An equivalent continuum multiscale formulation for 2D geometrical nonlinear analysis of lattice truss structure
An equivalent continuum multiscale formulation for 2D geometrical nonlinear analysis of lattice truss structure
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DOI：
10.1016/j.compstruct.2016.10.072
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发表时间：
2017-01
影响因子：
6.3
通讯作者：
Hui Liu;J. Lv
中科院分区：
文献类型：
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作者：
Hui Liu;J. Lv
在这项工作中，提出了一种等效连续多尺度公式，用于晶格桁架材料结构的几何非线性分析。该公式是通过结合扩展多尺度有限元法和同向旋转方法建立的。首先，利用局部坐标系下数值构造的插值函数，将点阵桁架晶胞等效为连续粗元。然后利用全局坐标系中同向旋转方法的基本思想推导出该粗单元的切向刚度矩阵。因此，可以利用通用位移控制算法来求解宏观层面结构的全局非线性平衡方程，捕获具有多个临界点的平衡路径。在执行完宏观尺度上的所有增量步骤和迭代步骤后，再次利用前面构建的数值插值函数可以轻松获得位移、应力和应变等微观信息。此外，还进行了几个数值算例来研究晶胞布局和尺寸的影响，研究粗尺度网格的敏感性并验证所提出的多尺度公式的有效性和效率。
In this work, an equivalent continuum multiscale formulation is presented for the geometrical nonlinear analysis of the structures with lattice truss materials. This formulation is established by combining the extended multiscale finite element method and the co-rotational approach. Firstly, the lattice truss unit cell is equivalent to a continuum coarse element by using a numerical constructed interpolation function in the local coordinate system. Then the tangent stiffness matrix of this coarse element is derived by employing the basic idea of the co-rotational approach in the global coordinate system. Thus, the global nonlinear equilibrium equations of the structure at the macroscopic level can be solved by using the general displacement control algorithm to capture the equilibrium path with multiple critical points. After performing all of the incremental steps and the iterative steps on the macroscopic scale, the microscopic information, such as the displacement, stress and strain, can be obtained easily by virtue of the afore-constructed numerical interpolation functions once again. In addition, several numerical examples are carried out to study the effects of the layout and size of unit cell, investigate the sensitivity of coarse-scale meshes and verify the validation and efficiency of the presented multiscale formulation.