Structural stress analysis

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.

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.

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.

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.

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.

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.

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.

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.