论文标题
晶格核心三明治结构的光束模型的层次结构
Hierarchy of beam models for lattice core sandwich structures
论文作者
论文摘要
开发了一个离散到2-D离散晶格的离散转换，作为能量等效的1D连续梁。该研究是在经典环境中开始的，但通过在二阶大晶型梯度与微极性抗对称剪切变形之间的晶胞中的新链路中导致了非古典的两尺度微极光束模型。通过连续近似，将剪切可变形的微极光束还原为夫妻压力和两个经典的晶格束模型。所有模型的刚度参数均由微极构成矩阵给出。通过研究各种载荷和边界条件下的拉伸和弯曲主导的晶格核心三明治束来比较这四个模型。经典的四阶Timoshenko光束是伸展主导的梁的恰当首选，而6阶微极模型也适用于弯曲主导的梁。六阶夫妻压力梁通常在点载荷和边界附近太僵硬。结果表明，即使在没有边界效应的情况下，当1-D梁（宏观结构）的长度等于2-D单位电池（微结构）时，即使在L = l时，也会导致精确的2-D晶格响应。
A discrete-to-continuum transformation to model 2-D discrete lattices as energetically equivalent 1-D continuum beams is developed. The study is initiated in a classical setting but results in a non-classical two-scale micropolar beam model via a novel link within a unit cell between the second-order macrorotation-gradient and the micropolar antisymmetric shear deformation. The shear deformable micropolar beam is reduced to a couple-stress and two classical lattice beam models by successive approximations. The stiffness parameters for all models are given by the micropolar constitutive matrix. The four models are compared by studying stretching- and bending-dominated lattice core sandwich beams under various loads and boundary conditions. A classical 4th-order Timoshenko beam is an apt first choice for stretching-dominated beams, whereas the 6th-order micropolar model works for bending-dominated beams as well. The 6th-order couple-stress beam is often too stiff near point loads and boundaries. It is shown that the 1-D micropolar model leads to the exact 2-D lattice response in the absence of boundary effects even when the length of the 1-D beam (macrostructure) equals that of the 2-D unit cell (microstructure), that is, when L=l.
