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利用拟膜法分析含周期性索-杆胞元的二维网格结构的面内有效弹性性能。拟膜法是将具有周期性微结构的平面网格结构在力学性能上比拟成均匀的连续体。根据两者在面内力学行为上的等效性,网格结构的拟膜的弹性本构参数可由网格结构中单胞的材料和几何参数解析表示。分析表明索-杆胞元存在拉压性能差异现象。这导致拟膜表现出双模量特点,即材料沿某一方向的拉伸弹性模量与压缩模量不同。采用悬臂梁算例考察这些参数的正确性:利用网格结构和其拟膜分别构造同尺寸和工况的两个悬臂梁;利用有限元方法分析两个梁;比较得出两个梁的中性层位置与解析解均吻合,且两个梁中性层挠度之间的相对误差极小。
Study on In-plane Effective Elastic Properties of Two-dimensional Mesh Structure with Periodic Cable-rod Cells by Means of Simulated Membrane Method. Pseudo-membrane method is to have a periodic microstructure of the planar grid structure in the mechanical properties compared to a uniform continuous body. According to the equivalence of the two in in-plane mechanics behavior, the elastic constitutive parameters of the meso-film of the lattice structure can be expressed by the material and geometric parameters of the unit cell in the lattice structure. Analysis shows that cable-rod cells exist tension and compression performance differences. This results in the bimodal appearance of the pseudomembrane, that is, the material has different tensile modulus of elasticity and compressive modulus along a certain direction. The validity of these parameters is investigated by using a cantilever beam example: two cantilevers of the same size and working condition are respectively constructed by using a mesh structure and a pseudo-film; the two beams are analyzed by a finite element method; The locations of the layers coincide with the analytic solutions, and the relative errors between the two beams’ neutral delamination are very small.