Transient Problem for a Accreted Thermoelastic Block

2015 ◽  
pp. 67-83
Author(s):  
Alexander L. Levitin ◽  
Sergei A. Lychev
Keyword(s):  
Transient Problem

Stationarity Detection in the Initial Transient Problem

1992 ◽  
Author(s):  
Soeren Asmussen ◽  
Peter W. Glynn ◽  
Hermann Thorisson
Keyword(s):  
Initial Transient ◽  
Transient Problem

Impact Response of a Cracked Orthotropic Medium

1983 ◽  
Vol 50 (3) ◽  
pp. 630-636 ◽  
Author(s):  
M. K. Kassir ◽  
K. K. Bandyopadhyay
Keyword(s):  
Stress Intensity ◽  
Dynamic Stress ◽  
Fourier Transforms ◽  
Dynamic Stress Intensity Factor ◽  
Orthotropic Materials ◽  
Dynamic Stress Intensity Factors ◽  
Transient Problem ◽  
Numerical Laplace Inversion ◽  
The Laplace Transform ◽  
Applied Stresses

A solution is given for the problem of an infinite orthotropic solid containing a central crack deformed by the action of suddenly applied stresses to its surfaces. Laplace and Fourier transforms are employed to reduce the transient problem to the solution of standard integral equations in the Laplace transform plane. A numerical Laplace inversion technique is used to compute the values of the dynamic stress-intensity factors, k1 (t) and k2 (t), for several orthotropic materials, and the results are compared to the corresponding elastostatic values to reveal the influence of material orthotropy on the magnitude and duration of the overshoot in the dynamic stress-intensity factor.

SCATTERING OF TRANSIENT WAVES BY FINITE CRACKS IN AN ANTI-PLANE STRAIN ELASTIC SOLID

1993 ◽  
Vol 01 (01) ◽  
pp. 101-116 ◽  
Author(s):  
YU-CHIUNG TENG
Keyword(s):  
Plane Wave ◽  
Plane Strain ◽  
Elastic Solid ◽  
Transient Problem ◽  
Whole Space ◽  
Crack Tips ◽  
Finite Line ◽  
Energy Sharing ◽  
Analytical Approaches ◽  
Line Crack

The transient problem of finite cracks with vanishing thickness in an anti-plane strain solid is investigated by finite element method. The infinitesimally thin crack with traction free on both faces of the crack is simulated by the energy-sharing-node technique. The following cases are considered: (a) One finite line crack in a whole space subjected to (i) a concentrated line source and (ii) an inclined incident SH plane wave. (b) Two cracks in a whole space subjected to an inclined incident SH plane wave. Emphasis has been laid on the quantitative evaluation of the dynamic disturbances for the problem in the interference stage, which is generally difficult to be obtained by analytical approaches. The synthetic seismograms for displacements along the crack surfaces, which cover a period up to an instant of time during which the second order scattering from crack tips can be observed, are presented. Snapshots of the scattered displacement field for each case are also displayed so that the generations of the scatterings and the processes of the wave propagations can be clearly visualized. The two-dimensional wave propagation for transient acoustic problem and electromagnetic problem with the same nature of boundaries can be analogously obtained.

Transient response of the ‘multiple water-bag’ plasma

1989 ◽  
Vol 421 (1860) ◽  
pp. 109-152 ◽  
Keyword(s):  
Large Time ◽  
Transient State ◽  
Dispersion Curves ◽  
Kelvin Waves ◽  
Thermal Front ◽  
Transient Problem ◽  
Warm Plasma ◽  
A Charge ◽  
Response Field ◽  
State Feature

A charge activates impulsively and then decays temporally within a MWB (multiple water-bag)-modelled warm plasma. The transient problem is formulated and asymptotically resolved for large time. The response potential comprises two characteristically distinct quantities W and W N : W is a superposition of spherically expanding, moderately attenuated Kelvin waves contributed by certain points on a subset of dispersion curves; W N is a superposition, associated with two other dispersion curves, of three spherical wavefunctions, one of which incorporates the Fresnel integrals. A transient state feature of the MWB discretization is the partitioning of the response field by growing (fast) fronts, (trailing) slow caustics and a j¯ , the fastest among these being an a N¯ surface (thermal front) which pushes back a quasi-static exterior. Contrary to expectations, there is no response jump across any of those growing partitions. Wavefunctions near the slow caustics possess Airy factors. A rest state ultimately develops behind the slowest slow caustic. An application is made to the fluid plasma.

