Three-dimensional vibration of a ring with a noncircular cross-section on an elastic foundation

2017 ◽  
Vol 232 (13) ◽  
pp. 2381-2393 ◽  
Author(s):  
Zhe Liu ◽  
Fuqiang Zhou ◽  
Christian Oertel ◽  
Yintao Wei
Keyword(s):  
Elastic Foundation ◽  
Cross Section ◽  
Three Dimensional ◽  
Theoretical Formula ◽  
Variation Principle ◽  
Displacement Fields ◽  
Element Analysis ◽  
Noncircular Cross Section ◽  
Truck Tire ◽  
Out Of Plane

The three-dimensional dynamic equations of a ring with a noncircular cross-section on an elastic foundation are obtained using the Hamilton variation principle. In contrast to the previous rings on elastic foundation model, the developed model incorporates both the in-plane and out-of-plane bend and the out-of-plane torsion in displacement fields. The errors in the derivation of the initial stress and the work of the internal pressure in previous rings on elastic foundation models have been corrected. The mode expansion was used to obtain the analytical solution of the natural frequency. The initial motivation is to develop a theoretical model for car tire dynamics. Therefore, to validate the proposed model, the in-plane and out-of-plane vibrations of a truck tire have been analyzed using the proposed method. To further verify the accuracy of the model, the results of the theoretical formula are compared with the finite element analysis and modal test, and good agreement can be found.

scholarly journals Free and Forced Vibration of Laminated and Sandwich Plates by Zig-Zag Theories Differently Accounting for Transverse Shear and Normal Deformability

Aerospace ◽  
2018 ◽  
Vol 5 (4) ◽  
pp. 108 ◽  
Author(s):  
Ugo Icardi ◽  
Andrea Urraci
Keyword(s):  
Transverse Shear ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Interfacial Stress ◽  
Sandwich Plates ◽  
Displacement Fields ◽  
Element Analysis ◽  
Out Of Plane ◽  
Elasticity Solutions ◽  
Displacement Based

A number of mixed and displacement-based zig-zag theories are derived from the zig-zag adaptive theory (ZZA). As a consequence of their different assumptions on displacement, strain, and stress fields, and layerwise functions, these theories account for the transverse shear and normal deformability in different ways, but their unknowns are independent of the number of layers. Some have features that are reminiscent of ones that have been published in the literature for the sake of comparison. Benchmarks with different length-to-thickness ratios, lay-ups, material properties, and simply supported or clamped edges are studied with the intended aim of contributing toward better understanding the influence of transverse anisotropy on free vibration and the response of blast-loaded, multilayered, and sandwich plates, as well as enhancing the existing database. The results show that only theories whose layerwise contributions identically satisfy interfacial stress constrains and whose displacement fields are redefined for each layer provide results that are in agreement with elasticity solutions and three-dimensional (3D) finite element analysis (FEA) (mixed solid elements with displacements and out-of-plane stresses as nodal degrees of freedom (d.o.f.)) with a low expansion order of polynomials in the in-plane and out-of-plane directions. The choice of their layerwise functions is shown to be immaterial, while theories with fixed kinematics are shown to be strongly case-sensitive and often inadequate (even for slender components).

Influence of Interference and Clamping on Fretting Fatigue in Single Rivet-Row Lap Joints

2000 ◽  
Vol 123 (4) ◽  
pp. 686-698 ◽  
Author(s):  
K. Iyer ◽  
C. A. Rubin ◽  
G. T. Hahn
Keyword(s):  
Crack Initiation ◽  
Three Dimensional ◽  
Fretting Fatigue ◽  
Cyclic Stress ◽  
Lap Joints ◽  
Element Analysis ◽  
Out Of Plane ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Fretting Damage

Primary fretting fatigue variables such as contact pressure, slip amplitude and bulk cyclic stresses, at and near the contact interface between the rivet shank and panel hole in a single rivet-row, 7075-T6 aluminum alloy lap joint are presented. Three-dimensional finite element analysis is applied to evaluate these and the effects of interference and clamping stresses on the values of the primary variables and other overall measures of fretting damage. Two rivet geometries, non-countersunk and countersunk, are considered. Comparison with previous evaluations of the fretting conditions in similar but two-dimensional connections indicates that out-of-plane movements and attending effects can have a significant impact on the fatigue life of riveted connections. Variations of the cyclic stress range and other proponents of crack initiation are found to peak at distinct locations along the hole-shank interface, making it possible to predict crack initiation locations and design for extended life.

An Exact Three-Dimensional Beam Element With Nonuniform Cross Section

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
M. Jafari ◽  
M. J. Mahjoob
Keyword(s):  
Cross Section ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Direct Method ◽  
Three Dimensional ◽  
Curved Beams ◽  
Element Analysis ◽  
Shear Loads ◽  
Line Passing ◽  
Exact Stiffness Matrix

In this paper, the exact stiffness matrix of curved beams with nonuniform cross section is derived using direct method. The considered element has two nodes and 12 degrees of freedom, with three forces and three moments applied at each node. The noncoincidence effect of shear center and center of area is also considered in this element. The deformations of the beam are due to bending, torsion, tensile, and shear loads. The line passing through center of area is a general three-dimensional curve and the cross section properties may change arbitrarily along it. The method is extended to deal with distributed loads on the curved beams. The stiffness matrix of some selected types of beams is determined by this method. The results are compared (where possible) with previously published results, simple beam finite element analysis and analytic solution. It is shown that the determined stiffness matrix is exact and that any type of beam can be analyzed by this method.

