Identification of welding residual stresses in rectangular plates using vibration responses(*)

(*) A preliminary version of this article has been presented in the 17th International Congress of Mechanical Engineering, promoted by Brazilian Society of Mechanical Sciences and Engineering, São Paulo, Brazil, 2003.

Abstract

A novel hybrid numerical/experimental identification procedure for the assessment of welding-induced residual stresses in rectangular plates is proposed and evaluated. This procedure explores the influence of the stress state on the dynamic responses of structural components, according to the so-named stress-stiffening effect. The technique consists in using a set of experimental natural frequencies of the welded plate and a mathematical model relating the residual stresses to the natural frequencies to formulate an optimization problem. The cost function represents the differences between the experimental and model-predicted dynamic responses and the design variables are interpreted as parameters of the mathematical model describing the stress distribution over the plate. A parameterized stress model suitable to the case of welding residual stresses is presented in terms of a differential equation that relates an Airy's stress function to the plastic strains resulting from the welding process. From this stress function, the stress components σ_x, σ_y and τ_xy (assuming plane stress state) are computed. Genetic Algorithms are used to solve the numerical optimization problem. To demonstrate the feasibility of the method, it is used for the assessment of residual stresses generated by TIG (GTAW) welding of a thin rectangular steel plate, for which experimentally measured natural frequencies and numerically computed residual stress distributions are available in the literature.

(*) A preliminary version of this article has been presented in the 17th International Congress of Mechanical Engineering, promoted by Brazilian Society of Mechanical Sciences and Engineering, São Paulo, Brazil, 2003.

Keywords:

• Stress-stiffening
• Inverse problems
• Genetic Algorithms
• Assumed-modes
• 2000 Mathematics Subject Classifications: 34A55
• 74F05
• 74H45

Acknowledgements

The authors gratefully acknowledge the Brazilian Research Council CNPq and State of Minas Gerais Research Foundation FAPEMIG for the support to their research work.

Notes

(*) A preliminary version of this article has been presented in the 17th International Congress of Mechanical Engineering, promoted by Brazilian Society of Mechanical Sciences and Engineering, São Paulo, Brazil, 2003.