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首页> 外文期刊>Computational Mechanics >A BEM formulation for analysing the coupled stretching–bending problem of plates reinforced by rectangular beams with columns defined in the domain
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A BEM formulation for analysing the coupled stretching–bending problem of plates reinforced by rectangular beams with columns defined in the domain

机译：BEM公式，用于分析矩形梁增强的板的拉伸-弯曲耦合问题，该矩形梁在域中定义

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摘要

In this work, a boundary element formulation to analyse plates reinforced by rectangular beams, with columns defined in the domain is proposed. The model is based on Kirchhoff hypothesis and the beams are not required to be displayed over the plate surface, therefore eccentricity effects are taken into account. The presented boundary element method formulation is derived by applying the reciprocity theorem to zoned plates, where beams are treated as thin sub-regions with larger rigidities. The integral representations derived for this complex structural element consider the bending and stretching effects of both structural elements working together. The standard equilibrium and compatibility conditions along interface are naturally imposed, being the bending tractions eliminated along interfaces. The in-plane tractions and the bending and in-plane displacements are approximated along the beam width, reducing the number of degrees of freedom. The columns are introduced into the formulation by considering domain points where tractions can be prescribed. Some examples are then shown to illustrate the accuracy of the formulation, comparing the obtained results with other numerical solutions.
机译：在这项工作中，提出了一种边界元公式，用于分析矩形梁加固的板，并在域中定义了柱。该模型基于基尔霍夫（Kirchhoff）假设，不需要在平板表面上显示光束，因此考虑了偏心率影响。所提出的边界元方法公式是通过将互易性定理应用于分区板而得出的，在分区板中，梁被视为具有较大刚度的薄分区。为此复杂的结构元素得出的整体表示考虑了两个结构元素共同作用的弯曲和拉伸效果。自然地会沿界面施加标准的平衡和相容性条件，因为沿界面消除了弯曲牵引力。沿梁的宽度近似于平面内的牵引力以及弯曲和平面内的位移，从而减少了自由度的数量。通过考虑可指定牵引力的域点将这些列引入到配方中。然后显示一些示例以说明配方的准确性，并将获得的结果与其他数值解进行比较。

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