# US 6,901,809 B2 · Structural stress analysis

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- Number: US 6,901,809 B2
- Document ID: US6901809B2
- Status: Granted
- Kind: B2
- Application number: 09/992,552
- Filed: 2001-11-16
- Published: 2002-08-22
- Granted: 2005-06-07
- Earliest claimed: 2000-11-17
- Assignees: Battelle Memorial Institute
- Inventors: Pingsha Dong; Jinmiao Zhang; Jeong Kyun Hong
- Web page: https://patentgrep.com/patent/US6901809B2

## CPC

- G01L 5/00: Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
- B23K 31/02: relating to soldering or welding
- G01M 5/0041: {by determining deflection or stress}
- G06F 30/23: using finite element methods [FEM] or finite difference methods [FDM]
- G01N 2203/0073: Fatigue
- G01N 2203/0214: Calculations a priori without experimental data
- G01N 2203/0216: Finite elements
- G01L: MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE (weighing G01G)
- B23K: SOLDERING OR UNSOLDERING; WELDING; CLADDING OR PLATING BY SOLDERING OR WELDING; CUTTING BY APPLYING HEAT LOCALLY, e.g. FLAME CUTTING; WORKING BY LASER BEAM
- G01M: TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)

## 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

### Claim 1

A method wherein mesh insensitive structural stress σs 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.

### Claim 2 (depends on 1)

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.

### Claim 3 (depends on 1)

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.

### Claim 4 (depends on 3)

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.

### Claim 5

A method of analyzing structural stress σs 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
σS=σB+σM
where σB is proportional to said sectional moment vector m and σM is proportional to said sectional force vector n.

### Claim 6 (depends on 5)

A method of analyzing structural stress as claimed in claim 5 wherein said structural stress is calculated utilizing the following equation
σ
s
=
σ
B
+
σ
M
=
12
⁢
mz
t
3
+
n
t
where t corresponds to the thickness of said structure in said fatigue-prone region and
−(t/2)≦z≦+(t/2).

### Claim 7 (depends on 5)

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.

### Claim 8 (depends on 5)

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.

### Claim 9 (depends on 5)

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.

### Claim 10 (depends on 5)

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.

### Claim 11 (depends on 10)

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.

### Claim 12 (depends on 5)

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.

### Claim 13 (depends on 5)

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

### Claim 14 (depends on 13)

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.

### Claim 15 (depends on 14)

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

### Claim 16 (depends on 14)

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.

### Claim 17

A method of analyzing structural stress σs 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
σ
s
=
σ
B
+
σ
M
=
12
⁢
mz
t
3
+
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.

### Claim 18

A device comprising: a computer-readable medium encoded with a computer program for analyzing structural stress σs 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
σS=σB+σM
where σB is proportional to said sectional moment vector m and σM is proportional to said sectional force vector n.

### Claim 19

A device comprising: a computer-readable medium encoded with a computer program for analyzing structural stress σs 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
σ
s
=
σ
B
+
σ
M
=
12
⁢
⁢
m
⁢
⁢
z
t
3
+
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.

### Claim 20

A system for analyzing structural stress σs 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
σS=σB+σM
where σB is proportional to said sectional moment vector m and σM is proportional to said sectional force vector n.

### Claim 21

A system for analyzing structural stress σs 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
σ
s
=
σ
B
+
σ
M
=
12
⁢
⁢
m
⁢
⁢
z
t
3
+
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.

### Claim 22

A device comprising:
a computer-readable medium encoded with a computer program for calculating structural stress σs 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.

### Claim 23

A system for calculating structural stress σs 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.