Parallel Finite Element Procedures for Generalized Eigen- Solution with Improved Damage Detection of Bridge-Type Structures

Abstract

Serial Jacobi transformation algorithm for the solution of standard eigen-problems is re-visited to facilitate the explanation of the proposed parallel transformation algorithm, for which computational efficiency can be realized in this study through pattern recognition for the development and explanation of explicit formulas to avoid costly matrix time matrix operations. The proposed parallel Subspace Iteration and Jacobi Transformation (SI-JT) algorithm for the solution of generalized eigen-problems has also been incorporated into the improved damage identification algorithm. Computational efficiency and robust behaviors for the entire proposed procedures (eigen-solution, damaged localization, and damaged quantification) are validated through several academic and real-life numerical examples. Numerical results obtained in this research work reveal that parallel SI-JT algorithm is more robust as compared to MATLAB eigen-solver. Furthermore, the proposed damage identification method for damage localization and quantification of bridge-type structures also gives better results than existing methods.