Deformations and Stress Intensities Due to a Craze in an Extended Elastic Material

1984 ◽  
Vol 51 (1) ◽  
pp. 84-92 ◽  
Author(s):  
J. R. Walton ◽  
Y. Weitsman
Keyword(s):  
Analytical Solution ◽  
Elastic Medium ◽  
Finite Length ◽  
Elastic Material ◽  
Integrodifferential Equation ◽  
Numerical Scheme ◽  
Time Dependent ◽  
Stress Fields ◽  
Singular Integrodifferential Equation

This paper presents an analytical solution, accompanied by a numerical scheme, to determine the displacement and stress fields in an extended elastic medium due to a thin craze of finite length directed transversely to the load at infinity. Crazes are thin elongated defects containing fine fibrils that connect their opposite interfaces. These fibrils are modeled as a distributed spring, leading to a formulation in terms of a singular integrodifferential equation. The paper also contains a treatment of central cracks within the craze and time-dependent craze response, and includes a discussion of “tip zone” correction.

Heat Transfer Analysis of Laminar Pulsating Flow in a Rectangular Channel Using Infrared Thermography

2021 ◽  
Author(s):  
Richard Blythman ◽  
Sajad Alimohammadi ◽  
Nicholas Jeffers ◽  
Darina B. Murray ◽  
Tim Persoons
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Analytical Solution ◽  
Local Time ◽  
Rectangular Channel ◽  
Pulsating Flow ◽  
Time Dependent ◽  
Heat Transfer Analysis ◽  
Flux Boundary Condition ◽  
Hydrodynamic Behaviour

Abstract While numerous applied studies have successfully demonstrated the feasibility of unsteady cooling solutions, a consensus has yet to be reached on the local instantaneous conditions that result in heat transfer enhancement. The current work aims to experimentally validate a recent analytical solution (on a local time-dependent basis) for the common flow condition of a fully-developed incompressible pulsating flow in a uniformly-heated vessel. The experimental setup is found to approximate the ideal constant heat flux boundary condition well, especially for the decoupled unsteady scenario where the amplitude of the most significant secondary contributions (capacitance and lateral conduction) amounts to 1.2% and 0.2% of the generated heat flux, respectively. Overall, the experimental measurements for temperature and heat flux oscillations are found to coincide well with a recent analytical solution to the energy equation by the authors. Furthermore, local time-dependent heat flux enhancements and degradations are observed to be qualitatively similar to those of wall shear stress from a previous study, suggesting that the thermal performance is indeed influenced by hydrodynamic behaviour.

An analytical solution for simulation of the fission gas behaviors with time-dependent piece-wise boundary resolution

2012 ◽  
Vol 424 (1-3) ◽  
pp. 109-115 ◽  
Author(s):  
Yi Cui ◽  
Yongzhong Huo ◽  
Shurong Ding ◽  
Lin Zhang ◽  
Yuanming Li
Keyword(s):  
Analytical Solution ◽  
Time Dependent ◽  
Fission Gas

scholarly journals On the Temperature Distribution Inside a Tree Under Fire Conditions

1991 ◽  
Vol 1 (2) ◽  
pp. 87 ◽  
Author(s):  
JJ Costa ◽  
LA Oliveira ◽  
DX Viegas ◽  
LP Neto
Keyword(s):  
Cross Section ◽  
Heat Conduction Equation ◽  
Numerical Scheme ◽  
Unit Length ◽  
Circular Cross Section ◽  
Time Dependent ◽  
Tree Trunk ◽  
Temperature Field Distribution ◽  
Ground Fire ◽  
Fire Conditions

A simple and efficient numerical scheme is presented for the prediction of temperature field distribution inside a tree trunk subjected to ground fire conditions. The trunk is modelled by a cylinder of circular cross section and unit length, through which the time-dependent heat conduction equation is numerically integrated. The model is partly validated in laboratory and then applied to the case of a prescribed ground fire inside a Pinus pinmter stand.

scholarly journals Application of hybrid asymptotic methods and modern software for mathematical models developing for nonlinear dynamics of structures with variables in time parameters

2021 ◽  
pp. 66-70
Author(s):  
S. Homeniuk ◽  
S. Grebenyuk ◽  
D. Gristchak
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Methods ◽  
Nonlinear Systems ◽  
Analytical Solution ◽  
Mathematical Models ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Hybrid Approach ◽  
Time Dependent ◽  
Forced Oscillations

The relevance. The aerospace domain requires studies of mathematical models of nonlinear dynamic structures with time-varying parameters. The aim of the work. To obtain an approximate analytical solution of nonlinear forced oscillations of the designed models with time-dependent parameters. The research methods. A hybrid approach based on perturbation methods, phase integrals, Galorkin orthogonalization criterion is used to obtain solutions. Results. Nonlocal investigation of nonlinear systems behavior is done using results of analytical and numerical methods and developed software. Despite the existence of sufficiently powerful numerical software systems, qualitative analysis of nonlinear systems with variable parameters requires improved mathematical models based on effective analytical, including approximate, solutions, which using numerical methods allow to provide a reliable analysis of the studied structures at the stage designing. An approximate solution in analytical form is obtained with constant coefficients that depend on the initial conditions. Conclusions. The approximate analytical results and direct numerical solutions of the basic equation were compared which showed a sufficient correlation of the obtained analytical solution. The proposed algorithm and program for visualization of a nonlinear dynamic process could be implemented in nonlinear dynamics problems of systems with time-dependent parameters.

Analytical Solutions of Stresses in Functionally Graded Circular Hollow Cylinder with Finite Length

2004 ◽  
Vol 261-263 ◽  
pp. 651-656 ◽  
Author(s):  
Z.S. Shao ◽  
L.F. Fan ◽  
Tie Jun Wang
Keyword(s):  
Young’S Modulus ◽  
Hollow Cylinder ◽  
Finite Length ◽  
Analytical Solutions ◽  
Radial Direction ◽  
Young's Modulus ◽  
Functionally Graded ◽  
Numerical Results ◽  
Stress Fields ◽  
Simply Supported

Analytical solutions of stress fields in functionally graded circular hollow cylinder with finite length subjected to axisymmetric pressure loadings on inner and outer surfaces are presented in this paper. The cylinder is simply supported at its two ends. Young's modulus of the material is assumed to vary continuously in radial direction of the cylinder. Moreover, numerical results of stresses in functionally graded circular hollow cylinder are appeared.

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