This paper presents a new displacement solution based on a Modified Fourier Series (MFS) for isotropic linear elastic solids under plane strain or plane stress states subject to continuous displacement and traction boundary conditions in a two-dimensional rectangular domain. In contrast with existing approaches that are restricted to Fourier series with a rate of convergence of second order O(m^-2), the MFS allows increasing the rate of convergence of the solution. The governing Partial Differential Equations (PDEs) are satisfied exactly by two displacement solutions while the boundary conditions are approximated after solving a finite system of algebraic equations. Numerical results for a solution with an MFS with rate of convergence O(m^-3) are compared with results from existing numerical and analytical methods, showing the enhanced behavior of the present solution.

本文提出了一种基于修正傅立叶级数 (MFS) 的新位移解，用于在二维矩形域中受连续位移和牵引边界条件影响的平面应变或平面应力状态下的各向同性线弹性固体。与限制为二阶收敛速度为 O(m ^-2 ) 的傅立叶级数的现有方法相比，MFS 允许提高解的收敛速度。控制偏微分方程 (PDE) 由两个位移解精确满足，而边界条件在求解有限代数方程组后近似。具有收敛速度为 O(m ^-3)的 MFS 解的数值结果) 与现有数值和分析方法的结果进行比较，显示了当前解决方案的增强行为。