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UBC Theses and Dissertations

The finite element solution of inverse problems in solid mechanics McCullough, Andrew David Barbour


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.

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