基于多层模拟方法的双层梁断裂有限元分析

本文提出一种用于含分层的双层梁线弹性断裂分析的有限元方法．将上下子梁均模拟为多个子层，采用只有平动位移自由度的新型梁单元，假设单元内的位移沿纵向和横向均线性变化，推导了该单元的单元刚度矩阵．将开裂部分和未开裂部分的子梁进行单元刚度矩阵组装，施加相应的等效结点力，得到整体平衡方程，并结合边界条件进行求解．为验证该方法的有效性和精度，开展非对称双悬臂梁(Asymmetric Double Cantilever Beam, ADCB)和单臂弯曲梁(Single Leg Bending, SLB)试样的断裂分析，利用虚拟裂纹闭合技术(Virtual Crack Closure Technique, VCCT)得到了试样的能量释放率及其分量，并将求得的结果与解析解和二维有限元解进行对比．计算结果表明，相对于传统双层模拟方法，该多层模拟方法能够精确、高效地计算各类梁试样的能量释放率及其分量，并且无需引入界面连续条件．

Fracture Analysis of Delaminated Bilayer Beam Using FEA Based on Multi-Layer Modelling Method

This paper presents a new finite element method for linear elastic fracture analysis of delaminated bilayer beams. The upper and lower layers are both simulated using a new multi-sublayer, beam element with only the displacement degree of freedom is adopted, and its element stiffness matrix is derived by using the linear interpolation shape function. The element stiffness matrices of cracked and uncracked portions are assembled, and the corresponding equivalent node forces are applied to obtain the overall equilibrium equation, which is solved combining with the boundary conditions. In order to verify effectiveness and accuracy of the method, linear elastic fracture analysis of asymmetric double cantilever beam (ADCB) and single leg bending (SLB) specimen is performed, and the total energy release rate (ERR) and its fracture mode components obtained using virtual crack closure technique (VCCT) are compared with the analytical and two-dimensional finite element solutions. The results show that this method is capable of calculating ERR and its mode components with high efficiency and accuracy, but without introducing the interface continuity condition when compared with the conventional simulation methods.