近场动力学与有限元混合模型研究
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苏州科技大学土木工程学院

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国家自然科学基金项目(面上项目,重点项目,重大项目)


Study on hybrid model of peridynamics and finite element method
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School of Civil Engineering, Suzhou University of Science and Technology

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The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan)

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    摘要:

    兼顾近场动力学(peridynamics, PD)模拟不连续问题的优势和有限单元法(finite element method, FEM)较高的计算效率,本文采用近场动力学与有限元混合建模方法,建立了新的混合模型。该模型在裂纹出现区域,采用近场动力学建模,其他区域采用八结点等参元建模。通过杆单元连接PD物质点与等参单元结点,将PD物质点对间相互作用视为杆单元,最后对单元刚度集成,实现了在有限元框架体系中两种方法的混合建模。该混合模型无需引入人工阻尼,提高了计算效率。此外,相较于四结点混合模型,采用高阶(八结点)等参元与近场动力学方法建立的混合模型具有更高的计算精度。通过数值算例验证了该方法的有效性,为断裂破坏问题的解决提供了一种新思路。

    Abstract:

    Considering the advantages of peridynamics in simulating discontinuities and low computational cost of finite element method (FEM), In this paper, a new hybrid model was established by using the hybrid modeling method of peridynamics and finite element method.The model was set up by peridynamics theory in the region where cracks appear, and the other regions were modeled by eight node isoparametric elements. The truss element was used to connect the material points with the isoparametric nodes, and the interaction between material points could be regarded as the truss element. Finally, the stiffness of the element was integrated to realize the hybrid modeling of the two methods in the finite element frame system.The model does not need to introduce artificial damping, which improves the calculation efficiency. In addition,compared with the four node hybrid model, the hybrid model based on high order (eight node) isoparametric element and peridynamics has higher accuracy.can be applied to complex stress-strain problems.The validity of the method is verified by the numerical example, which provides a new idea to solve fracture problems.

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  • 收稿日期:2020-01-17
  • 最后修改日期:2020-04-16
  • 录用日期:2020-04-20
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