Daxini S D, Prajapati J M
Department of Mechanical Engineering, Babaria Institute of Technology, Vadodara, Gujarat 391240, India.
Department of Mechanical Engineering, M. S. University, Vadodara, Gujarat 390020, India.
ScientificWorldJournal. 2014 Jan 2;2014:247172. doi: 10.1155/2014/247172. eCollection 2014.
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.
无网格方法被视为下一代计算技术。由于传统的基于网格的方法（如有限元法）在处理断裂力学、大变形和制造过程模拟等问题时存在明显局限性，无网格方法受到了研究人员的广泛关注。到目前为止，已经提出了许多无网格方法来分析工程各个领域中的复杂问题。目前的工作试图回顾一些著名的无网格方法（如无单元伽辽金法和移动最小二乘配点法）在各种结构力学和断裂力学应用（如弯曲、屈曲、自由振动分析、灵敏度分析和拓扑优化、单模和混合模式裂纹问题、疲劳裂纹扩展以及动态裂纹分析）方面的最新进展和一些早期应用，以及一些典型应用（如裂纹结构的振动、热弹性裂纹问题和冲击问题中的失效转变）。由于无网格形状函数的复杂性以及域内积分的计算，与传统的基于网格的方法相比，无网格方法的计算成本较高。本文还回顾了原始无网格方法的一些改进版本以及研究人员提出的其他提高无网格方法计算效率的技术。
