Large deflection nonlinear mechanics of curved cantilevers under contact point loading

2021 ◽  
pp. 1-35
Author(s):  
Geoffrey Garcia ◽  
Kody Wakumoto ◽  
Joseph Brown
Keyword(s):  
Large Deflection ◽  
Contact Point ◽  
Asymptotic Relation ◽  
Linear Functions ◽  
Contact Loading ◽  
Linear Portion ◽  
Physical Testing ◽  
Rapid Calculation ◽  
Bending Behavior ◽  
Good Agreement

Abstract Presented here is a comprehensive model for hook bending behavior under contact loading conditions, motivated by the relevance of this problem to reusable hook attachment systems in nature and engineering. In this work, a large deflection model that can describe the bending of hooks, taken as precurved cantilevers with uniform initial curvature, was derived and compared with physical testing. Physical testing was performed with stainless-steel and aluminum hooks shaped as semicircular arcs. The force versus displacement behavior exhibited a linear portion for small displacements but at large displacements there was an asymptotic relation where the force approached some limit and remained flat as further displacement occurred. Comparison with testing showed that the model developed in this paper gave good agreement with the physical testing. Surprisingly, in dimensionless form, all parameters to define the hook transform to approximately linear functions of displacement. Using these linear relations, several equations are presented that rapid calculation of the dimensional force versus displacement for a hook.

Bending Behavior of Simply-Supported Sandwich Beams Subjected to Large Deflection

2018 ◽  
Vol 777 ◽  
pp. 569-574
Author(s):  
Zhong You Xie
Keyword(s):  
Energy Absorption ◽  
Large Deflection ◽  
Absorption Efficiency ◽  
Sandwich Beams ◽  
Element Simulation ◽  
Energy Absorption Efficiency ◽  
Load Carrying ◽  
Absorption Performance ◽  
Bending Behavior ◽  
The Moment

Due to thin skins and soft core, it is apt to local indentation inducing the concurrence of geometrical and material nonlinearity in sandwich structures. In the paper, finite element simulation is used to investigate the bending behavior of lightweight sandwich beams under large deflection. A modified formulation for the moment at mid-span section of sandwich beams under large deflection is presented, and energy absorption performance is assessed based on energy absorption efficiency. In addition, it is found that no local indentation arises initially, while later that increases gradually with loading displacement increasing. The height of the mid-span section as well as load-carrying capacity decreases significantly with local indentation depth increasing.

LOAD-CARRYING CAPACITIES FOR CIRCULAR METAL FOAM CORE SANDWICH PANELS AT LARGE DEFLECTION

2008 ◽  
Vol 22 (31n32) ◽  
pp. 6218-6223 ◽  
Author(s):  
W. HOU ◽  
Z. WANG ◽  
L. ZHAO ◽  
G. LU ◽  
D. SHU
Keyword(s):  
Finite Element ◽  
Velocity Field ◽  
Large Deflection ◽  
Metal Foam ◽  
Yield Criterion ◽  
Metallic Foam ◽  
Foam Core ◽  
Element Simulation ◽  
Load Carrying ◽  
Good Agreement

This paper is concerned with the load-carrying capacities of a circular sandwich panel with metallic foam core subjected to quasi-static pressure loading. The analysis is performed with a newly developed yield criterion for the sandwich cross section. The large deflection response is estimated by assuming a velocity field, which is defined based on the initial velocity field and the boundary condition. A finite element simulation has been performed to validate the analytical solution for the simply supported cases. Good agreement is found between the theoretical and finite element predictions for the load-deflection response.

Predicting the Large Deflection Path of End-Loaded Tapered Cantilever Beams

2000 ◽  
Author(s):  
Matthew B. Parkinson ◽  
Gregory M. Roach ◽  
Larry L. Howell
Keyword(s):  
Mathematical Model ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Euler Equation ◽  
Large Deflection ◽  
Nonlinear Finite Element ◽  
Cantilever Beams ◽  
Element Analysis ◽  
Moments Of Inertia ◽  
Physical Testing

Abstract A simple (quadratic) mathematical model for predicting the deflection path of both non-tapered and continuously tapered cantilever beams loaded with a vertical end force is presented. It is based on the proposition that the path is a function of the ratio of the endpoints’ moments of inertia. The model is valid for both small and large (the tip makes a 70 degree angle with the horizontal) deflections. This was verified through physical testing, comparison to solution of the Bernoulli-Euler equation, and results obtained through nonlinear finite element analysis. Predicted endpoint deflections were found to be accurate within 1.8% of the actual deflection path for moment of inertia ratios varying from 1:1 to 1000:1.