Transient Solution of the Inhomogeneous Thermoelastic Contact Problem Using Fast Speed Expansion

2004 ◽  
Author(s):  
Jiayin Li ◽  
James R. Barber
Keyword(s):  
Contact Problem ◽  
Large Scale ◽  
Computation Time ◽  
Transient Solution ◽  
New Approach ◽  
Thermoelastic Contact ◽  
Fast Speed ◽  
Transient Problems ◽  
Transient Problem ◽  
Thermoelastic Contact Problem

Numerical integration has been widely used in commercial FEA software to solve transient problems. However, for the large-scale inhomogeneous thermoelastic contact problem (ITEC), this method is found to be extremely computation-intensive. This paper introduces a new approach to solve the ITEC transient problem with much lower computational complexity. The method is based on the transient modal analysis (TMA) method in conjunction with the fast speed expansion (FSE) method. The TMA method is used to obtain the inhomogeneous transient solution by expressing the solution in modal coordinates, corresponding to eigenfunctions of the homogeneous (unloaded) problem. If the sliding speed is constant, the eigenfunctions can be found by one run of the commercial software program ‘HotSpotter’. However, if the speed varies, the eigenfunctions change and numerous runs of HotSpotter are needed, making the method computationally inefficient. However, the FSE method employs an efficient algorithm to interpolate and expand the eigenfunctions and eigenvalues over a range of speeds. This reduces the number of eigenvalue solutions required and results in a significant reduction in computation time. The method is illustrated with application to an axisymmetric transmission clutch problem.

Fast Speed Expansion Technique for the Transient Analysis of Automotive Clutches

2004 ◽  
Author(s):  
Jiayin Li
Keyword(s):  
Large Scale ◽  
Expansion Method ◽  
Linear Interpolation ◽  
New Approach ◽  
Fast Speed ◽  
Transient Problem ◽  
Expansion Technique ◽  
Eigen Solutions ◽  
Modal Coordinates ◽  
Thermoelastic Contact Problem

The transient modal analysis method (TMA) has been used to solve the inhomogeneous (loaded) transient thermoelastic contact problem (ITTEC). In the TMA method, the solution of the inhomogeneous transient problem is expressed in modal coordinates, corresponding to eigenfunctions of the homogeneous (unloaded) problem. However, for the large-scale ITTEC problem, this method is found to be extremely time-consuming, because of the computation-intensive of the eigen-solutions. This paper describes a new approach to solve the large-scale ITTEC problem with a dramatic reduction in computational complexity. The method is referred to as fast speed expansion method (FSE). With the FSE method, full eigen-solutions are performed only at a limited number of sparsely located speeds. For speeds between these speeds, eigenvectors are solved by linear interpolation, while the eigenvalues are computed from Taylor series. The method is illustrated with application to an automotive clutches.

Stochastic Analysis of Groundwater Traveltime for Long-Term Repository Performance Assessment

1983 ◽  
Vol 26 ◽  
Author(s):  
P.M. Clifton ◽  
R.G. Baca ◽  
R.C. Arnett
Keyword(s):  
Monte Carlo ◽  
Random Number Generator ◽  
Monte Carlo Analysis ◽  
Effective Porosity ◽  
Specific Storage ◽  
Hanford Site ◽  
Transient Problem ◽  
Degree Of Confidence ◽  
Using Data

ABSTRACTThis paper describes a method of stochastically analyzing groundwater traveltime. The method uses a Monte Carlo technique to generate a suite of random spatial fields that are subsequently input to the groundwater flow and groundwater traveltime equations. Stochastic inputs to these equations can be (1) transmissivity (or hydraulic conductivity), (2) effective thickness (or effective porosity), or (3) boundary conditions. In a transient problem, storage coefficient (or specific storage) could also be stochastically treated. Spatial correlation in the random input fields is accounted for by means of a multivariate random-number generator, which requires the first two statistical moments of these fields to be specified. The output from the Monte Carlo analysis is a suite of groundwater traveltime realizations that can be used to derive exceedance probabilities. These probabilities provide a measure of the degree of confidence in meeting set criteria.A preliminary application of this method using data from the deep basalts beneath the Hanford Site is also presented. The results illustrate how this method can be used to evaluate compliance with a technical criterion relating to groundwater traveltime.

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