Browse Prior Art Database

LINEAR INTERPOLATION RATIO METHOD FOR RESERVE FACTOR ESTIMATION

IP.com Disclosure Number: IPCOM000245565D
Publication Date: 2016-Mar-17
Document File: 5 page(s) / 293K

Publishing Venue

The IP.com Prior Art Database

This text was extracted from a PDF file.
This is the abbreviated version, containing approximately 51% of the total text.

Page 01 of 5

LINEAR INTERPOLATION RATIO METHOD FOR RESERVE FACTOR ESTIMATION

INTRODUCTION

This disclosure is intended for Reserve Factor (RF) estimation in the case if the structure is not changed or changes are not sufficient. The method is based on the available Load Case and Reserve Factor data of previous analysis and new Load Case data.

The analysed Load Case can be presented as the N-dimensional vector in the space of generalized forces. The N components of this vector are the Generalized Forces of Load Case (Forces, Moments, Pressure, Surface or Volume distributed Forces).

F

Old j

1

F

New 1

 


F  

Old j

     

     

     

     

...

...

F

Old ij


F [1]

New i

New

F

...

...

F

Old Nj

F

New N

The Load Cases of previous analysis can be located column by column in rectangular matrix:

F

Old 11

...

F

Old j

1

...

F

Old

N

1

...

F

Old M

1

     

     

...

...

...

...

...

...

...

 

F

Old

F

Old 1

i

...

F

Old ij

...

F

Old iN

...

F

Old iM


[2]

...

...

...

...

...

...

...

F

Old 1

N

...

F

Old Nj

...

F

Old NM Old
NN

...

F

where:
i - The generalized force component number. j - The Load Case number.

The tip of the multiplied by RF Load Case vector is the point of Acceptable Region boundary.

Figure 1: Acceptable Region


Page 02 of 5

PROBLEM TO BE SOVED AND PRIOR ART

In the usual Ratio Method New

RF is calculated using the Allowable Load of previous analysis as

the Applied Load Old


F , multiplied by Reserve Factor Old

RF due to the following equation:

Old j

magnitude

j

j

F

New

RF

F

magnitude


New magnitude

j

Old

RF

j

j

where:

F

New magnitude

  

N

1

F

    2 New
i

and

F

  

N

1

Old

F

   2 Old
ij

, see [1], [2]

magnitude

j

i

i

i - The generalized force component number.

j - The Load Case number.

This approach is correct in the case if the previous and new Load Case vectors are approximately collinear. In other case this approach is not acceptable, see figure below.

Figure 2: Non-collinear Load Cases

If the directions are different the new Load Case with lower magnitude can be out of Acceptable Region instead of previous Load Case with higher magnitude.


Page 03 of 5

DESCRIPTION

The main assumption of the proposed method is that Acceptable Region in the space of generalized forces of applied loads is convex as presented on Figure 1.

If we have found the set of previous Load Case vectors, and the attempt to represent the new Load Case as the linear combination of them is successful:

j

F

New i

N

1

j

F

Old ij

RF

Old j

x


[3]


x - the coefficients of this combination are defined as solution of linear equation set [3].

j

If all 0

xj  , the direction of vector  

New

F is inside the simplex generated by this set of previous

Load Case vectors  

Old j

F , see figure below.

Figure 3: Idea of the Linear Interpolation Ratio Metho...