Application of large-deflection theory to normally loaded rectangular plates with clamped edges

1970 ◽  
Vol 5 (2) ◽  
pp. 140-144 ◽  
Author(s):  
A Scholes
Keyword(s):  
Large Deflection ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Non Linear ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Clamped Edges ◽  
Clamped Edge ◽  
Good Agreement

A previous paper (1)∗described an analysis for plates that made use of non-linear large-deflection theory. The results of the analysis were compared with measurements of deflections and stresses in simply supported rectangular plates. In this paper the analysis has been used to calculate the stresses and deflections for clamped-edge plates and these have been compared with measurements made on plates of various aspect ratios. Good agreement has been obtained for the maximum values of these stresses and deflections. These maximum values have been plotted in such a form as to be easily usable by the designer of pressure-loaded clamped-edge rectangular plates.

Large deflection of elastoplastic, non-linear strain-hardening cantilevers

2001 ◽  
Vol 216 (4) ◽  
pp. 433-446 ◽  
Author(s):  
X Huang ◽  
B Wang ◽  
G Lu ◽  
T X Yu
Keyword(s):  
Strain Hardening ◽  
Large Deflection ◽  
Rectangular Cross Section ◽  
Bending Moment ◽  
Linear Strain ◽  
Non Linear ◽  
Theoretical Predictions ◽  
Strain Relationship ◽  
Inclined Angle ◽  
Good Agreement

This paper concerns the large deflection of elastoplastic, non-linear strain-hardening cantilevers of rectangular cross-section, for which the stress-strain relationship after yielding is described by σ= K1εq. Both the bending moment and axial force are included in the yielding criterion, and the corresponding strain increments obey the associated normality rule. Comparisons between the experimental data and the theoretical predictions are made for mild steel cantilevers subjected to a tip force with an inclined angle ϕ = 67.5,90 and 157° respectively. Reasonable agreement is obtained. The theoretical analysis has described the large deflection behaviour of the cantilever and is in good agreement with tests.

scholarly journals 109Ag Nuclear Magnetic Resonance Studies of Organic and Inorganic Silver Complexes

1976 ◽  
Vol 31 (12) ◽  
pp. 1532-1538 ◽  
Author(s):  
K. Jucker ◽  
W. Sahm ◽  
A. Schwenk
Keyword(s):  
Aqueous Solutions ◽  
Chemical Exchange ◽  
Chemical Shifts ◽  
Linear Functions ◽  
Silver Salts ◽  
Two Samples ◽  
Chemical Shift Data ◽  
Limits Of Error ◽  
Ethyl Amine ◽  
Good Agreement

AbstractThe NMR lines of 109Ag have been investigated in solutions of several silver salts in acetonitrile, propionitrile, pyridine, and ethylenediamine, and also in aqueous solutions of Na2S2O3 and ethyl-amine. In these solvents the Ag+ -ions form one or several complexes. In any case a single NMR line was to be detected, i. e. a rapid chemical exchange between different complexes in a sample may be assumed. The concentration dependence of the chemical shifts was determined with high accuracy for these solutions. From these results the chemical shift data of some defined complexes were derived. The chemical shifts of mixtures of AgCl and AgBr and also of AgCl and Agl dissolved in 70% aqueous solution of ethylamine are linear functions of the anions mole fraction. In two samples of AgNO3 dissolved in organic solvents, the ratio υ(109Ag)/υ(107Ag) = 1.149 640 (1) was measured in good agreement with the value from silver salts in aqueous solutions; i. e. no primary isotopic effect was to be detected within these limits of error (0.9 ppm).

scholarly journals LARGE DEFLECTION OF CANTILEVER FUNCTIONALLY GRADED SANDWICH BEAM UNDER END FORCES BASED ON A TOTAL LAGRANGE FORMULATION

2020 ◽  
Vol 57 (6A) ◽  
pp. 32
Author(s):  
Hoai Bui Thi Thu
Keyword(s):  
Large Deflection ◽  
Control Method ◽  
Sandwich Beam ◽  
Point Load ◽  
Functionally Graded ◽  
Linear Functions ◽  
Element Formulation ◽  
Material Inhomogeneity ◽  
Lagrange Formulation ◽  
Layer Thickness Ratio

A two-node beam element for large deflection analysis of cantilever functionally graded sandwich (FGSW) beams subjected to end forces is formulated in the context of total Lagrange formulation. The beams consist of three layers, a homogeneous core and two functionally graded layers with material properties varying in the thickness direction by a power gradation law. Linear functions are adopted to interpolate the displacement field and reduced integral technique is applied to evaluate the element formulation. Newton-Raphson based iterative algorithm is employed in combination with arc-length control method to compute equilibrium paths of the beams. Numerical investigations are given for the beam under a transverse point load and a moment to show the accuracy of the element and to illustrate the effects of material inhomogeneity and the layer thickness ratio on the large deflection behavior of the FGSW beams.

