Integro-Differential Equations for Stress Analysis in the Bridged Zone of Interface Cracks

2011 ◽  
pp. 287-298 ◽  
Author(s):  
M. Perelmuter
Keyword(s):  
Differential Equations ◽  
Stress Analysis ◽  
Interface Cracks

A Direct-Stress Analysis of Orthotropic Cantilever Plates

1965 ◽  
Vol 32 (1) ◽  
pp. 67-70 ◽  
Author(s):  
A. Coull
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Shear Stress ◽  
Fourier Series ◽  
Differential Equations ◽  
Stress Analysis ◽  
Plate Theory ◽  
Linear Differential Equations ◽  
Linear Differential ◽  
Ordinary Linear Differential Equations

A method is given for the direct-stress analysis of orthotropic cantilever plates, without the usual need for intermediate deflection calculations. The partial differential equation of plate theory is reduced to a set of ordinary linear differential equations by assuming Fourier-series distributions of stress couples and shear-stress resultants in the plate: The coefficients of these series are determined by the principle of least work.

scholarly journals Generalization of Haefeli’s Creep-Angle Analysis

1972 ◽  
Vol 11 (63) ◽  
pp. 447-450 ◽  
Author(s):  
R. I. Perla
Keyword(s):  
Partial Differential Equations ◽  
Stress Field ◽  
Differential Equations ◽  
Stress Analysis ◽  
Continuum Mechanics ◽  
Deformation Rate ◽  
Rate Coefficient ◽  
Partial Differential ◽  
Key Parameter

Abstract Using geometrical arguments, Haefeli developed a stress analysis for slabs of compressible viscous materials. His analysis was based on a key parameter called the creep angle. A generalization of the creep angle, called the deformation-rate coefficient, is derived by replacing geometrical arguments with continuum mechanics. Once the deformation-rate coefficient is found from in situ measurements, the stress field of the slab can be determined from a set of hyperboic partial differential equations.

scholarly journals Generalization of Haefeli’s Creep-Angle Analysis

1972 ◽  
Vol 11 (63) ◽  
pp. 447-450 ◽  
Author(s):  
R. I. Perla
Keyword(s):  
Partial Differential Equations ◽  
Stress Field ◽  
Differential Equations ◽  
Stress Analysis ◽  
Continuum Mechanics ◽  
Deformation Rate ◽  
Rate Coefficient ◽  
Partial Differential ◽  
Key Parameter

AbstractUsing geometrical arguments, Haefeli developed a stress analysis for slabs of compressible viscous materials. His analysis was based on a key parameter called the creep angle. A generalization of the creep angle, called the deformation-rate coefficient, is derived by replacing geometrical arguments with continuum mechanics. Once the deformation-rate coefficient is found from in situ measurements, the stress field of the slab can be determined from a set of hyperboic partial differential equations.

A Strip Element Method for Stress Analysis of Anisotropic Linearly Elastic Solids

1994 ◽  
Vol 61 (2) ◽  
pp. 270-277 ◽  
Author(s):  
G. R. Liu ◽  
J. D. Achenbach
Keyword(s):  
Differential Equations ◽  
Stress Analysis ◽  
Data Storage ◽  
Virtual Work ◽  
The Finite Element Method ◽  
Elastic Solids ◽  
Nonreflecting Boundary Conditions ◽  
Infinite Elements ◽  
Good Agreement ◽  
Element Method

A new numerical method, the strip element method, is presented for the stress analysis of anisotropic linearly elastic solids. For two-dimensional problems the domain is discretized in one direction into strip elements. By using the principle of virtual work, approximate governing differential equations are derived for the field dependence in the second direction. These differential equations can be solved analytically. For infinite bodies, some special features such as infinite elements and nonreflecting boundary conditions are introduced and a viscoelastic nonreflecting boundary is also presented. Numerical results for static and dynamic problems are presented and compared with exact solutions. Very good agreement is observed. The strip element method maintains the advantages of the finite element method, but it requires much less data storage. The technique can easily be extended to solids that are inhomogeneous in one direction.

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