Analysis of Three-Dimensional Clamped Single Edge Notched Tension (SENT) Specimens

2018 ◽  
Author(s):  
Zheng Liu ◽  
Xu Chen ◽  
Xin Wang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Depth ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Width Ratio ◽  
Element Analysis ◽  
Out Of Plane ◽  
T Stress

In the present paper, three-dimensional clamped SENT specimens, which is one of the most widely used low-constraint and less-conservative specimen, are analyzed by using a crack compliance analysis approach and extensive finite element analysis. Considering the test standard (BS8571) recommended specimen sizes, the daylight to width ratio, H/W, is 10.0, the relative crack depth, a/W, is varied by 0.2, 0.3, 0.4, 0.5 or 0.6 and the relative plate thickness, B/W, is chosen by 1.0, 2.0 or 4.0, respectively. Complete solutions of fracture mechanics parameters, including stress intensity factor (K), in-plane T-stress (T11) and out-of-plane T-stress (T33) are calculated, and the results obtained from above two methods have a good agreement. Moreover, the combination of the effects of a/W and B/W on the stress intensity factor K, T11 and T33 stress are thus illustrated.

Failure of curved brittle layer systems from radial cracking in concentrated surface loading

2005 ◽  
Vol 20 (10) ◽  
pp. 2812-2819 ◽  
Author(s):  
Matthew Rudas ◽  
Tarek Qasim ◽  
Mark B. Bush ◽  
Brian R. Lawn
Keyword(s):  
Three Dimensional ◽  
Crack Evolution ◽  
Displacement Fields ◽  
Element Analysis ◽  
Direct Evaluation ◽  
Brittle Layer ◽  
Load To Failure ◽  
Dimensional Boundary ◽  
Ultimate Failure ◽  
The Stability

A study was made of radial crack evolution in curved brittle layers on compliant support substrates. Three-dimensional boundary element analysis was used to compute the stepwise growth of radial cracks that initiate at the bottom surfaces of glass on polymeric support layers, from initiation to final failure. The algorithm calculates reconstituted displacement fields in the near-tip region of the extending cracks, enabling direct evaluation of stress-intensity factors. Available experimental data on the same material systems with prescribed surface curvatures were used to validate the essential features of the predicted crack evolution, particularly the stability conditions prior to ultimate failure. It was shown that the critical loads to failure diminish with increasing surface curvature. Generalization of the ensuing fracture mechanics to include alternative brittle-layer/polymer-substrate systems enabled an explicit expression for the critical load to failure in terms of material properties and layer thicknesses. Implications concerning practical layer systems, particularly dental crowns, are briefly discussed.

Three-dimensional deformations in a single-lap joint

1994 ◽  
Vol 29 (2) ◽  
pp. 137-145 ◽  
Author(s):  
M Y Tsai ◽  
J Morton
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Stress Distributions ◽  
Lap Joint ◽  
Displacement Fields ◽  
Element Analysis ◽  
Linear Elastic ◽  
Non Linear ◽  
Linear Effects ◽  
Peel Stress

The three-dimensional nature of the state of deformation in a single-lap test specimen is investigated in a linear elastic finite element analysis in which the boundary conditions account for the geometrically non-linear effects. The validity of the model is demonstrated by comparing the resulting displacement fields with those obtained from a moiré inteferometry experiment. The three-dimensional adherend and adhesive stress distributions are calculated and compared with those from a two-dimensional non-linear numerical analysis, Goland and Reissner's solution, and experimental measurements. The nature of the three-dimensional mechanics is described and discussed in detail. It is shown that three-dimensional regions exists in the specimen, where the adherend and adhesive stress distributions in the overlap near (and especially on) the free surface are quite different from those occurring in the interior. It is also shown that the adhesive peel stress is extremely sensitive to this three-dimensional effect, but the adhesive shear is not. It is also observed that the maximum value of the peel stress occurs at the end of the overlap in the central two-dimensional core region, rather than at the corners where the three-dimensional effects are found. The extent of three-dimensional regions is also quantified.

Elastic-Plastic Finite Element Simulation of Bulge Forming Process Using a Variable Cross-Section Solid Bulging Mold

2011 ◽  
Vol 189-193 ◽  
pp. 4405-4408
Author(s):  
Ke Wang ◽  
Zhe Ying Wang ◽  
Xing Wei Sun
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Metal Flow ◽  
Three Dimensional ◽  
Variable Cross Section ◽  
Flow Mode ◽  
Variable Cross ◽  
Forming Process ◽  
Element Analysis ◽  
Screw Rotor

Bulge forming is a novel process aimed at common products including T-branches, cross branches and angle branches. But bulging forming has not applied for two-head abnormity-shaped hollow screw rotor reported in literature. Simulation of the bulging forming of two-head abnormity-shaped hollow screw rotor has not been reported. This paper presents a simulation of the bulge forming process of two-head abnormity-shaped hollow screw rotor using a variable cross-section solid bulging mold. Some conditions including the effect of friction, boundary conditions, contact conditions and the space motion, etc are presented. The mathematical model of three-dimensional finite element analysis has been established. The distribution of generalized plastic strain and general metal flow mode in cross section of two abnormity-shaped hollow screw rotor has been analyzed. It is an effective method for the analysis of other defects and the optimization of process parameters further.