Stress and Buckling of Internally Pressurized, Elastic-Plastic Torispherical Vessel Heads—Comparisons of Test and Theory

1977 ◽  
Vol 99 (1) ◽  
pp. 39-53 ◽  
Author(s):  
D. Bushnell ◽  
G. D. Galletly
Keyword(s):  
Mild Steel ◽  
Large Deflection ◽  
Plastic Material ◽  
Material Behavior ◽  
Nonlinear Material ◽  
Test Results ◽  
Elastic Plastic ◽  
State Of Stress ◽  
Elastic Plastic Material ◽  
Good Agreement

Several aluminum and mild steel torispherical heads were tested by Galletly and by Kirk and Gill and subsequently analyzed by Bushnell with use of the BOSOR5 computer program. The thinnest specimens buckled at pressures for which part of the toroidal knuckle was stressed well beyond the yield point. The analysis includes large deflection effects, nonlinear material behavior, and meridional variation of the thickness. The calculated strains in the thicker specimens agree reasonably well with the test results, but the calculated prebuckling strains in the thinnest specimens are generally greater than the values measured in the torodial knuckle after the onset of plastic flow. Reasonably good agreement between test and theory is obtained for the buckling pressures of aluminum specimens, but the calculated buckling pressures for mild steel specimens are much lower than the observed values, a discrepancy that is attributed to circumferentially varying thickness and possible inability of the analytical model of the elastic-plastic material to predict accurately the state of stress in the toroidal knuckle where loading is nonproportional once yielding has occurred.

Contact of an Inflated Toroidal Membrane with a Flat Surface as an Approach to the Tire Deflection Problem

1975 ◽  
Vol 3 (1) ◽  
pp. 43-61 ◽  
Author(s):  
J. DeEskinazi ◽  
W. Soedel ◽  
T. Y. Yang
Keyword(s):  
Finite Element ◽  
Stress Analysis ◽  
Nonlinear Effect ◽  
Reasonable Agreement ◽  
Large Deflection ◽  
Flat Surface ◽  
Nonlinear Load ◽  
Deflection Analysis ◽  
Finite Element Procedure ◽  
Good Agreement

Abstract A finite element procedure has been developed for the displacement and stress analysis of a homogeneous and isotropic inner tube mounted on a rim and in contact with a flat surface. The geometric nonlinear effect is accounted for by including the quadratic terms in the strain-displacement equations. The nonlinear load-displacement path is predicted by a linear incremental procedure. The procedure is first demonstrated by a large deflection analysis of a strip of a tire (a cable). The results are in good agreement with a known alternative solution. A homogeneous and isotropic inner tube is then pressurized and the displacements and stresses are found. The displacements are also found experimentally. Both results are in good agreement. Finally, the inner tube is mounted on a rim and pressed against a rigid flat surface. The resulting displacements and footprints are also measured experimentally. The computer results are shown to be in reasonable agreement with the experiment.

Analysis of Bending Behavior of Native Auricular and Costal Cartilage and Tissue Engineered Constructs

2001 ◽  
Author(s):  
Rani Roy ◽  
Sean S. Kohles ◽  
Victor Zaporojan ◽  
Lawrence Bonassar
Keyword(s):  
Articular Cartilage ◽  
Elastic Moduli ◽  
Large Deflection ◽  
Soft Tissues ◽  
Costal Cartilage ◽  
Deformation Mode ◽  
Auricular Cartilage ◽  
Mechanical Environment ◽  
Three Point Bending ◽  
Bending Behavior

Abstract The current literature presents many techniques for analysis of the mechanical properties of articular cartilage [1]. By comparison few techniques are available for analysis of auricular cartilage which experiences a different mechanical environment than articular cartilage. Specifically, large deflection bending is a deformation mode that is most relevant to auricular cartilage, but has not been studied thoroughly in soft tissues. The goals of this study were to: 1) apply an elasticity model to three point bending data from normal and engineered auricular and costal cartilage; and 2) use this model to determine the tensile elastic moduli.

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