Modeling Bicortical Screws Under a Cantilever Bending Load

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Thomas P. James ◽  
Brendan A. Andrade
Keyword(s):  
Cortical Bone ◽  
Elastic Foundation ◽  
Analytical Model ◽  
Bending Moment ◽  
Predictive Ability ◽  
Analytical Models ◽  
Synthetic Bone Substitute ◽  
Bending Load ◽  
Foundation Model ◽  
Cantilever Bending

Cyclic loading of surgical plating constructs can precipitate bone screw failure. As the frictional contact between the plate and the bone is lost, cantilever bending loads are transferred from the plate to the head of the screw, which over time causes fatigue fracture from cyclic bending. In this research, analytical models using beam mechanics theory were developed to describe the elastic deflection of a bicortical screw under a statically applied load. Four analytical models were developed to simulate the various restraint conditions applicable to bicortical support of the screw. In three of the models, the cortical bone near the tip of the screw was simulated by classical beam constraints (1) simply supported, (2) cantilever, and (3) split distributed load. In the final analytical model, the cortices were treated as an elastic foundation, whereby the response of the constraint was proportional to screw deflection. To test the predictive ability of the new analytical models, 3.5 mm cortical bone screws were tested in a synthetic bone substitute. A novel instrument was developed to measure the bending deflection of screws under radial loads (225 N, 445 N, and 670 N) applied by a surrogate surgical plate at the head of the screw. Of the four cases considered, the analytical model utilizing an elastic foundation most accurately predicted deflection at the screw head, with an average difference of 19% between the measured and predicted results. Determination of the bending moments from the elastic foundation model revealed that a maximum moment of 2.3 N m occurred near the middle of the cortical wall closest to the plate. The location of the maximum bending moment along the screw axis was consistent with the fracture location commonly observed in clinical practice.

Technique for the Measurement of Surgical Screw Deflection

2011 ◽  
Author(s):  
Brendan A. Andrade ◽  
Anil Saigal ◽  
Thomas P. James
Keyword(s):  
Analytical Model ◽  
Bone Substitute ◽  
Bending Moment ◽  
Predictive Ability ◽  
Screw Head ◽  
Mechanics Model ◽  
Synthetic Bone Substitute ◽  
Cortical Screw ◽  
Cyclical Loading ◽  
Bending Loads

Cyclical loading of surgical plating constructs can lead to screw failure through bending loads. In this research, an analytical beam mechanics model was developed to describe the elastic deflection of a cortical screw under a statically applied load. To test the predictive ability of the analytical model, a synthetic bone substitute was used for experiments. The bone substitute was a composite sandwich, consisting of two 6 mm cortical walls separated by a cancellous region. A novel instrument was developed to measure the bending deflection of screws under a radial load applied by a surgical plate at the screw head. A dial indicator and dowel pin arrangement was utilized to measure screw deflection at the screw head and along the length of the screw in order to determine a deflection curve for the screw axis. The analytical model accurately predicted deflection of the screw head at the location of the applied force, but overestimated deflection of the screw body in the cancellous region of the composite bone. Analytical predictions of location of the maximum bending moment matched the location of observed screw fracture in a clinical setting.

Analytical and Numerical Prediction of Springback of SS/Al-Alloy Cladded Sheet in V-Bending

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Pankaj Kumar Sharma ◽  
Vijay Gautam ◽  
Atul Kumar Agrawal
Keyword(s):  
Analytical Model ◽  
Outer Layer ◽  
Numerical Models ◽  
Yield Criterion ◽  
Bending Moment ◽  
Analytical Models ◽  
Bend Angle ◽  
Radius Of Curvature ◽  
Al Alloy ◽  
First Case

