Load paths visualization in plane elasticity using load function method

The interaction between the inclined and curved cracks is studied. Using the complex variable function method, the formulation in hypersingular integral equations is obtained. The curved length coordinate method and suitable quadrature rule are used to solve the integral equations numerically for the unknown function, which are later used to evaluate the stress intensity factor. There are four cases of the mode stresses; Mode I, Mode II, Mode III, and Mix Mode are presented as the numerical examples.

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Singularity functions revisited: Clarifications and extensions for construction of shear–moment diagrams in beams

International Journal of Mechanical Engineering Education ◽

10.1177/0306419019829437 ◽

2019 ◽

Vol 48 (4) ◽

pp. 351-370

Author(s):

Stephen Boedo

Keyword(s):

Shear Force ◽

Function Method ◽

Mathematical Formulation ◽

Bending Moment ◽

Distributed Load ◽

Subsequent Determination ◽

Main Emphasis ◽

Load Function ◽

Points Of Discontinuity

This paper provides clarification and extension of singularity functions for the construction of shear–moment diagrams in beams and the subsequent determination of beam deflections. The mathematical formulation for impulse, polynomial, and general-form singularity functions and their integral properties is reviewed, clarified, and provided graphically in tabular form. Several examples of various complexity are presented to assist the student at evaluating the constants of integration and properly interpreting the values of shear force and bending moment in the limit of approach to points of discontinuity. The main emphasis of the paper is to demonstrate the applicability of the singularity function method for any specified distributed load function.

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Asymptotic Expansions for the Thermal Stresses in Bonded Semi-Infinite Bimaterial Strips

Journal of Electronic Packaging ◽

10.1115/1.2905383 ◽

1991 ◽

Vol 113 (2) ◽

pp. 173-177 ◽

Cited By ~ 40

Author(s):

Mikyoung Lee ◽

I. Jasiuk

Keyword(s):

Asymptotic Behavior ◽

Conformal Mapping ◽

Asymptotic Expansions ◽

Function Method ◽

Mellin Transform ◽

Thermal Stresses ◽

Plane Elasticity ◽

Airy Stress Function ◽

Stress Function Method ◽

Plane Elasticity Problem

The plane elasticity problem of two semi-infinite bimaterial strips, that undergo constant temperature change, is considered. Following Bogy (1968), we use Airy stress function method, Mellin transform, and conformal mapping to investigate the asymptotic behavior of stresses at the interface near the edge of two strips.

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Some Properties of J-Integral in Plane Elasticity

Journal of Applied Mechanics ◽

10.1115/1.1432663 ◽

2001 ◽

Vol 69 (2) ◽

pp. 195-198 ◽

Cited By ~ 4

Author(s):

Y. Z. Chen ◽

K. Y. Lee

Keyword(s):

Function Method ◽

Infinite Plate ◽

Scalar Function ◽

Plane Elasticity ◽

Reciprocal Theorem ◽

J Integral ◽

Large Circle ◽

Complex Variable Function ◽

Variable Function ◽

Complex Variable Function Method

Some properties of the J-integral in plane elasticity are analyzed. An infinite plate with any number of inclusions, cracks, and any loading conditions is considered. In addition to the physical field, a derivative field is defined and introduced. Using the Betti’s reciprocal theorem for the physical and derivative fields, two new path-independent D1 and D2 are obtained. It is found that the values of Jkk=1,2 on a large circle are equal to the values of Dkk=1,2 on the same circle. Using this property and the complex variable function method, the values of Jkk=1,2 on a large circle is obtained. It is proved that the vector Jkk=1,2 is a gradient of a scalar function Px,y.

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