The present study investigates the static responses of a 3D-printed polymeric meta-sandwich curved beam with an auxetic honeycomb core, including buckling and nonlinear bending behavior. After extracting the mechanical properties of the core material, the nonlinear governing equations for the curved beam under two types of loading, namely uniform transverse and axial mechanical loads, are derived based on the first-order shear deformation theory and von-Kármán nonlinearity. After examining the convergence of the static responses and validating them by using the Ritz method, the influence of various geometrical parameters of the 3D-printed meta-sandwich structure on the results of buckling and nonlinear bending behavior as well as their optimization using the response surface methodology (RSM) are studied. The results indicate that by increasing the thickness-to-length ratio of the inclined wall, the critical load of the auxetic sandwich beam is enhanced due to improved stiffness, and its lateral displacement declines. The amount of buckling load increase from = 0.005 to = 0.1 is 1.92% in the clamped-clamped boundary conditions, 1.56% in the clamped-simply supported conditions, and 1.2% in the simply supported-simply supported edge conditions. Therefore, by selecting appropriate geometrical parameters for the core cells, the occurrence of instability can be delayed, leading to enhanced buckling resistance of the structure. Furthermore, optimizing the results by using the RSM showed that the highest critical load value and the lowest transverse deflection value of the meta-sandwich curved beam are obtained when = 15, = 1, = 0.1, = 30, = 0.07, = 1.1, = 1.2, and the edge conditions are of the clamped-clamped type.

中文翻译：

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具有拉胀蜂窝芯的 3D 打印超夹层曲梁的非线性弯曲和屈曲分析


本研究研究了具有拉胀蜂窝芯的 3D 打印聚合物超夹层曲梁的静态响应，包括屈曲和非线性弯曲行为。提取核心材料的力学性能后，基于一阶剪切变形理论和冯卡门非线性，推导了曲梁在均匀横向和轴向机械载荷两种载荷下的非线性控制方程。在检查静态响应的收敛性并使用 Ritz 方法对其进行验证后，3D 打印超三明治结构的各种几何参数对屈曲和非线性弯曲行为结果的影响以及使用响应面进行优化方法（RSM）进行了研究。结果表明，通过增加斜壁厚长比，拉胀夹芯梁的临界载荷因刚度提高而增大，横向位移减小。屈曲载荷从 = 0.005 到 = 0.1 的增加量在夹紧-夹紧边界条件下为 1.92%，在夹紧-简支条件下为 1.56%，在简支-简支边缘条件下为 1.2%。因此，通过为核心单元选择合适的几何参数，可以延迟失稳的发生，从而增强结构的抗屈曲能力。此外，利用RSM优化结果表明，当= 15、= 1、= 0.1、= 30、= 0.07、= 1.1时，获得了超夹层曲梁的最高临界荷载值和最低横向挠度值， = 1.2，边缘条件为夹紧-夹紧类型。