Kelvin半无限体内部受集中力作用时的粘弹性解

ANALYTICAL SOLUTIONS OF KELVIN′S VISCOELASTIC HALF-INFINITE SPACE SUBJECTED TO INTERIOR VERTICAL CONCENTRATED LOADING

假定半无限体为线性粘弹性介质,其在内部集中力作用下的应力为三维复杂力状态,应力球张量和应变球张量之间符合弹性关系,而应力偏张量和应变偏张量之间为Kelvin粘弹性应力应变关系。利用半空间体内部受竖向和水平向集中力的Mindlin弹性理论解,根据准静态粘弹性-弹性对应原理,在相同荷载条件下,首先对弹性解进行Laplace变换,然后将弹性解中的物理参数用线性粘弹性理论中经过Laplace变换的物理参数来替代,最后再进行Laplace逆变换,从而求得半无限体的位移、应力粘弹性解。结果验证表明,理论结果是正确的,并为实际工程的粘弹性沉降提供了理论依据。

By means of half-space Mindlin＇ s elastic solutions and correspondent principle between elasticity and viscoelasticity, the viscoelastic solutions of stress and displacement, subjected to suddenly applied vertical and horizontal concentrated forces and given elastic volume strain and standard linear solid model distortion constitutive relations, were systematically derived by Laplace transforms and Laplace inverse transforms. Finally, an example was given by making use of the presented method. The calculation results show that the new theory is feasible and applicable and can successfully predict the settlement of deep buried foundation. And the results show that it is necessary to take account of viscoelasticity effect of semi-infinite half-space in the calculation for stress and displacement. This study provides a theoretical basis for calculating viscoelastic settlement of actual projects.