Method for analyzing stress in an object

Patent metadata

Field	Value
Publication number	US-10036677-B2
Application number	US-201715653855-A
Country	US
Kind code	B2
Filing date	Jul 19, 2017
Priority date	Jul 22, 2016
Publication date	Jul 31, 2018
Grant date	Jul 31, 2018

Abstract

A method for analyzing stress in an object according to spectrum data is provided. The spectrum data is obtained from an interference fringe pattern of the object that results from performing photoelasticity. The method includes: analyzing the spectrum data to obtain three sets of intensity data related respectively to different wavelengths of light used in photoelasticity; calculating wrapped phases according to the three sets of intensity data, respectively; calculating preliminary stress values according to the wrapped phases, respectively; determining a system of stress equations according to a relation among the preliminary stress values; and calculating an estimated stress value using the system of stress equations.

First claim

What is claimed is:

1. A method for analyzing stress in an object according to spectrum data, the spectrum data being obtained from an interference fringe pattern (IFP) of the object that results from performing photoelasticity, the method comprising the steps of:
a) analyzing the spectrum data to obtain three sets of intensity data that are related respectively to different wavelengths of light used in photoelasticity;
b) calculating three wrapped phases according to the three sets of intensity data, respectively;
c) calculating three preliminary stress values according to the wrapped phases, respectively, wherein each of the preliminary stress values is directly proportional to a product of a corresponding one of the wrapped phases and a linear function of a corresponding one of the wavelengths;
d) determining a system of stress equations according to a relation among the preliminary stress values; and
e) calculating an estimated stress value based on the preliminary stress values using the system of stress equations determined in step d).

2. The method of claim 1 , wherein, in step b) each of the wrapped phases is calculated by substituting a corresponding one of the sets of intensity data into one of the inverse sine function, the inverse cosine function and the inverse tangent function.

3. The method of claim 1 , wherein, in step c), the preliminary stress values are calculated based on

S
w

=

A
⁢

⁢
λ

+
B

π

⁢

δ
w

,

where S w denotes the preliminary stress values, λ denotes a corresponding one of the wavelengths, A and B are known parameters related to characteristics of material of the object, and δ w denotes a corresponding one of the wrapped phases.

4. The method of claim 3 , wherein step d) includes the sub-steps of:
d10) determining whether the relation among the preliminary stress values satisfies S wλ 1 =S wλ 2 =S wλ 3 , where S wλ 1 denotes a first preliminary stress value of the preliminary stress values that corresponding a first wavelength λ 1 of the wavelengths, S wλ 2 denotes a second preliminary stress value of the preliminary stress values that corresponding a second wavelength λ 2 of the wavelengths, S wλ 3 denotes a third preliminary stress value of the preliminary stress values that corresponding a third wavelength λ 3 of the wavelengths, and λ 1 >λ 2 >λ 3 ; and
d11) when the determination made in sub-step d10) is affirmative, making the following system of candidate equations the system of stress equations
S= 2 i 1 ( Aλ 1 +B )+ S wλ 1
S= 2 i 1 ( Aλ 2 +B )+ S wλ 2 ,
S= 2 i 1 ( Aλ 3 +B )+ S wλ 3

where S denotes the estimated stress value, and i 1 denotes a rounding integer part of a fringe order of the IFP corresponding to the first wavelength λ 1 .

5. The method of claim 3 , wherein step d) includes the following sub-steps of:
d20) determining whether the relation among the preliminary stress values satisfies S wλ 1 =S wλ 2 ≠S wλ 3 , where S wλ 1 denotes a first preliminary stress value of the preliminary stress values that corresponding a first wavelength λ 1 of the wavelengths, S wλ 2 denotes a second preliminary stress value of the preliminary stress values that corresponding a second wavelength λ 2 of the wavelengths, S wλ 3 denotes a third preliminary stress value of the preliminary stress values that corresponding a third wavelength λ 3 of the wavelengths, and λ 1 >λ 2 >λ 3 ;
d21) when the determination made in sub-step d20) is affirmative, determining whether the relation between the second and third preliminary stress values S wλ 2 , S wλ 3 satisfies S wλ 2 >S wλ3 ; and
d22) when the determination made in sub-step d21) is negative, making the following system of candidate equations the system of stress equations
S= 2 i 1 ( Aλ 1 +B )− S wλ 1

S= 2 i 1 ( Aλ 2 +B )− S″ wλ 2 ,

S= 2 i 1 ( Aλ 3 +B )− S″ wλ 3

where S denotes the estimated stress value, and i 1 denotes a rounding integer part of a fringe order of the IFP corresponding to the first wavelength λ 1 .

