transmission shaft transfers the bending moment of corrugated diaphragm to the deflection of cantilever beam. When two Bragg gratings are axially mounted on the top and bottom surfaces of cantilever beam, the difference of relative wavelength doubles the pressure sensitivity of single grating. Theoretical analysis is presented, and the experimental results show that the level response sensitivity of the difference of relative Bragg wavelength shifts is 3.33×10−5 m−1 at the range of 0∼3.2 m, and the repetition is 0.48%FS. Because the densities of liquid are different at various temperatures, it is important that the sum of relative wavelength doubles the temperature sensitivity of single grating. The experiments indicate that the temperature response sensitivity of the sum of relative Bragg wavelength shifts is 1.24×10−5°C−1 at the range of 20∼70°C, and the repetition is 0.84%FS.

Bending of Flexible Joint Driven by Linear Expandable Artificial Muscle

A flexible finger joint is proposed and applied in multi-joint manipulator. The plate-spring composes of a flexible skeleton. The linear expandable elastomeric bellows by air pressure is used as an artificial muscle. Bend angle of the joint is related to air pressure in the bellows. Static model of the joint bend has been created by assuming that the counteracting force from elastic elongation of the bellows is negligible. The problems of pure mechanics and the model have been studied in detail. The numerical solution based on the model is obtained for the case of the large deflection of cantilever beam synchronously acted on cantilever end by a couple in variable scalar along with forces changing in both scalar and direction.

The in situ measurement of the intrinsic stresses in nanofilms

A method for the in situ measurement of intrinsic stresses in nanofilms is described. It is based on measuring the cantilever beam deflection during the vacuum deposition of thin films. Magnetron sputter deposition is used in this work. In order to determine the cantilever beam deflection, the capacity of a capacitor composed of a stationary plate fixed on a stand and a plate fixed on the free end of the specimen was measured. A condenser was inserted into the multivibrator circuit to measure the small condenser capacity. The in situ stress measurements for nanofilms of TI and Cu sputtered on Cu substrates were performed. The stresses that occurred in the TI film were found to be tensile, but stresses that occurred in the Cu film were compressive; the stress magnitude significantly changes when letting air into the vacuum chamber. The results show the perspective usage of this method for in situ stress measuring, as well as for a study of the effects of the interaction between gas and nanostructured films.

Evaluation of bimaterial cantilever beam for heat sensing at atmospheric pressure

The bimaterial cantilever beam is an important basic structure of microelectromechanical system thermal devices. The research described in this paper is a study of the deflection of the bimaterial cantilever beam operated in the air and irradiated with a laser beam at the free end. The bimaterial cantilever beam is a composite structure formed by layers of silicon nitride and gold. The temperature variations produce the deflection of the cantilever beam end due to different values of the thermal expansion coefficients of silicon nitride and gold. The deflection was experimentally measured in vacuum and atmospheric pressure when a laser beam was irradiated at the free end. A formula for the calculation of the deflection as a function of incident power applied at the free end of the cantilever beam operated in air was also demonstrated. The predicted values of the deflection calculated using this formula and the experimental values of the deflection were compared, and the results were in good agreement. A systematic investigation of the cantilever beam deflection in vacuum and atmospheric pressure as a function of the heat applied at the free end is important for chemical and biological applications.