Application of complex variables and pseudo-stress function to power-law materials and stress analysis of single rigid inclusion in power-law materials subjected to simple tension and pure shear

1987 ◽  
Vol 29 (10-11) ◽  
pp. 669-694 ◽  
Author(s):  
Y.S. Lee ◽  
H. Gong
Keyword(s):  
Stress Analysis ◽  
Power Law ◽  
Rigid Inclusion ◽  
Stress Function ◽  
Pure Shear ◽  
Complex Variables ◽  
Simple Tension

Constitutive Equations of Power-Law Composites and Failure of Materials Having Multiple Cracks

1994 ◽  
Vol 116 (3) ◽  
pp. 359-366 ◽  
Author(s):  
S. C. Lin ◽  
Y. Hirose ◽  
T. Mura
Keyword(s):  
Power Law ◽  
Constitutive Equations ◽  
Fracture Criterion ◽  
Volume Fraction ◽  
Piecewise Linear ◽  
Pure Shear ◽  
Failure Criteria ◽  
Multiple Cracks ◽  
Critical Volume Fraction ◽  
The Matrix

Based upon the Mori-Tanaka method, the constitutive equations of power-law materials and the failure criteria of multiple cracks materials are investigated. The piecewise linear incremental approach is also employed to analyze the effective stress and strain of the power-law materials. Results are presented for the case of pure shear where the matrix is a power-law material with rigid or void inhomogeneities. For the multiple cracked materials, the Griffith fracture criterion is applied to determine the critical volume fraction which causes the catastrophic failure of a material. The failure criteria of penny shaped, flat ellipsoidal, and slit-like cracked materials are examined and it is found that the volume fraction of cracks and critical applied stress are in linear relation.

Stress Analysis of the Rectangular Retaining Wall under Water Pressure Based on Elasticity Mechanics

2014 ◽  
Vol 578-579 ◽  
pp. 146-150
Author(s):  
Yong Wei Wang ◽  
Yan Qin Guo
Keyword(s):  
Stress Analysis ◽  
Normal Stress ◽  
Stress Function ◽  
Water Pressure ◽  
Retaining Wall ◽  
Rectangular Section ◽  
Limited Length ◽  
Length Direction ◽  
Distribution Of Stress

To study the distribution of stress in a dam with rectangular section under water, the dam was simplified a rectangular structure with limited length. Based on the theory of mechanics of elasticity a stress function was deduced which was used to calculate the stress and displacement in any point of the dam. The results show that the normal stress along the length direction was not equal to zero, but the strain along the direction equal to zero.

Stress analysis of a debonding and a crack around a circular rigid inclusion

1986 ◽  
Vol 32 (3) ◽  
pp. 169-183 ◽  
Author(s):  
Norio Hasebe ◽  
Mikiya Okumura ◽  
Takuji Nakamura
Keyword(s):  
Stress Analysis ◽  
Rigid Inclusion ◽  
Circular Rigid Inclusion

An Analysis of Power Law Viscous Materials Under a Plane-Strain Condition Using Complex Stream and Stress Functions

1981 ◽  
Vol 48 (3) ◽  
pp. 486-492 ◽  
Author(s):  
Y. S. Lee ◽  
L. C. Smith
Keyword(s):  
Stress Concentration ◽  
Stream Function ◽  
Power Law ◽  
Stress Concentration Factor ◽  
Stress Function ◽  
Concentration Factor ◽  
Viscous Medium ◽  
Biaxial Stress ◽  
Deformation Analysis ◽  
Axially Symmetric

The equilibrium and compatibility equations for nonlinear viscous materials described by the power law are solved by introducing the complex stream and stress function. The stresses, strain rates, and velocities derived from the summation form of the stream function and the product form of the stress function are identical to the results obtained from the axially symmetric field equation. The stream function solution is used in the deformation analysis of a viscous hollow cylindrical inclusion buried in an infinitely large viscous medium assuming an equal biaxial boundary stress. The stream function approach is used in determining the stress-concentration factor for a cavity in a viscous material subject to the identical boundary biaxial stress. The results agree with the results of Nadai. The effect of the strain-rate-hardening exponent, the geometry of the inclusion, and the material constants on the hoop stress-concentration factor in the interface between the inclusion and the matrix are discussed.

Coupled Thermo-Mechanical Transient Stress Analysis of Functionally Graded Gas Turbine Rotor

2015 ◽  
Author(s):  
Dinesh Patil ◽  
D. Koteswara Rao ◽  
Tarapada Roy
Keyword(s):  
Shear Stress ◽  
Stress Analysis ◽  
Gas Turbine ◽  
Power Law ◽  
Shear Deformation Theory ◽  
Axial Direction ◽  
Turbine Rotor ◽  
Functionally Graded ◽  
Graded Materials ◽  
Turbine Shaft

This paper is concerned with the coupled thermo-mechanical stress analysis of functionally graded (FG) gas turbine rotor shaft system. Gas turbine shaft may expose in high temperature environments which demands to use functionally graded materials (FGMs). The aim of the present work is to study the stresses developed in the FG turbine shaft due to temperature variations and mechanical loading due to unbalance masses. For the present analysis aluminum oxide (Al2O3) and stainless steel (SUS304) are taken as shaft materials, power law gradation is used for the determination of FG material properties of the turbine shaft. Three nodded Timoshenko beam element with six degree of freedom (DOF) per node is considered for the finite element modelling of FG shaft. First order shear deformation theory (FSDT) is used with rotary inertia, strain and kinetic energy. Solution for governing equation of motion is obtained by the Hamilton principle. Complete MATLAB code has been developed for thermosmechanical stress analysis. Comparative study between steel shaft and FG shaft have been carried out. Normal stress (σxx) on plane perpendicular to axial direction, shear stress (τxr) on plane perpendicular to axial direction in radial direction and shear stress (τxθ) on plane perpendicular to axial direction in circumferential direction are obtained against time and along radius of shaft. Also these stresses are obtained for different parameters like power law indexes and speed of rotation of shaft.

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