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A BEM solution to transverse shear loading of composite beams

机译：组合梁横向剪力的BEM解决方案

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In this paper a boundary element method is developed for the solution of the general transverse shear loading problem of composite beams of arbitrary constant cross-section. The composite beam consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli with same Poisson's ratio and are firmly bonded together. The analysis of the beam is accomplished with respect to a coordinate system that has its origin at the centroid of the cross-section, while its axes are not necessarily the principal ones. The transverse shear loading is applied at the shear centre of the cross-section, avoiding in this way the induction of a twisting moment. Two boundary value problems that take into account the effect of Poisson's ratio are formulated with respect to stress functions and solved employing a pure BEM approach, that is only boundary discretization is used. The evaluation of the transverse shear stresses is accomplished by direct differentiation of these stress functions, while both the coordinates of the shear center and the shear deformation coefficients are obtained from these functions using only boundary integration. Numerical examples with great practical interest are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The accuracy of the proposed shear deformation coefficients compared with those obtained from a 3-D FEM solution of the 'exact' elastic beam theory is remarkable. (C) 2004 Elsevier Ltd. All rights reserved.
机译：本文提出了一种边界元方法来解决任意恒定截面的组合梁的一般横向剪力荷载问题。复合梁由接触的材料组成，每种材料可以包围有限数量的夹杂物。具有相同泊松比的材料具有不同的弹性和剪切模量，并且牢固地粘合在一起。光束的分析是针对坐标系进行的，该坐标系的原点位于横截面的质心，而其轴不一定是主要轴。横向剪切载荷施加在横截面的剪切中心，从而避免了扭转力矩的产生。针对应力函数，提出了两个考虑泊松比影响的边值问题，并采用纯BEM方法解决，即仅使用边界离散化。横向剪切应力的评估是通过直接微分这些应力函数来完成的，而剪切中心的坐标和剪切变形系数都是从这些函数中仅使用边界积分获得的。数值算例表明了该方法的有效性，准确性和适用范围。与从“精确”弹性梁理论的3-D FEM解决方案获得的剪切变形系数相比，拟议的剪切变形系数的准确性非常出色。 （C）2004 Elsevier Ltd.保留所有权利。

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