辛解析奇异元在动荷载作用下V型切口问题中的应用

A symplectic analytical singular element for V-notch problem under dynamic loading condition

利用辛解析奇异单元,结合时域精细算法,研究了动荷载作用下的含平面V型切口问题。时域上,采用时域精细算法,并结合自适应算法控制展开项数,保证了计算精度。空间域上,切口尖端附近采用辛解析奇异单元,其余区域采用常规有限单元,避免了局部网格加密。本文使用的辛解析奇异单元不需要过渡单元和局部网格加密,且能够通过奇异单元内部的参数关系直接给出切口尖端的应力强度因子,不需要复杂的后处理过程。数值结果表明,本文方法具有良好的精度和稳定性,可以准确地计算动态应力强度因子。

The V-notch problem in a plane structure under dynamic loading condition was investigated in this paper,with a symplectic analytical singular element(SASE)combined with a precise time domain expanding algorithm(PTDEA).The PTDEA was used for the discretization of the time domain,where a self-adaptive technique was adopted out to determine the proper number of the expanding terms with required accuracy.In the space domain,the SASE was employed to occupy the area around the V-notch tip and conventional elements were used for the remaining area,so that local mesh refinement could be avoided.Taking advantages of the SASE,the dynamic stress intensity factors(DSIFs)were obtained directly via the relationship between the eigen expanding coefficients and the DSIFs,without the complex post-processing.Numerical results show that the proposed SASE for the dynamic V-notch problem is effective and efficient.