Abstract The present work deals with the development of an analytical model incorporating the effects of anisotropy and strain hardening to predict the springback in V-bending of two-ply sheet metal using a punch profile radius of 15 mm and included a bend angle of 90 deg. In the analytical model, the total bending moment is determined from resulting bending stresses for two different layers arranged in parallel planes one above the other and a new radius of curvature after springback is determined by applying a negative bending moment. The two-ply sheet composed of layers of AA1050 and SS430 is characterized for its tensile properties to be used in analytical and numerical models for prediction of springback. To study the effect of each layer during bending operation, two possible cases of sheet placements during bending and springback are studied; i.e., in the first case, the inner layer is of AA1050 while the SS430 layer is the outer layer whereas in the second case it is opposite. In all the cases of springback experiments when the outer layer is of SS430, the springback values are higher than the values obtained with the specimens when the inner layer is of SS430. This could be attributed to the higher tensile strength of the stainless steel layer and the higher bending radius experienced by it. The springback behaviors are also analyzed by simulations using Hill's anisotropic yield criterion in abaqus software. The springback results obtained by simulations and analytical models are in good agreement in general; however, in some cases, discrepancy of more than 15% is observed in the analytical results when compared with the experimental results.

Combined Loading Tests of Large Diameter Corroded Pipelines

2000 ◽  
Author(s):  
Marina Q. Smith ◽  
Christopher J. Waldhart
Keyword(s):  
Internal Pressure ◽  
Thermal Stresses ◽  
Failure Modes ◽  
Prediction Models ◽  
Large Diameter ◽  
Bending Moment ◽  
Combined Loading ◽  
Analytical Models ◽  
Bending Load ◽  
Full Scale Tests

Current methods for estimating the remaining strength of aging, corroded pipelines have been restricted to the capabilities of pressure based engineering models that rely on the definition of hoop stress in the pipe wall. Because in practice, pipelines are subjected to a variety of loading conditions (e.g.; axial bending from settlement and thermal stresses) that act in concert with those derived by internal pressure, a multi-year combined testing and analysis program was initiated by the Alyeska Pipeline Service Company aimed at developing computer tools for the prediction of rupture and wrinkling in corroded pipes. During the program, seventeen full-scale tests of mechanically corroded 48-inch diameter (1219-mm), X65 pipes subjected to internal pressure, axial bending, and axial compression were performed to provide data necessary for the verification of analytical models and failure prediction models. While all of the tests were designed to produce rupture, wrinkling, as defined by the occurrence of a limit moment during the application of bending loads, was produced in eleven of the tests either prior to or instead of rupture. Loading of the pipe was intended to simulate that which would be observed by a pipe in-service and included both load control and displacement control of the applied bending load, and in some tests, intended to define the amount of additional pressure required to cause burst after wrinkling was produced. Results of the tests showed that two different failure modes are produced depending on whether the bending moment is transmitted to the pipe as a fixed load or a fixed displacement, and consequently, the burst capacity of the corroded pipe may not be compromised by the presence of axial loads. This paper discusses the tests performed, including a description of the load schedule and corrosion geometries, and key results of the tests that were used in the development of a new strain-based burst prediction procedure for corroded pipes subjected to combined loads.

Buckling Behavior of Tire Breaker Structure

1983 ◽  
Vol 11 (1) ◽  
pp. 3-19
Author(s):  
T. Akasaka ◽  
S. Yamazaki ◽  
K. Asano
Keyword(s):  
Elastic Foundation ◽  
Elastic Moduli ◽  
Wave Length ◽  
Bending Moment ◽  
Experimental Results ◽  
Automobile Tire ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Steel Cord ◽  
Interlaminar Shear

Abstract The buckled wave length and the critical in-plane bending moment of laminated long composite strips of cord-reinforced rubber sheets on an elastic foundation is analyzed by Galerkin's method, with consideration of interlaminar shear deformation. An approximate formula for the wave length is given in terms of cord angle, elastic moduli of the constituent rubber and steel cord, and several structural dimensions. The calculated wave length for a 165SR13 automobile tire with steel breakers (belts) was very close to experimental results. An additional study was then conducted on the post-buckling behavior of a laminated biased composite beam on an elastic foundation. This beam is subjected to axial compression. The calculated relationship between the buckled wave rise and the compressive membrane force also agreed well with experimental results.

scholarly journals Novel Structure and Thermal Design and Analysis for CubeSats in Formation Flying

Aerospace ◽  
2021 ◽  
Vol 8 (6) ◽  
pp. 150
Author(s):  
Yeon-Kyu Park ◽  
Geuk-Nam Kim ◽  
Sang-Young Park
Keyword(s):  
Analytical Model ◽  
Formation Flying ◽  
Thermal Environment ◽  
Thermal Analyses ◽  
Thermal Design ◽  
Analytical Models ◽  
Test Results ◽  
Solar Panels ◽  
Novel Structure ◽  
Micro Propulsion

