质点积分无单元伽辽金法及其在金属挤压过程中的应用

Particle integration of element free galerkin method and its application in metal extrusion simulation

无单元伽辽金法需要在背景网格上积分,计算量大。节点积分无单元伽辽金法把对求解域的积分转化为对节点的求和,效率高,但因零能模态不受控制而会产生不稳定现象,需要采取一定的稳定化方案。本文采用应力点思想,通过Newton-Cotes法计算积分,建立了质点积分无单元伽辽金法,并通过小变形弹性静力学问题说明了该方法具有良好的稳定性,且计算效率远高于无单元伽辽金法。最后本文将质点积分无单元伽辽金法成功地应用于三维金属挤压成型过程的数值模拟,显示了该方法在分析此类问题时的优势和潜力。

Element Free Galerkin（EFG） method is very computationally intensive due to the requirement of elegant background cell quadratures. Nodal Integration of Element Free Galerkin （NIEFG） method converts the background cell quadrature into nodal integration, so that it is much more efficient than EFG. However, the existence of zero energy modes in NIEFG results in instability, and some stabilization scheme should be used to stabilize the method which may introduce significant extra errors. Based on the idea of stress points and Newton-Cotes integration, a particle integration of element free Galerkin （PIEFG） method is proposed in this paper. Numerical example of linear elasticity shows that the PIEFG is pretty stable and much more efficient than EFG. Furthermore, PIEFG is extended to the simulation of metal extrusion problems, which shows that PIEFG is very promising in metal extrusion simulation.