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.

Development of a novel non-positive definite correspondence modified optimality criteria method for multi-objective density-based topology optimization

“…Since several methods already exist to suppress grayscale, such as the Heavyside projection method, we plan to consider its application while paying attention to the deterioration of convergence. Our proposed method uses one type of update equations of the design variable in inverse analysis, and is applicable to the parameter identification problem as an example (Kurahashi et al, 2023). We anticipate that our proposed method will be expanded to other inverse problems in future.…”

“…For the aforementioned discussion of the performance functions, topology optimization using the modified OC method and actual experiments were used to investigate the optimal structure when tensile force is applied only in the uniaxial direction, as shown in Fig. 1 (Kishida et al, 2023). From Fig.…”

Numerical studies on a proposed stepwise binarization method for the topology optimization analysis of the sloshing control problem

“…The development of topology optimization as a design problem began with the stiffness maximization problem in structural mechanics proposed by Bendsøe and Kikuchi (1988). It was also studied by Kishida and Kurahashi (2022) and Kurahashi et al (2023). Subsequently, topology optimization was expanded to the fields of fluid mechanics and thermodynamics.…”