Crack identification in postbuckled plates using differential quadrature element method and sequential quadratic programming

In this study, an innovative method for crack identification in buckled plates using differential quadrature element method (DQEM) and sequential quadratic programming (SQP) method is proposed. This study consists of two steps. In first step, a numerical method is applied to calculate the frequencies of buckled cracked plates. Cracks are assumed to be open and modeled as linear rotational spring. Governing equations are extracted considering effects of shear deformations and initial geometric imperfection. Then, considering the solution as summation of static solution (postbuckling) and dynamic solution, the governing equations are converted into two different equation sets; postbuckling equations and vibration equations. The natural frequencies can be obtained solving these equation sets. In second step, SQP optimization method and the method used in first step combined to make a new method for identification of crack specification using natural frequencies. In this step, a weighted sum of square of differences between calculated frequencies and experimental frequencies considered as cost function and used to identify crack properties. Finally, the accuracy and precision of proposed method verified using some experimental and numerical case studies.