A necessary modification for the finite element analysis of cracked members detection, construction, and justification

The finite element analysis of cracked beam-like members is investigated. Through concise formulation, computer implementation, and numerical experiment, the necessity for a paramount modification in the governing differential equation is detected. In the course of numerical analysis, physical consideration, and mathematical theory, the structure of the modification and its relation with the member geometry and crack parameters is constructed and justified. Several new chain rules for use in the application of the method of weighted residual to differential equations containing the derivatives of the Dirac’s delta distribution is proposed. Through analysis of typical examples and comparison of the results with that of the others, the accuracy, efficiency and robustness of the work are verified.