Amirkabir University of Technology Amirkabir Journal of Mechanical Engineering 2008-6032 51 3 2019 08 23 Crack identification in postbuckled plates using differential quadrature element method and sequential quadratic programming Crack identification in postbuckled plates using differential quadrature element method and sequential quadratic programming 51 60 2906 10.22060/mej.2018.13543.5660 FA Hesam Makvandi Department of mechanical engineering, Faculty of engineering, Shahid Chamran university of Ahvaz, Ahvaz, Iran Shapour Moradi Davood Poorveis Department of Civil Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran Kourosh Heidari Shirazi Department of Mechanical Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz ,Ahvaz, Iran Journal Article 2017 10 14 <span style="letter-spacing: .05pt;">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.</span> <span style="letter-spacing: .05pt;">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.</span> https://mej.aut.ac.ir/article_2906_9e82757e9a1c12cb710ad680db11f6f1.pdf