Keywords: warping function, transverse shear stresses, shear center, shear deformation coefficients, composite, beam, boundary element method.

In this paper the boundary element method (BEM) is employed to develop a displacement solution for the general transverse shear loading problem of composite beams of arbitrary constant cross section. The composite beam (thin or thick walled) consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli 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 bending ones. The transverse shear loading is applied at the shear center of the cross section, avoiding in this way the induction of a twisting moment. The evaluation of the transverse shear stresses at any interior point is accomplished by direct differentiation of a warping function. The shear deformation coefficients are obtained from the solution of two boundary value problems with respect to warping functions appropriately arising from the aforementioned one using only boundary integration, while the coordinates of the shear center are obtained from these functions using again only boundary integration. Three boundary value problems are formulated with respect to corresponding warping functions and solved employing a pure BEM approach. In very thin-walled cross sections, special care is taken during the numerical evaluation of the line integrals in order to avoid their "near singular integral behaviour". According to this, boundary elements that are very close to each other (a distance smaller than their length) are divided in sub-elements, in each of which Gauss integration is applied. The essential features and novel aspects of the present formulation are summarized as follows:

1. The proposed displacement solution constitutes the first step to the solution of the nonuniform shear problem avoiding the use of stress functions.
2. All basic equations are formulated with respect to an arbitrary coordinate system, which is not restricted to the principal axes.
3. The boundary conditions at the interfaces between different material regions have been considered.
4. The shear deformation coefficients are evaluated using an energy approach instead of Timoshenko's and Cowper's definitions, for which several authors have pointed out that one obtains unsatisfactory results or definitions given by other researchers, for which these factors take negative values.
5. The proposed method can be efficiently applied to homogeneous and composite beams of thin walled cross section and to laminated composite beams, without the restrictions of the "refined models".
6. The developed procedure retains the advantages of a BEM solution over a pure domain discretization method since it requires only boundary discretization.

Numerical examples are worked out to illustrate the efficiency, the accuracy and the range of applications of the method developed. The accuracy of the values obtained for the resultant transverse shear stresses compared with those obtained from an exact solution is remarkable.

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