在保证级数的一致收敛的前提下,可以利用Laplace变换对有限一维空间弹性动力学边值问题给出公理化的严格求解过程,此过程能够作为Lavrentieff与Hilbert等著名学者的工作的补充。这一解答能够应用于岩土工程中的自由场计算问题,并且能够从原则上避免截断误差。在针对特定问题的计算中,该方法的效率明显高于有限元,并且在一定程度上弥补了现有的自由场专用计算软件不能计算纯弹性体的缺点。同时,作为解析解算法,该方法对于数值算法的精度分析有一定意义。 Laplace transform can be used to give an axiomatic rigorous solution to the finite-dimensional elasto-dynamic boundary value problem, which can complement the work of famous scholars such as Lavrentieff and Hilbert. This solution can be applied to free-field calculations in geotechnical engineering and truncation errors can in principle be avoided. The efficiency of this method is obviously higher than that of the finite element in the calculation of a specific problem, and to a certain extent, it remedies the defect that the existing free-field calculation software can not calculate the pure elastomer. Meanwhile, as an analytic solution algorithm, this method has certain significance for the accuracy analysis of numerical algorithms.