Open Access

ARTICLE

A Displacement Solution to Transverse Shear Loading of Composite Beams by BEM

by E.J. Sapountzakis¹, V.G. Mokos²

1 Associate Professor, School of Civil Engineering, National Technical University, Zografou Campus, GR–157 80, Athens, Greece. cvsapoun@central.ntua.gr
2 Dr. Civil Engineer, School of Civil Engineering, National Technical University, Zografou Campus, GR–157 80 Athens, Greece. vgmokos@central.ntua.gr

Computers, Materials & Continua 2009, 10(1), 1-40. https://doi.org/10.3970/cmc.2009.010.001

Abstract

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

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