The CANYVAL-C (CubeSat Astronomy by NASA and Yonsei using a virtual telescope alignment for coronagraph) is a space science demonstration mission that involves taking several images of the solar corona with two CubeSats—1U CubeSat (Timon) and 2U CubeSat (Pumbaa)—in formation flying. In this study, we developed and evaluated structural and thermal designs of the CubeSats Timon and Pumbaa through finite element analyses, considering the nonlinearity effects of the nylon wire of the deployable solar panels installed in Pumbaa. On-orbit thermal analyses were performed with an accurate analytical model for a visible camera on Timon and a micro propulsion system on Pumbaa, which has a narrow operating temperature range. Finally, the analytical models were correlated for enhancing the reliability of the numerical analysis. The test results indicated that the CubeSats are structurally safe with respect to the launch environment and can activate each component under the space thermal environment. The natural frequency of the nylon wire for the deployable solar panels was found to increase significantly as the wire was tightened strongly. The conditions of the thermal vacuum and cycling testing were implemented in the thermal analytical model, which reduced the differences between the analysis and testing.

The effects of geometric offsets on the dynamic responses of a Scott—Russell amplifying mechanism with flexible hinges

2009 ◽  
Vol 223 (10) ◽  
pp. 2413-2423 ◽  
Author(s):  
C-M Chen ◽  
R-F Fung
Keyword(s):  
Numerical Simulations ◽  
Analytical Model ◽  
Dynamic Responses ◽  
Analytical Models ◽  
Dynamic Equations ◽  
Magnification Factor ◽  
Flexure Hinges ◽  
Magnification Factors ◽  
Straight Line ◽  
Deviation Factor

The dynamic equations of a micro-positioning Scott—Russell (SR) mechanism associated with two flexible hinges and an offset are developed to calculate output responses. Both rigid and flexible hinges are considered to explore the results. The main features in the kinematics of the SR mechanism are its displacement amplification and straight-line motion, which are widely needed in practical industries. The manufacturing inaccuracy of the SR mechanism definitely causes geometric offsets of flexure hinges, and affects displacement amplification and straight-line output motion. Analytical models based on kinematics and Hamilton's principle are derived to explore the variation of linearity ratio, magnification factor, and deviation factor due to various offsets and link lengths. From numerical simulations for the SR mechanism with various offsets of flexible hinges in the conditions of different link lengths, it is found that offsets of flexure hinges obviously affect the amplifying factor and linearity ratio, and appear to dominate the changes of magnification factors. Moreover, an analytical model is also used to predict magnification factors due to various offsets. Finally, some conclusions concerning the effects of offset on the performance of the SR mechanism are drawn.

Bending of an Infinite Beam on an Elastic Foundation

1937 ◽  
Vol 4 (1) ◽  
pp. A1-A7 ◽  
Author(s):  
M. A. Biot
Keyword(s):  
Elastic Foundation ◽  
Poisson Ratio ◽  
Elementary Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Two Dimensional ◽  
Concentrated Load ◽  
Elastic Continuum ◽  
Infinite Beam ◽  
A Value

Abstract The elementary theory of the bending of a beam on an elastic foundation is based on the assumption that the beam is resting on a continuously distributed set of springs the stiffness of which is defined by a “modulus of the foundation” k. Very seldom, however, does it happen that the foundation is actually constituted this way. Generally, the foundation is an elastic continuum characterized by two elastic constants, a modulus of elasticity E, and a Poisson ratio ν. The problem of the bending of a beam resting on such a foundation has been approached already by various authors. The author attempts to give in this paper a more exact solution of one aspect of this problem, i.e., the case of an infinite beam under a concentrated load. A notable difference exists between the results obtained from the assumptions of a two-dimensional foundation and of a three-dimensional foundation. Bending-moment and deflection curves for the two-dimensional case are shown in Figs. 4 and 5. A value of the modulus k is given for both cases by which the elementary theory can be used and leads to results which are fairly acceptable. These values depend on the stiffness of the beam and on the elasticity of the foundation.

