An Application of Conformal Mapping to Fracture Analysis of Composite Plate with Curved Crack

2011 ◽  
Vol 121-126 ◽  
pp. 1759-1763
Author(s):  
Jun Lin Li ◽  
Hai Xia Cheng
Keyword(s):  
Stress Intensity Factor ◽  
Conformal Mapping ◽  
Composite Plate ◽  
Mapping Function ◽  
Fracture Analysis ◽  
Curved Crack ◽  
Special Stress ◽  
Parabolic Crack ◽  
Stress Boundary Conditions ◽  
Stress Boundary

Fracture problem about anisotropic composite plate of curved crack is researched with the help of appropriate conformal mapping. The crack curve is transformed into a unit circle by the quoted conformal mapping function. Based on the stress boundary conditions, the special stress function is found and the expressions for the stress field and the stress intensity factor near the parabolic crack tip are obtained.

A Complete Solution for Thermal-Elastohydrodynamic Lubrication of Line Contacts Using Circular Non-Newtonian Fluid Model

1992 ◽  
Vol 114 (3) ◽  
pp. 540-551 ◽  
Author(s):  
Hsing-Sen S. Hsiao ◽  
Bernard J. Hamrock
Keyword(s):  
Boundary Conditions ◽  
Newtonian Fluid ◽  
Energy Equation ◽  
Control Volume ◽  
Fluid Model ◽  
Complete Solution ◽  
Circular Model ◽  
Line Contacts ◽  
Stress Boundary Conditions ◽  
Stress Boundary

A complete solution is obtained for elastohydrodynamically lubricated conjunctions in line contacts considering the effects of temperature and the non-Newtonian characteristics of lubricants with limiting shear strength. The complete fast approach is used to solve the thermal Reynolds equation by using the complete circular non-Newtonian fluid model and considering both velocity and stress boundary conditions. The reason and the occasion to incorporate stress boundary conditions for the circular model are discussed. A conservative form of the energy equation is developed by using the finite control volume approach. Analytical solutions for solid surface temperatures that consider two-dimensional heat flow within the solids are used. A straightforward finite difference method, successive over-relaxation by lines, is employed to solve the energy equation. Results of thermal effects on film shape, pressure profile, streamlines, and friction coefficient are presented.

Boundary-layer equations in the linear theory of thin elastic shells

1962 ◽  
Vol 269 (1339) ◽  
pp. 481-491 ◽  
Keyword(s):  
Boundary Layer ◽  
Elastic Shell ◽  
Three Dimensional ◽  
Boundary Layer Equations ◽  
Smooth Edge ◽  
Elasticity Equations ◽  
Edge Conditions ◽  
Isotropic Elasticity ◽  
Stress Boundary Conditions ◽  
Stress Boundary

Starting with the three-dimensional equations of classical isotropic elasticity, equations are obtained for boundary-layer effects near any smooth edge of an elastic shell. Solutions of these equations are combined with solutions of the equations of the 'interior’ problem so that any specified edge conditions in terms of stresses can be satisfied. The usual Kirchhoff stress boundary conditions for the major terms of the interior stresses are deduced from the analysis.

Dynamic thermo-elastic response of a discrete multi-layered cylindrical shell subjected to transient thermal loading

2008 ◽  
Vol 222 (4) ◽  
pp. 549-561 ◽  
Author(s):  
J Y Zheng ◽  
X D Wu ◽  
Y J Chen ◽  
G D Deng ◽  
Q M Li ◽  
...  
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Thermal Loading ◽  
Elastic Response ◽  
Elastic Part ◽  
Dynamic Part ◽  
Layered Cylindrical Shell ◽  
Stress Boundary Conditions ◽  
Transient Thermal ◽  
Stress Boundary

Explosion containment vessels (ECVs) are used to fully contain the effects of explosion events. A discrete multi-layered cylindrical shell (DMC) consisting of a thin inner cylindrical shell and helically cross-winding flat steel ribbons has been proposed, which has obvious advantages of fabrication convenience and low costs. The applications of ECVs are closely associated with blast and thermal loads, and thus, it is important to understand the response of a DMC under transient thermal load in order to develop a design code and operation procedures for the use of DMC as ECV. In this paper, a mathematical model for the elastic response of a DMC subjected to thermal loading due to rapid heating is proposed. Based on the axisymmetric plane strain assumption, the displacement solution of the dynamic equilibrium equations of both inner shell and outer ribbon layer are decomposed into two parts, i.e. a thermo-elastic part satisfying inhomogeneous stress boundary conditions and a dynamic part for homogeneous stress boundary conditions. The thermo-elastic part is solved by a linear method and the dynamic part is determined by means of finite Hankel transform and Laplace transform. The thermo-elastic solution of a DMC is compared with the solution of a monobloc cylindrical shell, and numerical results are presented and discussed in terms of winding angle and material parameters.

scholarly journals Complex Variable Solutions for Forces and Displacements of Circular Lined Tunnels

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xingbo Han ◽  
Yongxu Xia ◽  
Xing Wang ◽  
Lunlei Chai
Keyword(s):  
Rock Mass ◽  
Complex Variable ◽  
Earth Pressure ◽  
Complex Variable Method ◽  
Complex Potentials ◽  
Variable Method ◽  
Lateral Earth Pressure ◽  
Series Expression ◽  
Stress Boundary Conditions ◽  
Stress Boundary

A complex variable method for solving the forces and displacements of circular lined tunnels is presented. Complex potentials for the stresses and displacements are expressed in the term of series expression. The undetermined coefficients of the complex potentials are obtained according to the stress boundary conditions along the lining inner surface and the displacement and surface traction boundary condition along the lining and rock-mass interface. Solutions for the stresses and displacements of the tunnel lining and rock-mass are then established by applying Muskhekishvili’s complex variable method. In addition, forces solutions for linings are presented based on the tangential stress at the two boundaries. Examples are finally established to reveal the applicability and accuracy of the proposed method. The effects of the degrees from the tunnel crown to the invert, coefficient of the lateral earth pressure, and distance from the rock-mass to the interface on the regulations of the lining forces and rock-mass stresses are also thoroughly investigated.

A Stress Analysis of the Circular Orifice Problem for 2k Periodic Radial Cracks

2015 ◽  
Vol 744-746 ◽  
pp. 1611-1617
Author(s):  
Lu Guan
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Analytical Solution ◽  
Conformal Mapping ◽  
Stress Analysis ◽  
Complex Analysis ◽  
Crack Tip ◽  
Circular Orifice ◽  
Radial Cracks

Using the method of complex analysis, the study investigates the circular orifice problem for 2k periodic radial cracks through constructing conformal mapping, and provides an analytical solution for the crack-tip stress intensity factor (SIF). From this we have simulated the circular orifice problems of cross-shaped cracks, symmetrical eight-cracks, single cracks, symmetrical double-cracks, and symmetrical four-cracks.

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