6. The method of claim 5 , wherein step d) further includes the sub-steps of:
d23) when the determination made in sub-step d21) is affirmative, determining whether the relation between the second and third preliminary stress values S wλ 2 , S wλ 3 satisfies S wλλ 2 =S′ wλ 3 =2(Aλ 3 +B)−S wλ 3 ; and
d24) when the determination made in sub-step d23) is affirmative, making the following system of candidate equations the system of stress equations
S= 2 i 1 ( Aλ 1 +B )+ S wλ 1
S= 2 i 1 ( Aλ 2 +B )+ S wλ 2
S= 2 i 1 ( Aλ 3 +B )+ S′ wλ 3 .

7. The method of claim 6 , wherein step d) further includes the sub-step of:
d25) when the determination made in sub-step d23) is negative, making the following system of candidate equations the system of stress equations
S= 2 i 1 ( Aλ 1 +B )+ S wλ 1
S= 2 i 1 ( Aλ 2 +B )+ S′ wλ 2 ,
S= 2 i 1 ( Aλ 3 +B )+ S′ wλ 3

where S′ wλ 2 =2(Aλ 2 +B)−S wλ2 .

8. The method of claim 3 , wherein step d) includes the following sub-steps of:
d30) determining whether the relation among the preliminary stress values satisfies S wλ 1 ≠S wλ 2 =S wλ 3 , where S wλ 1 denotes a first preliminary stress value of the preliminary stress values that corresponding a first wavelength λ 1 of the wavelengths, S wλ 2 denotes a second preliminary stress value of the preliminary stress values that corresponding a second wavelength λ 2 of the wavelengths, S wλ 3 denotes a third preliminary stress value of the preliminary stress values that corresponding a third wavelength λ 3 of the wavelengths, and λ 1 >λ 2 >λ 3 ;
d31) when the determination made in sub-step d30) is affirmative, determining whether the relation between the first and second preliminary stress values S wλ 1 , S wλ 2 satisfies S wλ 1 >S wλ 2 ; and
d32) when the determination made in sub-step d31) is affirmative, making the following system of candidate equations the system of stress equations
S= 2 i 1 ( Aλ 1 +B )− S wλ 1

S= 2 i 1 ( Aλ 2 +B )− S wλ 2 ,

S= 2 i 1 ( Aλ 3 +B )+ S wλ 3

where S denotes the estimated stress value, and i 1 denotes a rounding integer part of a fringe order of the IFP corresponding to the first wavelength λ 1 .

9. The method of claim 8 , wherein step d) further includes the sub-step of:
d33) when the determination made in sub-step d31) is negative, making the following system of candidate equations the system of stress equations
S= 2 i 1 ( Aλ 1 +B )+ S wλ 1
S= 2 i 1 ( Aλ 2 +B )+ S wλ 2 ,
S= 2 i 1 ( Aλ

Assignees

• Univ Nat Tsing Hua

Inventors

• Wang Wei-Chung
• Sung Po-Chi
• Chiang Yu-An
• HUNG Te-Heng

Classifications

• G06F2111/10

  Numerical modelling · CPC title

• G06F30/20

  Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30) · CPC title

• G06F17/17

  Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method ({G06F17/18 takes precedence } ; interpolation for numerical control G05B19/18) · CPC title

• G06F17/13

  Differential equations (using digital differential analysers G06F7/64) · CPC title

• G06F17/12

  Simultaneous equations {, e.g. systems of linear equations} · CPC title