面向增材制造的“快速－高原型度”热－结构耦合分析方法研究

Thermal residual stress and deformation exist in products by intense energy source based additive manufacturing. Characteristics in the process such as localized heating and layer-by-layer deposition lead to low efficiency and poor precision in thermo-mechanical simulation for additive manufacturng by numerical program and commercial software. In this project, a local-global two-scale extended finite element method (XFEM) is proposed for metallic components considering drastic variation of material nonlinearity induced by sharp thermal gradient in both time and space. The difficulties in mesh adaptivity caused by moving heat source are suppressed by developing time-dependent enrichment function constructed from numerical solution of the local domain. An isogeometric approach integrating CAD/CAE process is developed. The mixed spline basis functions are adopted to reproduce the fill-in process during the deposition of the part, meanwhile the exactness in geometry and advantage in mesh adaptivity are maintained. Given the localization feature of material nonlinearity in the course of forming, the combined approximation method is adopted to realize the model reduction on the system equations established by the aforementioned XFEM. Finally, a fast and generic thermo-mechanical simulation platform in macro-scale is established for additive manufacturing. This will lay a fundamental basis for the prediction of residual stress, control of deformation and parameters optimization in the process.

高能束增材制造热过程使得产品存在热残余应力与变形。由于工艺过程具有高能束热作用与逐层构建的特点，导致现有的数值程序与商业软件对于增材制造热-结构耦合模拟存在着效率低下与计算精度差等困难。本项目针对金属材料构件在增材制造成形过程中所受集中热梯度诱发的剧烈时空非线性变化特征，提出空间两尺度扩展有限元方法，通过局部区域数值解构造具备时间依赖性的加强基函数，以应对移动高能束热源加载的网格自适应困难；通过发展集成CAD/CAE的等几何方法，在保证其几何准确性与网格自适应优势的同时，采用混合样条基函数构造部件几何模型实现逐层构建中的物料填充过程；结合成形过程材料非线性变化具有局部性的特点，针对上述扩展有限元法建立的系统方程，发展组合近似法实现计算规模的减缩。最终建立工艺过程中宏观尺度的热－结构耦合快速－高原型度分析系统，为热残余应力预测与变形控制及工艺参数优化设计奠定基础。

高能束增材制造因热源集中作用导致剧烈的高温度梯度场的形成，由此引发的强烈局部非线性力学行为如变形和残余应力对机械构件的影响不容忽视。逐层构建与集中热源使得常规热弹塑性力学有限元计算在工业应用上举步维艰。为此，本项目围绕高能束增材仿真的计算瓶颈问题开展一系列快速-高原型度数值算法的研究。本项目主要贡献在于，1）发展了能够兼容物料填充、网格自适应细分与粗化以及精确保持构件几何的自适应Bézier单元方法用于传热学与热弹塑性应力的分析；2）发展了无附加自由度的扩展等几何方法，使得在不用细分网格的情况下，准确预测具有强烈局部特征问题的解（如高梯度或者应力奇异问题），同时系统方程保持良好的条件数，便于求解；3）构建了高能束热过程的快速等几何方法，对增材过程高能束热源移动所形成温度场与位移场作顺序耦合，结合子结构技术和所发展的扩展等几何方法降低模型对于网格局部细分的依赖性。本项目所发展的算法与模型为进一步对增材制造热-力过程开展研究提供高效灵活的数值工具。

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