Meshfree methods are viewed as next generation computational techniques. With evident limitations of conventional grid based methods, like FEM, in dealing with problems of fracture mechanics, large deformation, and simulation of manufacturing processes, meshfree methods have gained much attention by researchers. A number of meshfree methods have been proposed till now for analyzing complex problems in various fields of engineering. Present work attempts to review recent developments and some earlier applications of well-known meshfree methods like EFG and MLPG to various types of structure mechanics and fracture mechanics applications like bending, buckling, free vibration analysis, sensitivity analysis and topology optimization, single and mixed mode crack problems, fatigue crack growth, and dynamic crack analysis and some typical applications like vibration of cracked structures, thermoelastic crack problems, and failure transition in impact problems. Due to complex nature of meshfree shape functions and evaluation of integrals in domain, meshless methods are computationally expensive as compared to conventional mesh based methods. Some improved versions of original meshfree methods and other techniques suggested by researchers to improve computational efficiency of meshfree methods are also reviewed here.
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