As is known to all, there always exists the numerical dispersive effects of the standard finite element (FE) for the wave propagation problems and the corresponding FE solutions are usually unreliable in relatively high frequency range. In this work, a coupled “FE-Meshfree” element based on triangular mesh is introduced to reduce the dispersion effects for wave propagation problems. In this coupled element, the standard FE nodal shape functions are combined with the meshfree nodal shape functions to give a new hybrid nodal shape functions. As a result, both the individual advantages of the FE technique and the meshfree technique are strengthened by the present hybrid method. Through the dispersion analysis for the wave propagation problems, it is found that this coupled “FE-Meshfree” element could significantly reduce the numerical dispersive effects and it also have a higher tolerance to the mesh distortion than the other existing elements, hence the present method is quite promising to handle the general wave propagation problems in practical engineering application.

中文翻译：

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使用耦合的“FE-Meshfree”三角形单元减少波传播问题的色散

众所周知，标准有限元（FE）对于波的传播问题总是存在数值色散效应，相应的有限元解在相对较高的频率范围内通常是不可靠的。在这项工作中，引入了基于三角形网格的耦合“FE-Meshfree”单元，以减少波传播问题的色散效应。在这个耦合单元中，标准的有限元节点形状函数与无网格节点形状函数相结合，给出了一个新的混合节点形状函数。结果，本混合方法加强了有限元技术和无网格技术的各自优势。通过对波传播问题的色散分析，