Crack detection in circular cylindrical shells using differential quadrature method

• The problem of crack detection in cylindrical shell structures is investigated.
• To do this, the differential quadrature method and bees algorithm has been used.
• Numerical and experimental studies on the cracked free–free shells were conducted.
• The results showed that the crack locations, sizes and depths were predicted well.

The differential quadrature method combined with an evolutionary optimization algorithm has been proposed for crack detection in cylindrical shell structures. The circumferential crack, which is assumed to be open, is modeled by the extended rotational spring. A crack with finite length divides the shell into four segments. The governing differential equations of motion of the shell are formulated based on Flugge's shell theory. Applying differential quadrature to the differential equations of each segment and the corresponding boundary and continuity conditions results in an algebraic system of equations. Then, an eigenvalue analysis is performed to obtain the natural frequencies of the cracked shell. To identify the crack parameters, an optimization problem is defined and minimized by Bees algorithm, a swarm-based evolutionary optimization technique. The integrity and applicability of the proposed method is confirmed by some experimental case studies. The results show that the crack statuses are predicted well.