COUPLING OF PERIDYNAMIC THEORY AND THE FINITE ELEMENT METHOD
COUPLING OF PERIDYNAMIC THEORY AND THE FINITE ELEMENT METHOD
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DOI：
10.2140/jomms.2010.5.707
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发表时间：
2010-01-01
影响因子：
0.9
通讯作者：
Madenci, Erdogan
中科院分区：
文献类型：
--
作者：
Kilic, Bahattin;Madenci, Erdogan
有限元法被广泛用于结构问题的数值求解。然而，使用有限元法进行损伤预测可能非常麻烦，因为位移的导数在不连续处是不确定的。相比之下，周波理论在其公式中使用位移而不是位移导数。因此，周波方程在任何地方都是有效的，包括不连续性。此外，周向理论不需要裂纹萌生和扩展的外部标准，因为材料失效是通过材料响应来调用的。然而，有限元方法在数值上比周向理论更有效。因此，本研究提出一种方法，耦合的周波理论和有限元分析，以利用这两种方法。预计会发生故障的区域采用周向有限元法建模，而其余区域采用有限元法建模。最后，本方法通过一个简单的问题进行了演示，并将本方法的预测与周波理论和有限元方法进行了比较。通过考虑一个带有圆形切口的板，验证了本文方法的损伤模拟结果。
The finite element method is widely utilized for the numerical solution of structural problems. However, damage prediction using the finite element method can be very cumbersome because the derivatives of displacements are undefined at the discontinuities. In contrast, the peridynamic theory uses displacements rather than displacement derivatives in its formulation. Hence, peridynamic equations are valid everywhere, including discontinuities. Furthermore, the peridynamic theory does not require an external criterion for crack initiation and propagation since material failure is invoked through the material response. However, the finite element method is numerically more efficient than the peridynamic theory. Hence, this study presents a method to couple the peridynamic theory and finite element analysis to take advantage of both methods. The regions where failure is expected are modeled using peridynamics while remaining regions are modeled utilizing the finite element method. Finally, the present approach is demonstrated through a simple problem and predictions of the present approach are compared against both the peridynamic theory and finite element method. The damage simulation results for the present method are demonstrated by considering a plate with a circular cutout.