复杂荷载作用下带裂纹薄板SIFs的快速解法

Quick solution to SIFs of thin plate with cracks under complex loads

针对集成的总刚大小根据自由度数的增加出现剧增,导致计算机内存占用量过大、计算速度缓慢的问题,提出通用威廉姆斯(Williams)单元与矩阵压缩结合的SIFs(应力强度因子)快速解法,充分发挥Williams单元求解SIFs的直接性与矩阵压缩的高效性.在裂尖奇异区建立Williams单元得到所有SIFs的直接表达式,外围常规区按常规有限元法建模,对整体刚度矩阵采用压缩存储,并改进LU分解法以快速求解含压缩矩阵的刚度方程.算例分析表明:该方法能快速求解平面内与平面外荷载共同作用下带裂纹薄板所有裂尖SIFs,且具有较高的计算精度.

Aiming at the problem that excessive computer memory usage and slow calculation speed caused by rapid enlargement of the size of total stiffness matrix with the increase in the degrees of freedom,a quick solution to the stress intensity factors(SIFs)with combining general Williams element and matrix compression was proposed.Full play to the directness of Williams element for solving SIFs,and the efficiency of matrix compression were given.The Williams element was established in the singular region of the crack tip to obtain the direct expression of SIFs in all modes.The peripheral regular region was modeled by the conventional finite element method,the total stiffness matrix was compressed and stored,and the LU decomposition method was improved to quickly solve the stiffness equation containing the compression matrix.Example analysis shows that the proposed method can quickly solve crack tip SIFs in all modes with cracked thin plate under the plane and anti-plane loads,and high calculation accuracy is achieved.