Structural stress analysis
First Claim
1. A method wherein mesh insensitive structural stress σ
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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.
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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.
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Citations
49 Claims
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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. - View Dependent Claims (2, 3, 4, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26)
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s in a localized fatigue-prone weld region of a structure is calculated from a finite element model of said structure by;
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5. A method of analyzing structural stress σ
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s in a localized fatigue-prone region of a structure from a representation of the structure, said method comprising;
determining a through-thickness stress distribution σ
x(y) along a selected cross section of said structure, wherein said localized region lies adjacent to said selected cross section, and wherein said stress distribution σ
x(y) is determined from said representation of said structure;
determining a first component σ
M of said structural stress σ
s in said localized region by performing an operation having a result substantially equivalent to a result of the following first integrationwhere σ
x(y) represents said through-thickness stress distribution and t corresponds to the thickness of said structure in said selected cross section;
determining a second component σ
B of said structural stress σ
s in said localized region by performing an operation having a result substantially equivalent to a solution of the following equation for σ
Bwhere y corresponds to a distance from y=0 to a material point of interest along said selected cross section, t corresponds to the thickness of said structure in said selected cross section, 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. - View Dependent Claims (6, 7)
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s in a localized fatigue-prone region of a structure from a representation of the structure, said method comprising;
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15. A method of analyzing structural stress σ
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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
Mwhere σ
B is proportional to said sectional moment vector m and σ
M is proportional to said sectional force vector n.
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s in a localized fatigue-prone region of a structure, said method comprising;
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27. A method of analyzing structural stress σ
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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 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.
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s in a localized fatigue-prone region of a structure from a three-dimensional finite element solid model of the structure, said method comprising;
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28. 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 at least one local element for structural stress extraction, wherein said local element lies adjacent to said localized fatigue-prone region;
determining stress resultants ƒ
x′
, ƒ
z′
, and my, for said local element from said finite element solid model of said structure, wherein said stress resultants represent the sectional forces and moments for said local element; and
calculating structural stress σ
s in said localized fatigue-prone region utilizing the following equationwhere δ and
t represent dimensional values of said local element.
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s in a localized fatigue-prone region of a structure from a three-dimensional finite element solid model of the structure, said method comprising;
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29. A technique for analyzing structural stress σ
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s in a localized fatigue-prone region of a structure defining a substantially monotonic through thickness stress distribution, said technique comprising;
measuring displacement in the vicinity of said fatigue-prone region by configuring at least one measuring device to measure displacement along a first cross section of said structure offset a distance L from said fatigue-prone region, and measure displacement along a second cross section of said structure offset a distance L−
l from said fatigue prone region;
decomposing stress measurements at said strain gauges as follows where said superscript B corresponds to a measurement at said first cross section, said superscript C corresponds to a measurement at said second cross section, said subscript T corresponds to a measurement at a top surface of said structure, and said subscript B corresponds to a measurement at a bottom surface of said structure; and
approximating structural stress σ
s in said fatigue-prone region as followswhere the distances L and I are measured in terms of fractions of thickness t.
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s in a localized fatigue-prone region of a structure defining a substantially monotonic through thickness stress distribution, said technique comprising;
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30. A technique for analyzing structural stress σ
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s in a localized fatigue-prone region of a structure defining a non-monotonic through thickness stress distribution, said technique comprising;
measuring displacement in the vicinity of said fatigue-prone region by configuring at least one measuring device to measure displacement along a first cross section of said structure offset a distance L from said fatigue-prone region, measure displacement along a second cross section of said structure offset a distance L−
l from said fatigue prone region, andmeasure displacement along a third cross section of said structure, wherein said third cross section defines an approximately linear structural stress distribution;
decomposing stress measurements at said strain gauges as follows σ
bB=(σ
TB−
σ
m)σ
bC=(σ
TC−
σ
m)where said superscript B corresponds to a measurement at said first cross section, said superscript C corresponds to a measurement at said second cross section, said subscript T corresponds to a measurement at a top surface of said structure, and σ
m is a through thickness mean stress measurement taken at said third cross section; and
approximating structural stress σ
s in said fatigue-prone region as followswhere the distances L and I are measured in terms of fractions of thickness t.
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s in a localized fatigue-prone region of a structure defining a non-monotonic through thickness stress distribution, said technique comprising;
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31. 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;
determine a through-thickness stress distribution σ
x(y) along a selected cross section of said structure, wherein said localized region lies adjacent to said selected cross section;
determine a membrane component σ
M and a bending component σ
B of said structural stress σ
s in said localized region from said through thickness stress distribution σ
x(y), wherein said membrane and bending components comprise simple structural stress distributions that are equilibrium-equivalent to said through thickness stress distribution σ
x(y); and
calculate 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.
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s in a localized fatigue-prone region of a structure, said program being operative to;
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32. 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
Mwhere σ
B is proportional to said sectional moment vector m and σ
M is proportional to said sectional force vector n.
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s in a localized fatigue-prone region of a structure, said program being operative to;
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33. 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 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.
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s in a localized fatigue-prone region of a structure, said program being operative to;
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34. 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 at least one local element for structural stress extraction, wherein said local element lies adjacent to said localized fatigue-prone region;
determine stress resultants ƒ
x′
,ƒ
z′
, and my′
, for said local element from said finite element solid model of said structure, wherein said stress resultants represent the sectional forces and moments for said local element; and
calculate structural stress σ
s in said localized fatigue-prone region utilizing the following equationwhere δ and
t represent dimensional values of said local element.
