In this paper, we present a comprehensive investigation of stress propagation in a two-dimensional elastic circular disk. To accurately describe the displacements and stress fields within the disk, we employ a scalar and vector potential approach, representing them as sums of Bessel functions. The determination of the coefficients for these expansions is accomplished in the Laplace space, where we compare the boundary conditions. By converting the inverse Laplace transforms into complex integrals using residue calculus, we successfully derive explicit expressions for the displacements and stress fields. Notably, these expressions encompass primary, secondary, and surface waves, providing a thorough characterization of the stress propagation phenomena within the disk. Our findings contribute to the understanding of mechanical behavior in disk-shaped components and can be valuable in the design and optimization of such structures across various engineering disciplines.

在本文中，我们对二维弹性圆盘中的应力传播进行了全面的研究。为了准确描述圆盘内的位移和应力场，我们采用标量和矢量势方法，将它们表示为贝塞尔函数的和。这些展开式的系数的确定是在拉普拉斯空间中完成的，我们在其中比较边界条件。通过使用留数微积分将拉普拉斯逆变换转换为复积分，我们成功地导出了位移和应力场的显式表达式。值得注意的是，这些表达式涵盖了一次波、二次波和表面波，提供了盘内应力传播现象的全面表征。我们的研究结果有助于理解盘形部件的机械行为，并且对于跨不同工程学科的此类结构的设计和优化具有重要价值。