Photoelastic studies of the two-dimensional dynamic stress-optic law

A semi-analytical method is proposed to determine the dynamic stress intensity factor of two-dimensional V-notch problems. A group of geometrically similar elements is automatically generated layer by layer around the point of singularity. The large number of degrees of freedom around the V-notch tip are transformed to a small set of generalized coordinates by means of the series expansion formulas of the displacement field. By taking advantage of the same stiffness and similar mass of 2D similarly shaped elements, a single transformation of the stiffness and mass for the first two layers of mesh is enough for all. As an example, the three points bending specimen with V-notch is analyzed.

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Ivestigation of the Dynamic Stress State of Foam Media in Cosserat Elasticity

Mechanics and Mechanical Engineering ◽

10.2478/mme-2018-0058 ◽

2020 ◽

Vol 22 (3) ◽

pp. 739-750

Author(s):

Heorhiy Sulym ◽

Olena Mikulich ◽

Vasyl’ Shvabyuk

Keyword(s):

Fourier Transform ◽

Stress State ◽

Dynamic Stress ◽

Integral Equation Method ◽

Stationary Problem ◽

Cosserat Continuum ◽

Boundary Integral ◽

Two Dimensional ◽

The Fourier Transform ◽

The Time Domain

AbstractThe paper presents studies on the application of the boundary integral equation method for investigation of dynamic stress state of foam media with tunnel cavities in Cosserat continuum. For the solution of the non-stationary problem, the Fourier transform for time variable was used. The potential representations of Fourier transform displacements and microrotations are written. The fundamental functions of displacements and microrotations for the two-dimensional case of Cosserat continuum are built. Thus, the fundamental functions of displacement for the time-domain problem are derived as the functions of the two-dimensional isotropic continuum and the functions, which are responsible for the effect of shear-rotation deformations. The method of mechanical quadrature is applied for numerical calculations. Numerical example shows the comparison of distribution of dynamic stresses in the foam medium with the cavity under the action of impulse load accounting for the shear-rotation deformations effect and without accounting for this effect.

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Shear Difference Method and Application in Orthotropic Photoelasticity

Journal of Engineering Materials and Technology ◽

10.1115/1.3443391 ◽

1976 ◽

Vol 98 (4) ◽

pp. 369-374 ◽

Cited By ~ 10

Author(s):

C. E. Knight ◽

H. Pih

Keyword(s):

Plane Stress ◽

Difference Method ◽

Two Dimensional ◽

The Third ◽

Material Orientation ◽

Stress Components ◽

Tensile Strip ◽

Principal Directions ◽

Stress Optic Law ◽

Good Agreement

The shear difference method is developed here for application to orthotropic photoelasticity problems. The two-dimensional stress-optic law which was presented in another paper is used. The stress-optic law provides two equations for the three plane stress components and the shear difference method may be used to obtain the third relation. This paper presents the development of the general orthotropic shear difference method for any material orientation. For orientations aligned with the material principal directions, the relations are identical to the isotropic shear difference method. The solution of an orthotropic tensile strip with a central hole demonstrates application of the orthotropic shear difference method and further confirms the orthotropic stress-optic law. Good agreement was found between the photoelastic and theoretical solutions.

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Two-Dimensional Dynamic Stress Behavior of Sheet Glass Caused by a Continuous Step Input from a Cylindrical Loader

International Journal of Automation Technology ◽

10.20965/ijat.2016.p0401 ◽

2016 ◽

Vol 10 (3) ◽

pp. 401-410 ◽

Cited By ~ 1

Author(s):

Akira Chiba ◽

◽

Hirofumi Hidai ◽

Souta Matsusaka ◽

Noboru Morita ◽

...

Keyword(s):

Stress Distribution ◽

Sheet Glass ◽

Contact Stress ◽

Glass Surface ◽

Dynamic Stress ◽

Stress Component ◽

Stress Model ◽

Two Dimensional ◽

Stress Behavior ◽

Contact Stress Distribution

The distribution of dynamic stress in sheet glass, stress which is caused by a continuous step input from a cylindrical loader, was estimated by considering elastic wave propagation. In modeling the dynamic stress behavior, we used a two-dimensional dynamic stress model combining a plane stress model and the equations of motion. A finite-difference method was used in the numerical calculation. Under damped vibration mode conditions, the dynamic stress behavior in the sheet glass was investigated in both the depth (Z) and horizontal (X) directions. The stress component in the Z direction changed from tensile to compressive near the outside glass surface of the contact stress distribution. The stress component in the X direction changed from compressive to tensile in the Z direction under the glass surface at the center of the contact stress distribution. The overshoot of the dynamic stress in the Z direction was 1.8 times that of the steady stress during an elapsed time of less than 1 ns from the beginning of loading.

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Dynamic Stress Analysis Around a Circular Cavity in Two-Dimensional Inhomogeneous Medium with Density Variation

Journal of Mechanics ◽

10.1017/jmech.2016.7 ◽

2016 ◽

Vol 32 (5) ◽

pp. 519-526

Author(s):

B.-P. Hei ◽

Z.-L. Yang ◽

B.-T. Sun ◽

D.-K. Liu

Keyword(s):

Stress Concentration ◽

Helmholtz Equation ◽

Inhomogeneous Medium ◽

Dynamic Stress ◽

Complex Function ◽

Transformation Method ◽

Dynamic Stress Concentration ◽

Circular Cavity ◽

Two Dimensional ◽

Complex Function Theory

AbstractBased on the complex function theory and the homogenization principle, an universal approach of solving the dynamic stress concentration around a circular cavity in two-dimensional (2D) inhomogeneous medium is developed. The Helmholtz equation with variable coefficient is converted to the standard Helmholtz equation by means of the general conformal transformation method (GCTM) analytically. As an example, the inhomogeneous medium with density varying as a function of two spatial coordinates and the constant elastic modulus is studied. The dynamic stress concentration factors (DSCF) are calculated numerically. It shows that medium inhomogeneous parameters and wave numbers have significant influence on the dynamic stress concentration by the circular cavity in two-dimensional inhomogeneous medium.

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