The finite element solution of inverse problems in solid mechanics

Abstract

This paper presents a numerical procedure for solving inverse/parameter identification problems in solid mechanics. Given exterior measurements the algorithm is capable of identifying geometric and material parameters within an inaccessible region. The algorithm incorporates the finite element (FE) method and its substructuring capabilities in conjunction with nonlinear programming techniques to solve for the unknown design parameters. To demonstrate the generality and effectiveness of the proposed method, a parameter identification problem of subsurface cavity detection is examined. In particular, the two-dimensional problem of an inclusion with a circular periphery and arbitrarily chosen interior geometry, in an irregularly shaped plate, is considered. Traction and displacement boundary conditions are specified on the plate boundaries. The problem involves determining the center location (C{sub x}, C{sub y}), radius (R), Young`s modulus (E) and rotation ({theta}) of the inclusion, given displacement measurements taken at various sensor locations on the exterior boundaries of the plate, In addition, the value of the above design parameters are subject to upper and lower bounds as well as linear and nonlinear geometric constraint equations. The effects of altering various input parameters such as the number of sensor locations and their positioning, and the starting values (initial guess) for the design parametersmore » are examined. To further demonstrate the effectiveness of the algorithm the practical application of subsurface crack detection is examined. The inverse/parameter identification problem reduces to determining the centroid of the superelement (C{sub x}, C{sub y}), its angle of rotation ({theta}), and the radius of the superelement (R). This paper also examines the use of the finite element method and nonlinear programming to predict fatigue crack propagation paths.« less