This paper is concerned with the deformation of beams in the framework of the linear theory of micromorphic elastic solids. First, the plane strain of anisotropic and homogeneous elastic cylinders is investigated. Existence and uniqueness results are presented. Then, Saint-Venant’s problem for micromorphic beams is formulated. A method is established to reduce the extension, bending and torsion to the study of some plane problems. Finally, the deformation of beams loaded on the lateral surface is investigated. As a special case, the solution of the flexure problem is obtained. The method is used to study the deformation of a micromorphic rod subjected to a uniform pressure on the lateral surface.

本文在微形弹性固体线性理论的框架内关注梁的变形。首先，研究了各向异性弹性圆柱体的平面应变。给出了存在性和唯一性结果。然后，提出了微形梁的Saint-Venant问题。建立了一种减少延伸，弯曲和扭转的方法来研究某些平面问题。最后，研究了加载在侧面的梁的变形。作为一种特殊情况，可以获得挠曲问题的解决方案。该方法用于研究微变形棒在侧面上受到均匀压力的变形。