Structural stress analysis

• US 7,516,673 B2
• Filed: 06/15/2006
• Issued: 04/14/2009
• Est. Priority Date: 11/17/2000
• Status: Expired due to Term

• Current Assignee: Battelle Memorial Institute
• Original Assignee: Battelle Memorial Institute
• Inventors: Dong, Pingsha, Hong, Jeong Kyun, Zhang, Jinmiao
• Primary Examiner(s): Noori; Max
• Application Number:
  US11/424,404
• Publication Number:
  US 20060219026A1
• Time in Patent Office: 1,034 Days
• Field of Search: 737/60, 738/04, 738/08
• US Class Current: 73/760
• 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

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

 

where σ

_x(y) represents a 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

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

 

or, its mathematical equivalent

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

 

where y corresponds to a position along said selected cross section, t corresponds to said 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

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

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

${\mathrm{\sigma <br><br>}}_B=\frac{6}{t^2}<br><br>{\int <br><br>}_0^t<br><br>{\mathrm{\sigma <br><br>}}_x<br><br>\left(y\right)<br><br>\left(y-\frac{t}{2}\right)<br><br>d<br><br>y.$

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.

9. A method as claimed in claim 1, further comprising manufacturing a structure utilizing the calculated structural stress σ

_s.

10. A method as claimed in claim 9, wherein the structure comprises welded and non-welded joints, notches, ridges, bends, sharp corners, or discontinuities or sudden changes in geometry.

11. A method as claimed in claim 9, wherein the structure comprises a metallic, plastic, or ceramic structure.

12. A method as claimed in claim 9, wherein the structure is selected from the group consisting of aircraft or aerospace equipment, agricultural equipment, agricultural structures, automobiles or trucks, construction or lifting equipment, forestry equipment, minimg equipment, rail car frames, ships, submarines and submersibles;

ports and port equipment, bridges, channels or canals, tunnels, building components, building materials, appliances, buildings/skyscrapers, housing, heating and cooling systems, home improvement equipment, fencing and gates, plumbing, irrigation and drainage equipment, manufacturing equipment and machinery, diving equipment, nuclear containers and facilities, offshore oil rigs, diesel and gas turbines, pipelines, derricks and digger derricks, cooling towers, radio towers/transmitters, welded structures, tanks and cisterns, automotive parts, footwear, household components, sporting goods, ceramics, concrete, porcelain enamel, sealants and sealed structures, adhesively bonded structures, and components thereof.

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 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

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

 

where σ

_x(Y) represents a 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

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

 

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

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.

13. A method as claimed in claim 6, further comprising manufacturing a structure utilizing the calculated structural stress σ

_s.

14. A method as claimed in claim 13, wherein the structure comprises welded and non-welded joints, notches, ridges, bends, sharp corners, or other discontinuities or sudden changes in geometry.

15. A method as claimed in claim 13, wherein the structure comprises a metallic, plastic, or ceramic structure.

16. A method as claimed in claim 13, wherein the structure is selected from the group consisting of aircraft or aerospace equipment, agricultural equipment, agricultural structures, automobiles or trucks, construction or lifting equipment, forestry equipment, minimg equipment, rail car frames, ships, submarines and submersibles;

ports and port equipment, bridges, channels or canals, tunnels, building components, building materials, appliances, buildings/skyscrapers, housing, heating and cooling systems, home improvement equipment, fencing and gates, plumbing, irrigation and drainage equipment, manufacturing equipment and machinery, diving equipment, nuclear containers and facilities, offshore oil rigs, diesel and gas turbines, pipelines, derricks and digger derricks, cooling towers, radio towers/transmitters, welded structures, tanks and cisterns, automotive parts, footwear, household components, sporting goods, ceramics, concrete, porcelain enamel, sealants and sealed structures, adhesively bonded structures, and components thereof.