半解析有限元法分析非线性粘弹体在板材模具中的流动

Analysis of Nonlinear Viscoelastic Melt Flow in Plate Die by Half Analytical Finite Element Method

聚合物熔体在模具中的均匀性决定板材成型的质量。熔体具有非线性记忆性的粘弹效应,同时流道十分复杂。为准确、简便地分析熔体流动情况,针对板材机头流道的特点,提出了流动计算新的方法——有限柱半解析法,即在流道的厚度方向采用富氏级数描述流动分布,把三维有限元方程简化成为二维,得到以流量和压力为未知量的有限元方程。同时采用K-BKZ积分型本构模型描述熔体的非线性记忆性,给出求解非线性方程组的迭代方法,取得较好的收敛性。对两种典型的板材模具进行了分析计算,得出模具出口处的流量分布,通过把结果与三维有限元分析的结果相比较,表明该方法可以准确地分析板材模具中熔体的流动。

The quality of plastic plate is decided by uniformity of flow in die. Polymer melt characterizes nonlinear memory viscoelastic and the channel in die is very complex. To accurately and simply analyze the flow of polymer, a new method named finite strip half analytical element method was proposed according to the channel character of plate extruding die, the curve of flow in thickness was described by Fourier series. Three dimensional finite element equation can be simplified to a two dimensional equation with unknown parameters of flow and press. And nonlinear memory viscoelastic melt was described by K-BKZ integral constitutive equation. Suitable iteration with rapid convergence was given to solve nonlinear equation. Two typical plate dies were calculated for the comparison to those of three dimensional finite element method. Results show that the method is accurate to analyze the flow of polymer in plate extruding die.