In this paper, we present a novel formulation for the time-dependent three-dimensional bending analysis of a viscoelastic solid by defining a time function with unknown coefficient. The advantage of this method is that there is no need to follow the time-displacement curve; instead, the time-dependent responses of the viscoelastic solid are obtained only by bending analysis of the elastic solid with low computational cost and high computational speed. The relationship between stress and strain is written for linear viscoelastic materials employing the Boltzmann integral law. The displacement field is approximated through the combination of two functions, a function of geometrical parameters and a function of time. The equilibrium discretized equations are written based on the virtual work principle using the finite element method. The numerical results are compared with other available references. To determine the effects of geometry and material on the coefficient of the time function, the results are extracted for square, rectangular, skew, circular, and triangular prismatic solids as well as for different materials.

在本文中，我们通过定义具有未知系数的时间函数，提出了一种用于粘弹性固体的瞬态三维弯曲分析的新公式。这种方法的优点是不需要遵循时间-位移曲线；相反，粘弹性固体的瞬态响应仅通过弹性固体的弯曲分析获得，计算成本低，计算速度快。使用玻尔兹曼积分定律为线性粘弹性材料编写应力和应变之间的关系。位移场通过两个函数的组合来近似，几何参数的函数和时间的函数。平衡离散方程是根据虚功原理用有限元方法编写的。将数值结果与其他可用参考进行比较。为了确定几何形状和材料对时间函数系数的影响，提取了方形、矩形、倾斜、圆形和三角棱柱实体以及不同材料的结果。