分数导数粘弹性模型描述的土体中球形空腔的稳态响应

Steady state response of a spherical cavity in soil described by fractional derivative viscoelastic model

利用分数导数粘弹性模型描述土体的应力和应变关系,建立了球坐标下分数导数粘弹性土体的运动方程。通过引入势函数的方法求解了分数导数粘弹性球形空腔的稳态响应,得到了简谐动荷载作用下球形空腔的径向位移、径向应力的表达式。以算例的形式分析讨论了分数导数的阶数和土体本构模型参数对球形空腔稳态响应的影响。

Stress-strain relationship of soil surrounding the spherical cavity was described by fractional derivative viscoelastic model,and the motion equations of the fractional derivative viscoelastic soil in spherical coordinates were established.The steady state response of fractional derivative viscoelastic spherical cavity was investigated by using potential function,and the expression formulas of radial displacement and stress of spherical cavity under harmonic dynamic load were obtained.The effects of order of fractional derivative and constitutive model parameters of the soil on the steady state response of spherical cavity were analyzed with numerical examples.