ANALYSIS OF MECHANICAL PERFORMANCES OF CYLINDER IN 3D CONCRETE PRINTING PROCESSES
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摘要: 3D混凝土打印(3DCP)技术由于其快速制造的优势，在过去几十年里得到了迅速的发展。然而，在印刷过程中仍有许多问题需要解决，例如：目前的相关研究尚未建立能准确预测与分析3DCP圆柱壳的力学模型。该文利用 Goldenveizer-Novozhilov壳体理论，加入打印进程参数，包括打印速率、打印材料固化特征、柱壳几何特征、以及自重作用影响，对3DCP圆柱壳的两种破坏机理：弹性屈曲和塑性破坏进行了分析，并在此基础上描述了柱壳形直立墙弹性屈曲与塑性坍塌间的竞争关系。参数模型、有限元模拟与已有相关试验的对比结果表明：该文提出的模型可以较好地预测3DCP圆柱壳的失效高度与失效形式，并为找寻最佳打印参数集给予理论指导。Abstract: Because of the advantages in rapid manufacturing, 3D concrete printing (3DCP) technology has developed rapidly in the past decades. However, there are still many problems to be solved in the printing process. For example, the current related studies have not established a mechanical model that can accurately predict and analyze 3DCP cylinders. Two failure mechanisms of 3DCP cylindrical shell, namely elastic buckling and plastic failure, are analyzed by using Goldenveizer-Novozhilov shell theory and adding printing process parameters, including printing rate, curing characteristics of printing materials, geometric characteristics of 3DCP cylinders and the effect of dead weight. On this basis, the competitive relationship between elastic buckling and plastic collapse of cylindrical shell vertical wall is described. The results of parameter model and finite element simulation were compared with the existing experiments, which verify that the proposed model can better predict the failure length and failure form of 3DCP cylinders, and provide a theoretical guidance for finding the optimal printing parameters set.
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Key words:
- 3D concrete printing /
- cylinder /
- plastic collapse /
- elastic buckling /
- competitive relationship
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图 2 3D打印进程中失效机制示意图
Figure 2. Failure mechanism of cylinder in 3D concrete printing (3DCP) processes
图 4 塑性坍塌长度
${\overline l_{\rm{p}}}$ 随固化速率${\overline \xi _{\text{σ}} }$ 变化曲线图Figure 4. Plastic collapse length
${\overline l_{\rm{p}}}$ vs. curing rate${\overline \xi _{\text{σ}} }$ 
图 5 无量纲屈曲长度
${\overline l_{{\rm{cr}}}}$ 随无量纲固化速率${\overline \xi _{\rm{E}}}$ 变化曲线Figure 5. Critical buckling length
${\overline l_{{\rm{cr}}}}$ vs. curing rate${\overline \xi _{\rm{E}}}$ 
图 6 3DCP圆柱壳临界屈曲长度
${\overline l_{{\rm{cr}}}}$ 随固化速率${\overline \xi _{\rm{E}}}$ 变化曲线Figure 6. Critical buckling length
${\overline l_{{\rm{cr}}}}$ vs. curing rate${\overline \xi _{\rm{E}}}$ for 3DCP cylinder
图 8 3DCP圆柱壳圆角梯形层截面示意图
Figure 8. Rounded trapezoid schematic diagram of 3DCP cylinder model
图 10 3DCP圆柱壳圆角矩形层截面示意图
Figure 10. Rounded rectangle schematic diagram of 3DCP cylinder model
图 11 最大径向位移
$ {w_{\max }} $ 随层高变化曲线Figure 11. Max. radial deflection
$ {w_{\max }} $ vs. layer number
图 12 3DCP圆柱壳无量纲失效长度
$\bar{l}$ 随径厚比${r \mathord{\left/ {\vphantom {r h}} \right. } h}$ 变化图Figure 12. The dimensionless failure length
$\bar{l}$ of 3DCP cylinders vs. the radius-thickness ratio${r \mathord{\left/ {\vphantom {r h}} \right. } h}$ 表 1 无量纲参数与其物理含义
Table 1. Dimensionless parameter and physical significance
无量纲参数 补充公式 物理含义 $\overline w = {w / h}$ 径向位移 $\overline r = {\left( {\dfrac{{\rho gh}}{{{D_0}}}} \right)^{{1 / 3}}}r$ ${D_0} = \dfrac{{{E_0}{h^3}}}{{12\left( {1 - {\nu ^2}} \right)}}$ 柱壳半径 $\overline h = {\left( {\dfrac{{\rho gh}}{{{D_0}}}} \right)^{{1 / 3}}}h$ 柱壳厚度 ${\overline l_{\rm cr} } = {\overline \xi _{\rm{E}}}\kappa = {\left( {\dfrac{ {\rho gh} }{ { {D_0} } } } \right)^{ {1 / 3} } }{l_{\rm cr} }$ $\kappa = \dfrac{ { {\xi _{\rm{E}}}l} }{ {\dot l} }$ 屈曲长度 ${\overline \xi _{\rm{E} } } = {\left( {\dfrac{ { {D_0} } }{ {\rho gh} } } \right)^{ {1 /3} } }\dfrac{ { {\xi _{\rm{E}}} } }{ {\dot l} }$ 固化速率 
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