Numerical studies for defect topology identification based on the adjoint variable and the finite element methods

Abstract

This paper describes the visualization of defect regions in a structure via hammering test that employs the level set type topology optimization based on the concept of the phase-field method. In this study, the residual between the calculated displacement and the observed displacement is defined as the performance function, with the identification problem of defect regions being formulated based on the adjoint variable and finite element methods. Numerical experiments were performed to investigate the effect of the regularization parameter, the number of observation point, the evaluation equation of convergence and the application of the weighted gradient. Consequently, it was found that the number, position and size of defect can be adjusted using the regularization parameter τ. In addition, it was seen that if the number of observation points and the evaluation equation in the iterative computation of topology update are appropriately given, the identified defect topology is close to the exact defect topology. Furthermore, it was found that defect topologies can be more accurately identified by applying weighted sensitivities.

Keywords

• topology optimization
• level set method
• phase-field method
• shape identification
• adjoint variable method
• finite element method
• hammering test
• weighted sensitivity