Integral Representation for the Solution of a Crack Problem Under Stretching Pressure in Plane Asymmetric Elasticity

2007 ◽  
pp. 247-256
Author(s):  
E. Shmoylova ◽  
S. Potapenko ◽  
L. Rothenburg
Keyword(s):  
Integral Representation ◽  
Crack Problem ◽  
Asymmetric Elasticity

The Crack Problem for an Orthotropic Half Plane Stiffened by Elastic Films

1992 ◽  
Author(s):  
R. Mahajan ◽  
F. Erdogan ◽  
Y. T. Chou
Keyword(s):  
Half Plane ◽  
Crack Problem

scholarly journals Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 984
Author(s):  
Pedro J. Miana ◽  
Natalia Romero
Keyword(s):  
Integral Representation ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Function Spaces ◽  
Laguerre Functions ◽  
Addition Formula ◽  
Lebesgue Spaces ◽  
Rodrigues Formula ◽  
Generalized Laguerre Polynomials ◽  
New Family

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials. As a consequence, we give a new addition formula and an integral representation for these polynomials. Finally, we introduce a new family of fractional Lebesgue spaces and show that some of these special functions belong to them.

scholarly journals Modified duality methods for solving an elastic crack problem with Coulomb friction on the crack faces

2020 ◽  
Vol 10 (1) ◽  
pp. 276-282
Author(s):  
Robert V. Namm ◽  
Georgiy I. Tsoy
Keyword(s):  
Variational Inequality ◽  
Elastic Body ◽  
Approximation Method ◽  
Coulomb Friction ◽  
Auxiliary Problem ◽  
Crack Problem ◽  
Successive Approximation Method ◽  
Elastic Crack ◽  
Quasi Variational Inequality ◽  
Crack Faces

AbstractWe consider an equilibrium problem for an elastic body with a crack, on the faces of which unilateral non-penetration conditions and Coulomb friction are realized. This problem can be formulated as quasi-variational inequality. To solve it, the successive approximation method is applied. On each outer step of this method, we solve an auxiliary problem with given friction. We solve the auxiliary problem by using modified Lagrange functionals. Numerical results are presented.

scholarly journals On a class of analytic functions related to Robertson’s formula and subordination

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Adam Lecko ◽  
Gangadharan Murugusundaramoorthy ◽  
Srikandan Sivasubramanian
Keyword(s):  
Integral Representation ◽  
Analytic Functions ◽  
Boundary Point ◽  
Unit Disc ◽  
Starlike Functions ◽  
Analytic Formula ◽  
Growth Theorem

AbstractIn this paper, we define and study a class of analytic functions in the unit disc by modification of the well-known Robertson’s analytic formula for starlike functions with respect to a boundary point combined with subordination. An integral representation and growth theorem are proved. Early coefficients and the Fekete–Szegö functional are also estimated.

scholarly journals Two-Variable Type 2 Poly-Fubini Polynomials

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 281
Author(s):  
Ghulam Muhiuddin ◽  
Waseem Ahmad Khan ◽  
Ugur Duran
Keyword(s):  
Integral Representation ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Higher Order ◽  
Variable Type ◽  
Summation Formulas

In the present work, a new extension of the two-variable Fubini polynomials is introduced by means of the polyexponential function, which is called the two-variable type 2 poly-Fubini polynomials. Then, some useful relations including the Stirling numbers of the second and the first kinds, the usual Fubini polynomials, and the higher-order Bernoulli polynomials are derived. Also, some summation formulas and an integral representation for type 2 poly-Fubini polynomials are investigated. Moreover, two-variable unipoly-Fubini polynomials are introduced utilizing the unipoly function, and diverse properties involving integral and derivative properties are attained. Furthermore, some relationships covering the two-variable unipoly-Fubini polynomials, the Stirling numbers of the second and the first kinds, and the Daehee polynomials are acquired.

Influence of the Material and Thickness of the Specimen on an Infrared Stress Image

2004 ◽  
Vol 261-263 ◽  
pp. 1641-1646
Author(s):  
Kenji Machida ◽  
Mamtimin Gheni
Keyword(s):  
Thermal Conductivity ◽  
Hybrid Method ◽  
Thermal Conduction ◽  
Crack Problem ◽  
High Stress ◽  
High Accuracy ◽  
Problem Analysis ◽  
Principal Stresses ◽  
Distribution Form ◽  
Stress Components

The thickness dependency of the temperature image obtained by an infrared thermography was investigated using specimens with three kinds of materials and four kinds of the thickness of the specimen. Only the sum of the principal stresses which is the first invariant of stress tensor is measured, and it is impossible to measure individual stress components directly. Then, the infrared hybrid method was developed to separate individual stress components. Although the form of the contour line of low stress side differs greatly, the distribution form of high stress side was considerably alike. The stress intensity factor of material with low thermal conductivity can be estimated with high accuracy by the infrared hybrid method. On the crack problem, it was elucidated that the influence of thermal conduction is large and an inverse problem analysis is required.

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