Defect topology identification analysis using hammering response data based on level-set type topology optimization

Abstract

In this study, we present numerical results for the defect topology identification based on the adjoint variable and the finite element methods. The performance function is defined by the time integration of square value of difference between the computed and the observed displacements, and we solve the problem that unknown defect topology is identified so as to minimize the performance function. As for the constraint condition for the performance function, the equation of motion is introduced, and the performance function is extended by the adjoint variable method. We can obtain the Lagrange function, the first variation of the Lagrange function is calculated. Consequently, the gradient of the Lagrange function with respect to the level-set function is obtained, and the defect topology is finally obtained by solving the reaction diffusion equation using this gradient. Some numerical results are shown in this study.