The Saint-Venant problem for porous elastic cylinders is of interest both from the technical and mathematical point of view. The intended applications of solution are to mechanics of bone and to some engineering structures. This work investigates the Saint-Venant problem for almost prismatic bars made of an isotropic porous material. We express the solution in terms of the solutions of two problems concerning the deformation of a right cylinder. We use the method to study the extension of an almost prismatic conical frustum. It is found that the displacement vector is a polynomial of two degree in the cartesian coordinates. The volume fraction field depends linearly on the axial coordinate. The solution contains terms characterizing the influence of the material porosity and the dependence on the lateral surface.

中文翻译：

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关于几乎圆柱形弹性梁的变形

从技术和数学角度来看，多孔弹性圆柱体的Saint-Venant问题都是令人关注的问题。解决方案的预期应用是骨骼力学和某些工程结构。这项工作研究了由各向同性多孔材料制成的几乎棱柱形钢筋的Saint-Venant问题。我们用有关右圆柱体变形的两个问题的解来表示该解。我们使用该方法来研究几乎棱柱形的圆锥形截头圆锥体的延伸。发现位移矢量是笛卡尔坐标中的二阶多项式。体积分数场线性依赖于轴向坐标。该解决方案包含表征材料孔隙率的影响和对侧面的依赖性的术语。