On the Extension of an Infinite Elastic Plate Containing an Axisymmetric Hole

1972 ◽  
Vol 39 (2) ◽  
pp. 507-512 ◽  
Author(s):  
E. E. Burniston
Keyword(s):  
Asymptotic Expansion ◽  
Elastic Plate ◽  
Three Dimensional ◽  
Simple Tension

The problem of a thin isotropic elastic plate containing an axisymmetric hole, under simple tension at infinity is considered. The method used is to extend the plate theories which have appeared in recent years, which employ asymptotic expansion techniques to determine systematic approximations to the three-dimensional equations of elastostatics.

Consistent Asymptotic Expansion Multiscale Formulation for Heterogeneous Column Structure

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Dongdong Wang ◽  
Pinkang Xie ◽  
Lingming Fang
Keyword(s):  
Asymptotic Expansion ◽  
Displacement Field ◽  
Three Dimensional ◽  
Axial Direction ◽  
Unit Cell ◽  
Local Unit ◽  
Cell Problem ◽  
Element Discretization ◽  
Free Condition ◽  
Column Structure

A consistent asymptotic expansion multiscale formulation is presented for analysis of the heterogeneous column structure, which has three dimensional periodic reinforcements along the axial direction. The proposed formulation is based upon a new asymptotic expansion of the displacement field. This new multiscale displacement expansion has a three dimensional form, more specifically, it takes into account the axial periodic property but simultaneously keeps the cross section dimensions in the global scale. Thus, this formulation inherently reflects the characteristics of the column structure, i.e., the traction free condition on the circumferential surfaces. Subsequently, the global equilibrium problem and the local unit cell problem are consistently derived based upon the proposed asymptotic displacement field. It turns out that the global homogenized problem is the standard axial equilibrium equation, while the local unit cell problem is completely three dimensional which is subjected to the periodic boundary condition on axial surfaces as well as the traction free condition on circumferential surfaces of the unit cell. Thereafter, the variational formulation and finite element discretization of the unit cell problem are discussed. The effectiveness of the present formulation is illustrated by several numerical examples.

scholarly journals A Justification of Two-Dimensional Nonlinear Viscoelastic Shells Model

2012 ◽  
Vol 2012 ◽  
pp. 1-24
Author(s):  
Fushan Li
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Analysis ◽  
Laplace Transformation ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Nonlinear Viscoelastic ◽  
Leading Term ◽  
Viscoelastic Shells

By applying formal asymptotic analysis and Laplace transformation, we obtain two-dimensional nonlinear viscoelastic shells model satisfied by the leading term of asymptotic expansion of the solution to the three-dimensional equations.

Irrotational flow past bodies close to a plane surface

1971 ◽  
Vol 50 (3) ◽  
pp. 481-491 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Asymptotic Expansion ◽  
Numerical Computation ◽  
Potential Flow ◽  
Close Agreement ◽  
Plane Surface ◽  
Three Dimensional ◽  
Ground Surface ◽  
Two Dimensional ◽  
General Shape ◽  
Irrotational Flow

A theroetical analysis is given for potential flow over, around and under a vehicle of general shape moving close to a plane ground surface. Solutions are given both in the form of a small-gap asymptotic expansion and a direct numerical computation, with close agreement between the two for two-dimensional flows with and without circulation. Some results for three-dimensional bodies are discussed.

Fatigue life prediction for a barrelled spline coupling under torque overload

2003 ◽  
Vol 217 (3) ◽  
pp. 123-142 ◽  
Author(s):  
S B Leen ◽  
I R McColl ◽  
C H H Ratsimba ◽  
E J Williams
Keyword(s):  
Finite Element ◽  
Fatigue Life ◽  
Life Prediction ◽  
Plastic Material ◽  
Three Dimensional ◽  
Fretting Wear ◽  
Life Assessment ◽  
Simple Tension ◽  
Wide Range ◽  
Spline Coupling

Aeroengine spline couplings experience a wide range of loading conditions leading to contrasting service life limiting phenomena, including fatigue, fretting fatigue and fretting wear. Highly loaded couplings may employ incomplete contact axial profiles, while the contact geometry transverse to the spline axis is nominally complete with theoretical stress singularities at the contact edges. Life assessment of such components is consequently complex. The effect of torque overload conditions on the fatigue life of a barrelled, aeroengine type spline coupling is investigated experimentally. The experimental results are interpreted using three-dimensional finite element analyses, incorporating frictional contact and elastic-plastic material behaviour and the results of simple tension-tension fatigue tests. Torque-life and finite element predicted stress-life relationships are generated for spline life prediction purposes. Good correlation is obtained between the spline coupling and simple tension-tension fatigue test results, interpreted via the finite element predicted stress ranges.

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