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s in a localized fatigue-prone region of a structure, said program being operative to;
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35. A system for analyzing structural stress σ
-
s in a localized fatigue-prone region of a structure, said system including a controller programmed to;
determine a through-thickness stress distribution σ
x(y) along a selected cross section of said structure, wherein said localized region lies adjacent to said selected cross section;
determine a membrane component σ
M and a bending component σ
B of said structural stress σ
s in said localized region from said through thickness stress distribution σ
x(y), wherein said membrane and bending components comprise simple structural stress distributions that are equilibrium-equivalent to said through thickness stress distribution σ
x(y); and
calculate 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.
-
s in a localized fatigue-prone region of a structure, said system including a controller programmed to;
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36. A system for analyzing structural stress σ
-
s in a localized fatigue-prone region of a structure, said system including a controller programmed to;
identify local elements for structural stress extraction, wherein said local elements lie adjacent to said localized fatigue-prone region;
determin 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
Mwhere σ
B is proportional to said sectional moment vector m and σ
M is proportional to said sectional force vector n.
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s in a localized fatigue-prone region of a structure, said system including a controller programmed to;
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37. A system for analyzing structural stress σ
-
s in a localized fatigue-prone region of a structure, said system including a 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 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.
-
s in a localized fatigue-prone region of a structure, said system including a controller programmed to;
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38. A system for analyzing structural stress σ
-
s in a localized fatigue-prone region of a structure, said system including a controller programmed to;
identify at least one local element for structural stress extraction, wherein said local element lies adjacent to said localized fatigue-prone region;
determine stress resultants ƒ
x′
,71 z′
, and my, for said local element from said finite element solid model of said structure, wherein said stress resultants represent the sectional forces and moments for said local element; and
calculate structural stress σ
s in said localized fatigue-prone region utilizing the following equation
where σ and
t represent dimensional values of said local element.
-
s in a localized fatigue-prone region of a structure, said system including a controller programmed to;
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39. A system for analyzing structural stress σ
-
s in a localized fatigue-prone region of a structure, said system comprising;
at least one measuring device configured to measure displacement in the vicinity of said fatigue-prone region by measuring displacement along a first cross section of said structure offset a distance L from said fatigue-prone region, and measuring displacement along a second cross section of said structure offset a distance L−
l from said fatigue prone region; and
a controller programmed to decompose stress measurements at said strain gauges as follows
where said superscript B corresponds to a measurement at said first cross section, said superscript C corresponds to a measurement at said second cross section, said subscript T corresponds to a measurement at a top surface of said structure, and said subscript B corresponds to a measurement at a bottom surface of said structure, andapproximate structural stress σ
s in said fatigue-prone region as follows
where the distances L and l are measured in terms of fractions of thickness t.
-
s in a localized fatigue-prone region of a structure, said system comprising;
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40. A system for analyzing structural stress σ
-
s in a localized fatigue-prone region of a structure, said system comprising;
at least one measuring device configured to measure displacement in the vicinity of said fatigue-prone region by measuring displacement along a first cross section of said structure offset a distance L from said fatigue-prone region, measuring displacement along a second cross section of said structure offset a distance L−
l from said fatigue prone region, andmeasuring displacement along a third cross section of said structure, wherein said third cross section defines an approximately linear structural stress distribution; and
a controller programmed to decompose stress measurements at said strain gauges as follows σ
bB=(σ
TB−
σ
m)σ
bC=(σ
TC−
σ
m)
where said superscript B corresponds to a measurement at said first cross section, said superscript C corresponds to a measurement at said second cross section, said subscript T corresponds to a measurement at a top surface of said structure, and σ
m is a through thickness mean stress measurement taken at said third cross section; and
approximate structural stress σ
s in said fatigue-prone region as follows
where the distances L and l are measured in terms of fractions of thickness t.
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s in a localized fatigue-prone region of a structure, said system comprising;
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41. A method of analyzing structural stress in a localized fatigue-prone region of a structure, said method comprising:
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determining a through-thickness stress distribution along a selected cross section of said structure, wherein said localized region lies adjacent to said selected cross section and said through-thickness stress distribution is determined from a finite element model of said structure;
determining a membrane component and a bending component of said structural stress in said localized region from said through thickness stress distribution, wherein said membrane and bending components comprise simple structural stress distributions that are equilibrium-equivalent to said through thickness stress distribution; and
calculating said structural stress by combining said first component of said structural stress and said second component of said structural stress, wherein said membrane component and said bending component are determined such that said structural stress calculation is substantially independent of the size, shape and distribution of mesh elements defining said finite element model of said structure. - View Dependent Claims (42, 43, 44, 46, 47)
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45. A method of analyzing structural stress σ
-
s in a localized fatigue-prone region of a structure, said method comprising;
determining a through-thickness stress distribution ox(y) along a selected cross section of said structure, wherein said localized region lies adjacent to said selected cross section;
determining a membrane component σ
M and a bending component σ
B of said structural stress σ
s in said localized region from said through thickness stress 25 distribution σ
x(y), wherein said membrane and bending components comprise simple structural stress distributions that are equilibrium-equivalent to said through thickness stress distribution σ
x(y); 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.
-
s in a localized fatigue-prone region of a structure, said method comprising;
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48. 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.
-
s in a localized fatigue-prone weld region of a structure from a finite element model of said structure, said program being operative to;
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49. 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 including a 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.
-
s in a localized fatigue-prone weld region of a structure from a finite element model of said structure, said system including a controller programmed to;
Specification