非线性粘弹性力学边值问题的逐次逼近解法

该文从非线性粘弹性力学的基本方程出发,运用逐次逼近法,导出逐次边值问题。然后,作为实例,就内表面有规定的位移、外表面无面力的厚壁圆筒,求出其一次解和二次解,从而获得筒内应力场的二级近似公式。最后,将其线性解与非线性解作了数值对比。

SOLUTION OF BOUNDARY-VALUE PROBLEMS IN NONLINEAR VISCOELASTICITY BY SUCCESSIVE APPROXIMATIONS

Starting from the basic equations of the nonlinear theory of viscoelasticity,we deduce the successive boundary-value problems by the method of successiveapproximations. As a concrete example, we find the first-and second-order solutionsfor a thick-walled cylinder. On the inner surface of the cylinder, the displacementis prescribed, and on the outer surface, the traction is null. We thus obtain theformula in the second approximation for the stress field in the cylinder, Finally,we compare numerically the linear solution with the nonlinear one.