- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- The finite element solution of inverse problems in...
Open Collections
UBC Theses and Dissertations
UBC Theses and Dissertations
The finite element solution of inverse problems in solid mechanics McCullough, Andrew David Barbour
Abstract
This thesis presents numerical procedures for solving inverse parameter identification problems in solid mechanics. These procedures are applied to the detection of subsurface flaws or cracks and to the study of propagating cracks. The procedure for detecting subsurface defects is based on the process of over-specifying the boundary conditions on the exposed surface of the structure, making an initial assessment about the damage, and then, with the use of nonlinear programming techniques, rninimizing a residual vector to reach an optimum solution. The residual vector contains unknown system parameters that characterize the internal defect. The finite element method is combined with a sequential quadratic programming algorithm to solve for these unknown parameters. The procedure utilizes finite element substructuring capabilities in order to minimize the processing and solution time for practical problems. The results obtained from the numerical study verify the accuracy of the algorithm. The finite element method and nonlinear optimization are also used to solve the inverse parameter identification problem of determining the direction a crack will propagate in a heterogeneous planar domain. This procedure involves determining the direction which produces the maximum strain energy release for a given increment of crack growth. The procedure is applied to four fracture cases of increasing complexity: a horizontal throughthickness crack in a finite plate; an inclined through-thickness crack in a finite plate; a crack parallel to a bimaterial interface; and a transverse crack in two fiber-reinforced composite materials. The results of this numerical study coincide with theoretical predictions and experimentally observed crack growth behavior.
Item Metadata
Title |
The finite element solution of inverse problems in solid mechanics
|
Creator | |
Publisher |
University of British Columbia
|
Date Issued |
1995
|
Description |
This thesis presents numerical procedures for solving inverse parameter identification
problems in solid mechanics. These procedures are applied to the detection of subsurface
flaws or cracks and to the study of propagating cracks. The procedure for detecting subsurface
defects is based on the process of over-specifying the boundary conditions on the
exposed surface of the structure, making an initial assessment about the damage, and then,
with the use of nonlinear programming techniques, rninimizing a residual vector to reach an
optimum solution. The residual vector contains unknown system parameters that characterize
the internal defect. The finite element method is combined with a sequential quadratic programming
algorithm to solve for these unknown parameters. The procedure utilizes finite
element substructuring capabilities in order to minimize the processing and solution time for
practical problems. The results obtained from the numerical study verify the accuracy of the
algorithm.
The finite element method and nonlinear optimization are also used to solve the inverse
parameter identification problem of determining the direction a crack will propagate in
a heterogeneous planar domain. This procedure involves determining the direction which
produces the maximum strain energy release for a given increment of crack growth. The
procedure is applied to four fracture cases of increasing complexity: a horizontal throughthickness
crack in a finite plate; an inclined through-thickness crack in a finite plate; a crack
parallel to a bimaterial interface; and a transverse crack in two fiber-reinforced composite
materials. The results of this numerical study coincide with theoretical predictions and experimentally
observed crack growth behavior.
|
Extent |
8079675 bytes
|
Genre | |
Type | |
File Format |
application/pdf
|
Language |
eng
|
Date Available |
2009-01-28
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
|
DOI |
10.14288/1.0080913
|
URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
|
Graduation Date |
1995-11
|
Campus | |
Scholarly Level |
Graduate
|
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.