Structural stress analysis

• US 6,901,809 B2
• Filed: 11/16/2001
• Issued: 06/07/2005
• 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
• Primary Examiner(s): Lefkowitz, Edward
• Assistant Examiner(s): Martir, Lilybett
• Application Number:
  US09/992,552
• Publication Number:
  US 20020112548A1
• Time in Patent Office: 1,299 Days
• Field of Search: 737/89, 738/04, 738/05, 737/90, 737/91, 737/92, 737/93, 737/94, 345/420, 345/427, 345/473, 345/474, 702/42
• US Class Current: 73/789
• 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

This need is met by the present invention wherein structural stress in a fatigue-prone region of a structure is determined by using the nodal forces and displacement values in the fatigue-prone region, or equilibrium-equivalent simple stress states consistent with elementary structural mechanics in the fatigue-prone region. The determination is substantially independent of mesh size and is particularly well-suited for applications where S-N curves are used in weld fatigue design and evaluation, where S represents nominal stress or stress range and N represents the number of cycles to failure. The present invention is directed to structural stress analysis through various combinations of modeling, calculation, and direct measurement schemes.

Claims

1. A method wherein mesh insensitive structural stress σ

_s in a localized fatigue-prone weld region of a structure is calculated from a finite element model of said structure by;

identifying local elements for structural stress extraction, wherein said local elements lie adjacent to said weld region;

determining nodal displacements and nodal force and moment vectors for said local elements from said finite element model;

converting selected ones of said nodal force and moment vectors to sectional force vectors n and moment vectors m, wherein said conversion is performed in a work equivalent manner with respect to said nodal displacements determined for said nodal force and moment vectors; and

calculating said structural stress from said sectional force vectors n and moment vectors m.

2. A method as claimed in claim 1 wherein said conversion is performed such that a quantity of work corresponding to said nodal displacements and nodal force and moment vectors is equivalent to a quantity of work for said nodal displacements and said sectional force and moment vectors n and m.

3. A method as claimed in claim 1 wherein said nodal force and moment vectors are converted to sectional force vectors n and moment vectors m with a mapping function corresponding to said finite element model.

4. A method as claimed in claim 3 wherein said mapping function is selected such that said sectional force vector n has units of force per unit length and said sectional moment vector m has units of moment per unit length.

5. A method of analyzing structural stress σ

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

identifying local elements for structural stress extraction, wherein said local elements lie adjacent to said localized fatigue-prone region;

determining nodal force and moment vectors for said local elements;

converting selected ones of said nodal force and moment vectors to sectional force vectors n and moment vectors m with an appropriate mapping function, wherein said mapping function is selected such that said sectional force vector n has units of force per unit length and said sectional moment vector m has units of moment per unit length; and

calculating said structural stress utilizing the following equation

σ

_S=σ

_B+σ

_M

where σ

_B is proportional to said sectional moment vector m and σ

_M is proportional to said sectional force vector n.

6. A method of analyzing structural stress as claimed in claim 5 wherein said structural stress is calculated utilizing the following equation ${\sigma }_{}$

s=σ

B+σ

M=12⁢

mzt3+nt

where t corresponds to the thickness of said structure in said fatigue-prone region and

−

(t/2)≦

z≦

+(t/2).

7. A method of analyzing structural stress as claimed in claim 5 wherein said nodal force and moment vectors are retrieved directly from a finite element model of said structure.

8. A method of analyzing structural stress as claimed in claim 5 wherein said nodal force and moment vectors are determined by generating a stiffness matrix for said local element from a finite element model of said structure and computing said nodal force and moment vectors from said stiffness matrix.

9. A method of analyzing structural stress as claimed in claim 5 wherein said nodal force and moment vectors are determined by:

generating from a finite element model of said structure stiffness matrices and nodal displacements for the local elements in said fatigue-prone region;

multiplying said stiffness matrices and said nodal displacements to obtain global nodal force and moment vectors at nodal points of said local elements; and

transforming global force and moment vectors from the global coordinate system to the local coordinate system of an element of interest.

10. A method of analyzing structural stress as claimed in claim 5 wherein said nodal force and moment vectors are determined by transforming stiffness matrices and nodal displacements to global and local coordinates and solving for force and moment vectors of said local element.

11. A method of analyzing structural stress as claimed in claim 10 wherein said global coordinates of said stiffness matrices and nodal displacements are used to determine nodal force and moment vectors of said local element of interest.

12. A method of analyzing structural stress as claimed in claim 5 wherein said fatigue-prone region includes a weld and wherein said mapping function is selected according to characteristics of said weld.

13. A method of analyzing structural stress as claimed in claim 5 wherein said mapping function is a linear function.

14. A method of analyzing structural stress as claimed in claim 13 wherein said mapping function defines a magnitude that progresses linearly from a minimum value to a maximum value between adjacent nodes of said local element.

15. A method of analyzing structural stress as claimed in claim 14 wherein said mapping function is a non-linear function.

16. A method of analyzing structural stress as claimed in claim 14 wherein said mapping function is a bi-linear mapping function comprising a combination of a first linear mapping function from a first node N₁ to a virtual node N₃ and a second linear function from said virtual node N₃ to a second node N₂.

