B样条小波基自适应无网格迦辽金法应用于刚塑性成形模拟

无网格方法适合大变形计算和自适应分析,是进行刚塑性成形过程仿真的比较有潜力的方法。利用样条小波的多分辨分析特性,基于刚塑性变形的特点,通过实现刚塑性场量的两尺度分解技术,将场变量分解成低尺度成分和高尺度成分,利用高尺度成分判断求解高梯度区域;利用基于局部Delaunay三角化的细分方案实现高梯度区域节点的自适应细分,最终实现一个应用于刚塑性成形仿真的样条小波基自适应无网格迦辽金法,并用实例验证算法的稳定性和有效性。

ADAPTIVE ELEMENT-FREE GALERKIN METHOD BASED ON B SPLINE WAVELET FOR RIGID PLASTIC SIMULATION

The element-free Galerkin method,which is suitable for large deformation and adaptive analysis,is one of attractive meshless methods for rigid plastic forming simulation.Employing multi-resolution analysis of B spline wavelets and according to characteristics of rigid plastic forming,the two scale decomposition technology of field variables for rigid plastic forming has been established to decompose field variables into high and low scales components,the high scale components of which can commonly represent the gradient of solution according to inherent characteristic of wavelets,and then the Delaunay triangulation technique can be applied to develop the adaptive refinement scheme for those high gradient nodes.Finally,based on B spline wavelets,an adaptive element-free Galerkin method for rigid plastic forming simulation is presented.Numerical example shows the effectiveness of the present adaptive refinement scheme.