基于分布阶导数的本构方程模型的理论分析

发布时间：2018-05-05 12:18

  本文选题：分数阶微积分 + 本构方程　； 参考：《内蒙古大学学报(自然科学版)》2017年04期

【摘要】：研究基于分布阶导数的固体型黏弹材料的本构方程,方程中涉及到关于应变的分数阶导数的阶的积分.用分数阶导数算子_0D_t~α,Laplace变换及其数值逆方法,讨论了本构方程模型的松弛模量和蠕变柔量,谐变应力下应变的瞬态响应和滞后圈的形成.用分数阶导数算子_-∞D_t~α和待定系数方法,研究了模型在谐变应力下的稳态响应.模型能够合理地表示材料的黏弹特性,参数能够特征黏性或弹性的强弱.
[Abstract]:The constitutive equation of a solid viscoelastic material based on distributed order derivative is studied. The integral of fractional derivative of strain is involved in the equation. In this paper, the relaxation modulus and creep compliance of constitutive equation model, the transient response of strain under harmonic stress and the formation of hysteresis cycle are discussed by means of the operator of fractional derivative O D _ T ~ 伪 -T ~ + Laplace transform and its numerical inverse method. In this paper, the steady-state response of the model under harmonic stress is studied by means of the fractional derivative operator-鈭，

本文编号：1847660