基于隶属度函数模糊弹塑性本构模型的研究

Constitutive model of fuzzy elastoplasticity based on membership functions

为了解决循环加卸载问题,将隶属度函数和模糊截集引入到塑性屈服函数中,并采用米塞斯屈服准则,将屈服函数模糊化,推导得到了模糊弹塑性本构模型。随着隶属度值的变化,该模型的弹塑性界面能连续过渡,且表达式简单,加卸载路径明了;利用该模型对钢桥面板在循环荷载作用下进行了分析,并通过有限单元法得到了数值解。通过分析发现,模糊弹塑性模型通过隶属度的演化能代替硬化规律,能很好地反映循环加卸载过程,是解决循环加卸载作用下弹塑性连续过渡的一种有效途径。

Membership functions and fuzzy cut sets were induced into a plastic yield function to solve cyclic loading-unloading problems. Von Mises yield criterion was adopted to deduce the fuzzy plastic yield function. Taking the strain rate into consideration,the fuzzy elastic-plastic constitutive model was obtained. It was shown that the elastic-plastic interface of this model can transit continuously with the changes in the membership,the model is simple in expression and clear in route of loading and unloading. A steel panel under the action of cyclic loading was analyzed with the model,its numerical solutions were obtained using the finite element method. It was shown that the cyclic loading and unloading process can be simulated well with the proposed model and it is an effective way to solve the consecutive elastic-plastic problem under cyclic loading.