17. A method of analyzing structural stress σ

_s in a localized fatigue-prone region of a structure from a three-dimensional finite element solid model of the structure, said method comprising;

identifying a group of elements for structural stress extraction, wherein said local elements lie adjacent to said localized fatigue-prone region;

determining nodal forces for said local elements from said finite element solid model of said structure;

converting selected ones of said nodal force vectors to equivalent sectional forces and moments along a selected cross section including said localized fatigue-prone region; and

calculating said structural stress utilizing the following equation ${\mathrm{\sigma <br><br>}}_s={\mathrm{\sigma <br><br>}}_B+{\mathrm{\sigma <br><br>}}_M=\frac{12<br><br>\mathrm{mz}}{t^3}+\frac{n}{t}$

where m comprises a sectional moment vector, n comprises a sectional force vector, t corresponds to the thickness of said structure in the fatigue-prone region, and z ranges from +t/2 at a top surface of said structure to −

t/2 at a bottom surface of said structure.

18. A device comprising:

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

_s in a localized fatigue-prone region of a structure, said program being operative to;

identify local elements for structural stress extraction, wherein said local elements lie adjacent to said localized fatigue-prone region;

determine nodal force and moment vectors for said local elements;

convert selected ones of said nodal force and moment vectors to sectional force vectors n and moment vectors m with an appropriate mapping function, wherein said mapping function is selected such that said sectional force vector n has units of force per unit length and said sectional moment vector m has units of moment per unit length; and

calculate said structural stress utilizing the following equation

σ

_S=σ

_B+σ

_M

where σ

_B is proportional to said sectional moment vector m and σ

_M is proportional to said sectional force vector n.

19. A device comprising:

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

_s in a localized fatigue-prone region of a structure, said program being operative to;

identify a group of elements for structural stress extraction, wherein said local elements lie adjacent to said localized fatigue-prone region;

determine nodal forces for said local elements from said finite element solid model of said structure;

convert selected ones of said nodal force vectors to equivalent sectional forces and moments along a selected cross section including said localized fatigue-prone region; and

calculating said structural stress utilizing the following equation ${\mathrm{\sigma <br><br>}}_s={\mathrm{\sigma <br><br>}}_B+{\mathrm{\sigma <br><br>}}_M=\frac{12<br><br>\text{\hspace{1em}<br><br>}<br><br>m<br><br>\text{\hspace{1em}<br><br>}<br><br>z}{t^3}+\frac{n}{t}$

where m comprises a sectional moment vector, n comprises a sectional force vector, t corresponds to the thickness of said structure in the fatigue-prone region, and z ranges from +t/2 at a top surface of said structure to −

t/2 at a bottom surface of said structure.

20. A system for analyzing structural stress σ

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

a programmable controller programmed to

identify local elements for structural stress extraction, wherein said local elements lie adjacent to said localized fatigue-prone region;

determine nodal force and moment vectors for said local elements;

convert selected ones of said nodal force and moment vectors to sectional force vectors n and moment vectors m with an appropriate mapping function, wherein said mapping function is selected such that said sectional force vector n has units of force per unit length and said sectional moment vector m has units of moment per unit length; and

calculate said structural stress utilizing the following equation

σ

_S=σ

_B+σ

_M

 

where σ

_B is proportional to said sectional moment vector m and σ

_M is proportional to said sectional force vector n.

21. A system for analyzing structural stress σ

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

a programmable controller programmed to

identify a group of elements for structural stress extraction, wherein said local elements lie adjacent to said localized fatigue-prone region;

determine nodal forces for said local elements from said finite element solid model of said structure;

convert selected ones of said nodal force vectors to equivalent sectional forces and moments along a selected cross section including said localized fatigue-prone region; and

calculate said structural stress utilizing the following equation

${\mathrm{\sigma <br><br>}}_s={\mathrm{\sigma <br><br>}}_B+{\mathrm{\sigma <br><br>}}_M=\frac{12<br><br>\text{\hspace{1em}<br><br>}<br><br>m<br><br>\text{\hspace{1em}<br><br>}<br><br>z}{t^3}+\frac{n}{t}$

 

where m comprises a sectional moment vector, n comprises a sectional force vector, t corresponds to the thickness of said structure in the fatigue-prone region, and z ranges from +/2 at a top surface of said structure to −

t/2 at a bottom surface of said structure.

22. A device comprising:

a computer-readable medium encoded with a computer program for calculating structural stress σ

_s in a localized fatigue-prone weld region of a structure from a finite element model of said structure, said program being operative to;

identify local elements for structural stress extraction, wherein said local elements lie adjacent to said weld region;

determine nodal displacements and nodal force and moment vectors for said local elements from said finite element model;

convert selected ones of said nodal force and moment vectors to sectional force vectors n and moment vectors m, wherein said conversion is performed in a work equivalent manner with respect to said nodal displacements determined for said nodal force and moment vectors; and

calculate said structural stress from said sectional force vectors n and moment vectors m.

23. A system for calculating structural stress σ

_s in a localized fatigue-prone weld region of a structure from a finite element model of said structure, said system comprising;

a programmable controller programmed to

identify local elements for structural stress extraction, wherein said local elements lie adjacent to said weld region;

determine nodal displacements and nodal force and moment vectors for said local elements from said finite element model;

convert selected ones of said nodal force and moment vectors to sectional force vectors n and moment vectors m, wherein said conversion is performed in a work equivalent manner with respect to said nodal displacements determined for said nodal force and moment vectors; and

calculate said structural stress from said sectional force vectors n and moment vectors m.