Tilt scanning interferometry: a novel technique for mapping structure and three-dimensional displacement fields within optically scattering media

2006 ◽  
Vol 462 (2072) ◽  
pp. 2481-2502 ◽  
Author(s):  
Pablo D Ruiz ◽  
Jonathan M Huntley ◽  
Alejandro Maranon
Keyword(s):  
Phase Change ◽  
Three Dimensional ◽  
Phase Volume ◽  
Scattering Media ◽  
Displacement Fields ◽  
Novel Technique ◽  
Constant Rate ◽  
Out Of Plane ◽  
The Difference ◽  
Temporal Sequences

We describe a novel technique that we call tilt scanning interferometry to measure depth-resolved structure and displacement fields within semi-transparent scattering materials. The method differs significantly from conventional optical coherence tomography, in that only one wavelength is used throughout the whole measurement process. Temporal sequences of speckle interferograms are recorded while the illumination angle is tilted at constant rate. Fourier transformation of the resulting three-dimensional intensity distribution along the time axis reconstructs the scattering potential within the medium. Repeating the measurements with the object wave at equal and opposite angles about the observation direction results in two three-dimensional phase-change volumes, the sum of which gives the out-of-plane-sensitive phase volume and the difference between which gives the in-plane phase volume. From these phase-change volumes the in-plane and out-of-plane depth-resolved displacement fields are obtained. The theoretical framework for the technique is explained in detail and a practical optical implementation is described. Finally, results from proof-of-principle experiments involving a semi-transparent beam undergoing bending are presented.

Off-Road Tire-Soil Modeling Using Finite Element Analysis Technique

2009 ◽  
Author(s):  
Jeff Slade ◽  
Moustafa El-Gindy ◽  
Ryan Lescoe ◽  
Fredrik O¨ijer ◽  
Mukesh Trivedi ◽  
...  
Keyword(s):  
Published Data ◽  
Element Analysis ◽  
Rigid Ring ◽  
Dense Sand ◽  
Ring Model ◽  
Truck Tire ◽  
Analysis Technique ◽  
Out Of Plane ◽  
Wheel Model ◽  
Soil Flow

A new rigid ring model with additional parameters was developed to model an off-road tire running on soil. In order to create this new rigid ring model, an FEA off-road truck tire was created and used to determine the in-plane and out-of-plane parameters for a tire running on soil. The soil, dense sand in this case, was modeled as an elastic-plastic solid with material properties obtained from published data. The longitudinal forces and the normal stress and shear stress distributions in the soil are compared with published data as preliminary validation. The general trends of soil flow from a rigid wheel model running on soil were used to validate the soil model. In addition, a model of a standard circular plate was used to determine the vertical pressure-sinkage curves and then these simulations were compared with available published measured data.

scholarly journals An Analysis of Local and Combined (Global) Scours on Piers-on-Bank Bridges

CivilEng ◽  
2021 ◽  
Vol 3 (1) ◽  
pp. 1-20
Author(s):  
Vidya Subhash Chavan ◽  
Shen-En Chen ◽  
Navanit Sri Shanmugam ◽  
Wenwu Tang ◽  
John Diemer ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Bending Moments ◽  
Lateral Loads ◽  
Displacement Fields ◽  
Element Analysis ◽  
Dimensional Finite Element ◽  
Moment Effect ◽  
Drilled Shaft Foundations ◽  
Three Dimensional Finite Element ◽  
Element Removal

This paper examines the scour problems related to piers-on-bank bridges resulting from frequently flooded and/or constricted waterways. While local scour problems for bridge piers in riverine channels have been addressed extensively in the literature, there have been few studies addressing piers-on-bank scour scenarios. A comprehensive three-dimensional finite element analysis using the element removal (ER) technique has been performed on a recently constructed bridge with an observable scour problem on multiple piers. The analysis is further extended to study the effect of “combined scour” or extensive erosion of soil between adjacent piles. Three different loading cases were considered in the study, and the results demonstrated that the effects of local and combined scours on bridge drilled shaft foundations can be significant under the combined actions of axial, lateral loads and bending moments. Specifically, the most critical case of combined scour is when maximum moment effect is applied to the piers. The results of this study show that the interaction of soil displacement fields between adjacent piles should be investigated for bridge crossings with piers-on-bank, with a high risk of flooding during the moderate-to-low probability of the occurrence of precipitation events, as they can increase the pile head displacements and the bending moments in the soil and result in the early failure of bridges.

Sign in / Sign up

Export Citation Format

Share Document