Theoretical modeling and dynamic analysis of designable grillages for repairing material surface defect

Abstract

Designing structural grillages is an innovative solution to repair material surface defects. The grillages have advantages as lightweight and directionally enhanced, but their stability and stress concentration under dynamic loads may pose significant risks. Three analytical models of grillages above a semicircular defect are constructed. The analytical solution of the frequency-domain wave field around the semicircular defect under SH wave incidence is solved. The complex variable function method is introduced to simplify the wave field expression. The accuracy is verified by comparing it with classic examples. Applying the Modified Time-Frequency Transform to obtain the time-domain wave field. Based on the Multipoint Transient Input Method (MTIM), the transient surface displacement response of the grillage above the defect is derived, mainly discussing the superposition behavior of input waves in the grillage. MTIM is based on the analytical solution of local time-domain wave field and takes the time histories of the surface characteristic points as the wave input. It has been validated as an effective method for studying the dynamic response of structures. The numerical results show that grillage form, incident angle, and wave velocity ratio are important factors affecting the structural responses of grillage above the defect. This research aims to reveal the propagation characteristics of waves in grillages in filling material defects, providing theoretical guidance for the design and application of grillages in this field.

Keywords:

• Designable grillage
• wave superposition
• multipoint input
• dynamic response
• surface defect

Data availability statement

The data that support the findings of this study are available upon reasonable request from the authors.

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [11872156], the Special Fund for Basic Scientific Research in Central Universities of China-Doctoral Research and Innovation Fund Project, and the Natural Science Foundation of Heilongjiang Province of China [No. ZD2021A001].