In this paper, the analytical displacement solution at the point of the application of a concentrated force is derived using elastic mechanics. Then, the concentrated-force asymptotic function is obtained. Next, by introducing the concentrated-force asymptotic functions into finite element analysis, a method of simulating concentrated forces is developed. The proposed method can obtain an accurate stress field without any mesh refinement at the point of the application of a concentrated force. Meanwhile, the proposed method has considered the effect of the direction of the concentrated forces. The numerical tests reveal that the proposed method is convergent, accurate and feasible for obtaining satisfactory results.

中文翻译：

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一种在有限元分析中精确模拟集中力的新方法

在本文中，使用弹性力学推导出集中力作用点处的解析位移解。然后，得到集中力渐近函数。接下来，通过将集中力渐近函数引入有限元分析，开发了一种模拟集中力的方法。所提出的方法可以在施加集中力的点处获得准确的应力场，而无需任何网格细化。同时，所提出的方法考虑了集中力方向的影响。数值试验表明，该方法收敛性好，准确可行，能得到满意的结果。