Modeling of residual stresses by correlating surface topography in machining of AISI 52100 steel

2021 ◽  
pp. 1-26
Author(s):  
Chao Liu ◽  
Yan He ◽  
Yufeng Li ◽  
Yulin Wang ◽  
Shilong Wang ◽  
...  
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Cutting Force ◽  
Surface Topography ◽  
Analytical Model ◽  
Analytical Models ◽  
Workpiece Surface ◽  
Dynamic Cutting Force ◽  
Intermittent Cutting ◽  
Effect Of Surface

Abstract The residual stresses could affect the ability of components to bear loading conditions and also the performance. The researchers considered workpiece surface as a plane and ignored the effect of surface topography induced by the intermittent cutting process when modeling residual stresses. The aim of this research develops an analytical model to predict workpiece residual stresses during intermittent machining by correlating the effect of surface topography. The relative motions of tool and workpiece are analyzed for modeling thermal-mechanical and surface topography. The influence of dynamic cutting force and thermal on different positions of surface topography is also considered in analytical model. Then the residual stresses model with the surface topography effect can be developed in intermittent cutting. The analytical models of dynamic cutting force, surface topography and residual stresses are verified by the experiments. The variation trend of evaluated values of the residual stress of workpiece is basically consistent with that of measured values. The compressive residual stress of workpiece surface in highest point of the surface topography are higher than that in the lowest point.

scholarly journals Approximate Analytical Models of Shock-Wave Structure at Steady Mach Reflection

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 305
Author(s):  
Mikhail V. Chernyshov ◽  
Karina E. Savelova ◽  
Anna S. Kapralova
Keyword(s):  
Experimental Data ◽  
Shock Wave ◽  
Comparative Analysis ◽  
Analytical Model ◽  
Mach Reflection ◽  
Supersonic Jet ◽  
Wave Structure ◽  
Analytical Models ◽  
Analytical Prediction ◽  
Shock Wave Structure

In this study, we obtain the comparative analysis of methods of quick approximate analytical prediction of Mach shock height in planar steady supersonic flows (for example, in supersonic jet flow and in narrowing channel between two wedges), that are developed since the 1980s and being actively modernized now. A new analytical model based on flow averaging downstream curved Mach shock is proposed, which seems more accurate than preceding models, comparing with numerical and experimental data.

scholarly journals Experimental and Simulation Investigation of Bending Moment Effect on Hollow Columns of Multi-layers of Hybrid Materials

2019 ◽  
Vol 12 (1) ◽  
pp. 44-55
Author(s):  
Ayad A. Ramadhan
Keyword(s):  
Hybrid Materials ◽  
Volume Fraction ◽  
Load Capacity ◽  
Testing Machine ◽  
Bending Moment ◽  
Maximum Load ◽  
Experimental Procedure ◽  
Bending Load ◽  
Alumina Composite ◽  
Moment Effect

This paper presented the effect of bending on multi-layer of hollow columns of Hybrid materials (Carbon-Glass /epoxy-Alumina) composite this effect occurred and volume fraction of fibers. An experimental procedure was developed to study the performance of these effects under bending load using a hydraulic bending device type (MATEST. SRL) testing machine. This study has three forms through the selection of columns hollows width to thickness (a/b) (0.5, 1 and 2) with three types of layers of samples (2,4 and8) layers. The ultimate load of failure for each Hybrid/epoxy-Al2O3 had been determined and specified the optimum volume fraction (Vf) due to the effect of mixing 50% and 60% were low in the case for compared 55% volume fraction. To simulate this problem the researcher used Explicit Mesh for AUTODYN under ANSYS-15 software, it was found that maximum bending load for Hybrid/ Epoxy-Al2O3 Specimens, the maximum load of specimens increased with increasing number of layers from 2L to 8L. The results also identified that the maximum load capacity by 55% volume fraction and a/b=0.5 of all composite specimens was highest from the others types of (50% and 60%) volume fractions and (a/b=1 and a/b=2) .Also, the Increasing ratio of stress capacity for specimens have 4 to 2 layers (4/2)  and 8 to 4  (8/4) for experimental results have maximum value with increasing by 48.19%  and 46.84% at (Sp.4#8/Sp.2#4) and (Sp.8#6/Sp.4#6) respectively.

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