STRUCTURAL STRESS ANALYSIS

• US 20060219026A1
• Filed: 06/15/2006
• Published: 10/05/2006
• Est. Priority Date: 11/17/2000
• Status: Active Grant

• Current Assignee: Battelle Memorial Institute
• Original Assignee: Battelle Memorial Institute
• Inventors: Dong, Pingsha, Hong, Jeong Kyun, Zhang, Jinmiao
• Granted Patent: US 7,516,673 B2
• Time in Patent Office: Days
• US Class Current: 73/808
• CPC Class Codes: B23K 31/02 relating to soldering or welding dip or wave soldering in the manufacture of printed circuits H05K3/34
• CPC Class Codes: G01L 5/00 Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
• CPC Class Codes: G01M 5/0041 by determining deflection or stress
• CPC Class Codes: G01N 2203/0073 Fatigue
• CPC Class Codes: G01N 2203/0214 Calculations a priori without experimental data
• CPC Class Codes: G01N 2203/0216 Finite elements
• CPC Class Codes: G06F 30/23 using finite element methods [FEM] or finite difference methods [FDM]

Abstract

Structural stress in a fatigue-prone region of a structure is determined and analyzed by using: i) the nodal forces and displacement values in the fatigue-prone region, or ii) equilibrium equivalent simple stress states consistent with elementary structural mechanics in the fatigue-prone region. Of course, it is contemplated that combinations, equivalents, or variations of the recited bases may alternatively be employed.

Claims

1. A method of analyzing structural stress σ

_s in a fatigue-prone region of a structure, said method comprising;

determining a stress distribution σ

_x(y) along a selected cross section of said structure;

determining a first component σ

_M of said structural stress σ

_s in said fatigue-prone region by performing an operation having a result substantially equivalent to a result of the following first integration

${\mathrm{\sigma <br><br>}}_M=\frac{1}{t}<br><br>{\int <br><br>}_0^t<br><br>{\mathrm{\sigma <br><br>}}_X<br><br>\left(y\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>y$

where σ

_x(y) represents said through-thickness stress distribution and t corresponds to a thickness of said structure;

determining a second component σ

_B of said structural stress σ

_s in said fatigue-prone region by performing an operation having a result substantially equivalent to a solution of the following equation for σ

_B

$\left(\frac{t^2}{2}\right)<br><br>{\mathrm{\sigma <br><br>}}_M+\left(\frac{t^2}{6}\right)<br><br>{\mathrm{\sigma <br><br>}}_B={\int <br><br>}_0^t<br><br>{\mathrm{\sigma <br><br>}}_X<br><br>\left(y\right)<br><br>y<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>y$

or, its mathematical equivalent

${\mathrm{\sigma <br><br>}}_B=\frac{6}{t^2}<br><br>{\int <br><br>}_0^t<br><br>{\mathrm{\sigma <br><br>}}_X<br><br>\left(y\right)<br><br>\left(y-\frac{t}{2}\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>y$

where y corresponds to a position along said selected cross section, t corresponds to a thickness of said structure, and σ

_x(y) represents said through-thickness stress distribution; and

calculating said structural stress σ

_s by combining said first component σ

_M of said structural stress and said second component σ

_B of said structural stress.

2. A method of analyzing structural stress as claimed in claim 1 wherein said second component σ

_B of said structural stress σ

_s in said fatigue-prone region is determined by solving the following equation for σ

_B

$\left(\frac{t^2}{2}\right)<br><br>{\mathrm{\sigma <br><br>}}_M+\left(\frac{t^2}{6}\right)<br><br>{\mathrm{\sigma <br><br>}}_B={\int <br><br>}_0^t<br><br>{\mathrm{\sigma <br><br>}}_X<br><br>\left(y\right)<br><br>y<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>y.$

3. A method of analyzing structural stress as claimed in claim 1 wherein said second component σ

_B of said structural stress σ

_s in said fatigue-prone region is determined by solving the following equation for σ

_B

${\mathrm{\sigma <br><br>}}_B=\frac{6}{t^2}<br><br>{\int <br><br>}_0^t<br><br>{\mathrm{\sigma <br><br>}}_X<br><br>\left(y\right)<br><br>\left(y-\frac{t}{2}\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>y$

4. A computer-readable medium encoded with a computer program for analyzing structural stress σ

_s in a fatigue-prone region of a structure according to the method of claim 1.

5. A system for analyzing structural stress σ

_s in a fatigue-prone region of a structure according to the method of claim 1.

6. A method of analyzing structural stress σ

_s in a fatigue-prone region of a structure, said method comprising;

determining a stress distribution σ

_x(y) along a selected cross section of said structure;

determining a first component σ

_M of said structural structural stress σ

_s in said fatigue-prone region by performing an operation having a result substantially equivalent to a result of the following first integration

${\mathrm{\sigma <br><br>}}_M=\frac{1}{t}<br><br>{\int <br><br>}_0^t<br><br>{\mathrm{\sigma <br><br>}}_X<br><br>\left(y\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>y$

where σ

_x(y) represents said through-thickness stress distribution and t corresponds to the thickness of said structure;

determining a second component σ

_B of said structural stress σ

_s in said fatigue-prone region by performing an operation having a result substantially equivalent to a solution of the following equation for σ

_B

$\left(\frac{t^2}{2}\right)<br><br>{\mathrm{\sigma <br><br>}}_M+\left(\frac{t^2}{6}\right)<br><br>{\mathrm{\sigma <br><br>}}_B={\int <br><br>}_0^t<br><br>{\mathrm{\sigma <br><br>}}_X<br><br>\left(y\right)<br><br>y<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>y+\mathrm{\delta <br><br>}<br><br>{\int <br><br>}_0^t<br><br>{\mathrm{\tau <br><br>}}_{\mathrm{xy}}<br><br>\left(y\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>y$

where y corresponds to a position along said selected cross section, t corresponds to a thickness of said structure, 6 is a value defined in said representation of said structure, σ

_x(y) represents said through-thickness stress distribution, and τ

_xy(y) represents a through-thickness shear stress distribution of said structure; and

calculating said structural stress σ

_s by combining said first component σ

_M of said structural stress and said second component σ

_B of said structural stress.

7. A computer-readable medium encoded with a computer program for analyzing structural stress σ

_s in a fatigue-prone region of a structure according to the method of claim 6.

8. A system for analyzing structural stress σ

_s in a fatigue-prone region of a structure according to the method of claim 6.