Modal analysis of cracked plates by way of discrete least squares meshless method

For over two decades, mesh-free methods have been developed to avoid costly mesh generation in structural analysis using computational dynamics. Among these methods, the discrete least squares meshless (DLSM) method has shown significant potential. Previous studies have introduced DLSM for cracked plates but with limited validation (single crack configuration, few frequencies, no mode shape presentation and regular nodal distributions only). The present study provides a substantially more comprehensive assessment. Two distinct crack configurations (edge crack and centre crack) are analysed using moving least squares approximation and a cubic spline weight function. The visibility technique models crack-induced discontinuities. Novel contributions include: (i) first ten natural frequencies and corresponding mode shapes, (ii) validation against Abaqus software as a commercial benchmark, (iii) examination of irregular nodal distributions to demonstrate robustness and (iv) two benchmark problems for broader validation. Results show excellent agreement with the finite-element method, establishing the DLSM method as a reliable tool for structural dynamics and paving the way for complex engineering applications.