Anisotropic materials are those that the value of a property depends on the direction of analysis. This article addresses both analytical and numerical stress computation for orthotropic beams under normal and shear loads. The analytical solution is based on potential polynomial functions and the present work establishes general strategies which allow systematic evaluation of the polynomial coefficients. The numerical approximation uses an alternative formulation of finite volumes based on an area weighted average associated with parabolic interpolation functions. The numerical scheme is verified against results obtained for orthotropic beams using both the analytical method and a classical finite volume approximation. Assessment of the global error based on the \(L_2\) norm indicates a high convergence rate and substantially smaller absolute differences when compared to the conventional finite volume approximation.

各向异性材料是指属性值取决于分析方向的材料。本文讨论了在法向荷载和剪力荷载下正交异性梁的解析应力和数值应力计算。解析解决方案基于潜在的多项式函数，本工作建立了可对多项式系数进行系统评估的通用策略。数值近似基于与抛物线插值函数相关的面积加权平均值，使用有限体积的替代形式。使用解析方法和经典的有限体积近似，针对正交异性梁的结果验证了数值方案。基于\（L_2 \）的全局误差评估 与常规的有限体积近似法相比，范数表示较高的收敛速度和绝对较小的绝对差。