几种变截面点阵承受面外压缩载荷的力学行为

增材制造工艺的出现使得轴向变截面点阵结构设计成为可能，变截面点阵的刚度、强度和稳定性等力学行为研究具有重要的工程意义。假定杆件横截面沿轴向呈双曲线或椭圆型变化，积分推导变截面对于杆件刚度产生的影响，在平衡方程中进行参数变换，推导出变截面对于杆件失稳特征值的解析解，并最终将椭圆型截面杆件应用于实际的金字塔点阵设计。最后引入了特征值算法和弧长法，前者证实了解析解的正确性，后者用于计算含几何缺陷的金字塔胞元后屈曲行为。解析解与数值方法均表明，对于相对密度较低的金字塔点阵，椭圆型轴向变截面杆件设计可以使得点阵刚度在基本保持不变的情况下，有效提高点阵等效压缩强度。研究结果可以为高性能变截面点阵的设计提供理论基础。

MECHANICAL BEHAVIOR OF SEVERAL LATTICE WITH NON-UNIFORM LONGITUDINAL CROSS-SECTION UNDER OUT-OF-PLANE COMPRESSION LOAD

It is possible to design lattice with non-uniform cross-section in longitudinal direction using additive-manufacturing, which makes it crucial to studying the corresponding mechanical behaviors, including stiffness, strength and buckling. The longitudinal cross-section of truss is assumed to be hyperbolic or elliptic form, which effect on stiffness is calculated analytically by axial integration and that on buckling eigenvalue is deduced explicitly through introducing parameter variation in equilibrium equation. The truss with elliptic cross-section is applied in the practical pyramid lattice, and the analytical solutions are validated by eigenvalue buckling method. Moreover, the riks method is applied in calculated the post-buckling behaviors for pyramid lattice with geometric imperfection. Both analytical solution and numerical results show that the elliptic cross-section in longitudinal direction of truss can obviously improve equivalent compressive strength in condition that the stiffness is decreased slightly for pyramid lattice with low relative density. The research results provide theoretical basis to design of lattice material with higher performance.