Indeterminacy of first order stress functions and the stress- and rotation-based formulation of linear elasticity

1994 ◽  
Vol 14 (3) ◽  
pp. 249-265 ◽  
Author(s):  
E. Bert�ti
Keyword(s):  
Linear Elasticity ◽  
First Order ◽  
Stress Functions ◽  
Order Stress

scholarly journals Hypersingular boundary integral equations for plane orthotropic elasticity in terms of first-order stress functions

2020 ◽  
Vol 15 (2) ◽  
pp. 185-207
Author(s):  
Sándor Szirbik
Keyword(s):  
Stress Distribution ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Arbitrary Point ◽  
Boundary Integral ◽  
Computational Technique ◽  
First Order ◽  
Orthotropic Elasticity ◽  
Stress Functions ◽  
Order Stress

This paper is intended to present an implementation of the hypersingular boundary integral equations in terms of first-order stress functions for stress computations in plane orthotropic elasticity. In general, the traditional computational technique of the boundary element method used for computing the stress distribution on the boundary and close to it is not as accurate as it should be. In contrast, the accuracy of stress computations on the boundary is greatly increased by applying the hypersingular integral equations. Contrary to the method in which the solution is based on an approximation of displacement field, here the first-order stress functions and the rigid body rotation are the fundamental variables. An advantage of this approach is that the stress components can be obtained directly from the stress functions, there is, therefore, no need for Hooke's law, which should be used when they are computed from displacements. In addition, the computational work can be reduced when the stress distribution is computed at an arbitrary point on the boundary. The numerical examples presented prove the efficiency of this technique.

Nonlinear Theory for Flexural Motions of Thin Elastic Plate, Part 3: Numerical Evaluation of Boundary Layer Solutions

1982 ◽  
Vol 49 (2) ◽  
pp. 409-416
Author(s):  
N. Sugimoto
Keyword(s):  
Boundary Layer ◽  
Stress Singularity ◽  
Free Edge ◽  
Thin Elastic Plate ◽  
Normal Stresses ◽  
Interior Region ◽  
First Order ◽  
Plausible Values ◽  
Bending Stresses ◽  
Order Stress

The boundary layer solutions previoulsy obtained in Part 2 of this series for the cases of the built-in edge and the free edge are evaluated numerically. For the built-in edge, a characteristic penetration depth of the boundary layer toward the interior region is given by 0.13 εh, εh being the normalized thickness of the plate, while for the free edge, it is given by 0.32 εh. Thus the boundary layer for the free edge penetrates more deeply toward the interior region than that for the built-in edge. The first-order stress distribution in each boundary layer is displayed. For the built-in edge, the stress singularity appears on the edge. It is shown that, in the boundary layer, the shearing and normal stresses become comparable with the bending stresses. Similarly for the free edge, the shearing stress also becomes comparable with the twisting stress. It should be remarked that, in the boundary layer, the shearing or the normal stress plays a primarily important role as the bending or the twisting stress. But the former decays toward the interior region and remains higher order than the latter. Finally owing to these numerical results, the coefficients involved in the “reduced” boundary conditions for the built-in edge are evaluated for the various plausible values of Poisson’s ratio.

The flow properties of honey–malt spread

2017 ◽  
Vol 23 (5) ◽  
pp. 415-425 ◽  
Author(s):  
M Dianat ◽  
M Taghizadeh ◽  
F Shahidi ◽  
SMA Razavi
Keyword(s):  
Flow Behavior ◽  
Time Dependent ◽  
Malt Extract ◽  
Barley Malt ◽  
First Order ◽  
Dependent Behavior ◽  
Thixotropic Behaviour ◽  
Order Stress ◽  
Temperature Levels ◽  
Independent Behavior

In this study, the effect of barley malt extract at two brix levels (74 and 79 °Bx) and three ratios of malt extract/honey (65:35, 70:30 and 75:25) on the flow behavior properties of honey–malt spread at three temperature levels (35 ℃, 45 ℃ and 55 ℃) was investigated. Time-dependent behavior data of the spread samples were appropriately fitted to the Weltman, first-order stress decay with a zero stress value and first-order stress decay with a non-zero stress value models. Also, the Power-law, Herschel–Bulkley, Casson and Bingham models were used for curve fitting the time-independent behavior data. Regarding the R2 and root mean square error coefficients, the first-order stress decay with a non-zero stress value and Herschel–Bulkley models were selected as the suitable models to describe the flow behavior of samples. The results for time-dependent properties showed that spread samples exhibit a thixotropic behaviour, as the viscosity for all samples decreased with increase in shearing time at a constant shear rate of 50 s−1.

First-Order System Least Squares (FOSLS) for Spatial Linear Elasticity: Pure Traction

2000 ◽  
Vol 38 (5) ◽  
pp. 1454-1482 ◽  
Author(s):  
Sang Dong Kim ◽  
Thomas A. Manteuffel ◽  
Stephen F. McCormick
Keyword(s):  
Least Squares ◽  
Linear Elasticity ◽  
Order System ◽  
First Order

Analytical Solutions for Crack-Tip Higher Order Stress Fields in Thermal Barrier Coating

2008 ◽  
Vol 47-50 ◽  
pp. 1023-1026
Author(s):  
Yao Dai ◽  
Chang Qing Sun ◽  
Sun Qi ◽  
Wei Tan
Keyword(s):  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Stress Fields ◽  
Thermal Barrier ◽  
Barrier Coating ◽  
Graded Material ◽  
Stress Functions ◽  
Order Stress ◽  
Analytical Expressions

Analytical expressions for crack-tip higher order stress functions for a plane crack in a special functionally graded material (FGM), which has an variation of elastic modulus in 1 2 power form along the gradient direction, are obtained through an asymptotic analysis. The Poisson’s ratio of the FGM is assumed to be constant in the analysis. The higher order fields in the asymptotic expansion display the influence of non-homogeneity on the structure of crack-tip fields obviously. Furthermore, it can be seen from expressions of higher order stress fields that at least three terms must be considered in the case of FGMs in order to explicitly account for non-homogeneity effects on the crack- tip stress fields. These results provide the basis for fracture analysis and engineering applications of this FGM.

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