| 陈白斌,李建波,林皋.无需裂尖增强函数的扩展比例边界有限元法[J].水利学报,2015,46(4): |
| 无需裂尖增强函数的扩展比例边界有限元法 |
| An extended scaled boundary finite element method without asymptotic enrichment of the crack tip |
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| DOI： |
| 中文关键词: 断裂力学 裂纹面荷载 扩展有限元法 比例边界有限元法 扩展比例边界有限元法 |
| 英文关键词: fracture mechanics surface tractions extended finite element method scale boundary finite element method extended scale boundary finite element method |
| 基金项目: |
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| 中文摘要: |
| 扩展有限元法（XFEM）在模拟裂纹扩展时无需进行网格重构，但需预先获得裂尖解析形式的渐进解去构造复杂的增强函数，在形成单元刚度阵时常需采用特殊的数值积分技术；比例边界有限元法（SBFEM）作为一种半解析的方法可以高精度地由统一的公式直接求出广义应力强度因子而无需预先知道应力奇异的类型。将二者相结合，建立扩展比例边界有限元法（X-SBFEM），可提高算法处理复杂断裂问题的能力。该方法利用SBFEM 描述裂尖的奇异应力场而在裂纹主体段仍用传统的XFEM 模拟。随后，从虚功原理出发，推导了在裂纹面受荷载作用
时，裂尖超单元的等效节点荷载以及位移场和应力场的求解公式。数值算例中，求解了半无限大板在裂纹面受各种分布荷载作用下的应力强度因子及矩形板的裂纹扩展问题，计算结果显示X-SBFEM是有效的。 |
| 英文摘要: |
| It is not necessary to remesh when the extended finite element method simulates crack propagation. But the complex enrichment functions based on a priori knowledge of the asymptotic expansions of the displacements in the crack-tip are required. Besides， the special numerical integration techniques are always inevitable. The generalized stress intensity factors could be accurately calculated by the scale boundary finite element method directly from the consistent formula without the knowledge on the type of singularity. Therefore， a coupling model i.e. the extended SBFEM can be established to improve the capability to model complex fracture problems. In this method， the nonsmooth behavior around the crack tip is modeled by SBFEM while the split elements are modeled by XFEM. Furthermore， based on the principle of virtual work，the equivalent node loads，the displacement and the stress fields in super element are derived in detail including the effect of surface tractions. During its numerical evaluation， the stress intensity factors of semi-infinite plate with different kinds of surface tractions are calculated， the results show that the X-SB?FEM is effective. |
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