We address the challenging issue of simultaneously finding transverse shear and normal stresses at all points in a plate from a priori known values of the in-plane stresses at plate's interior points. The principle of virtual work is employed to equate the work done by the transverse stresses to the difference between the work done by the external forces (applied surface tractions and body forces) and that by the in-plane stresses. The three transverse stresses and the virtual displacements are expressed in terms of polynomial (for example, those used in the finite element method) basis functions to deduce a system of simultaneous algebraic equations for the transverse stresses. The integrands for the right-hand side of these equations can be evaluated from the values of the in-plane stresses. The proposed scheme is advantageous over the current methods in economically evaluating accurate values of transverse stresses from the knowledge of the in-plane stresses at the Barlow points where they are most accurate. Since no spatial derivatives of the in-plane stresses are needed, this technique provides excellent values of transverse stresses. Results for three example problems are provided to illustrate the methodology and the accuracy of computed transverse stresses.

我们解决了从先验同时找到板中所有点的横向剪应力和法向应力的挑战性问题板内点处平面内应力的已知值。虚功原理用于将横向应力所做的功等同于外力（施加的表面牵引力和体力）所做的功与平面内应力所做的功之差。三个横向应力和虚拟位移以多项式（例如，在有限元方法中使用的那些）基函数表示，以推导出横向应力的联立代数方程组。这些方程右侧的被积函数可以从面内应力的值进行评估。所提出的方案优于目前的方法，在根据巴洛点处的平面应力的知识经济地评估横向应力的准确值方面，它们是最准确的。由于不需要平面内应力的空间导数，因此该技术提供了出色的横向应力值。提供了三个示例问题的结果来说明计算横向应力的方法和准确性。