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# Flexural - Torsional Nonlinear Analysis of Timoshenko Beam-Column of Arbitrary Cross Section by BEM

E.J. Sapountzakis1, J.A. Dourakopoulos1

School of Civil Engineering, National Technical University, Zografou Campus, GR–157 80,Athens, Greece. cvsapoun@central.ntua.gr

Computers, Materials & Continua 2010, 18(2), 121-154. https://doi.org/10.3970/cmc.2010.018.121

## Abstract

In this paper a boundary element method is developed for the nonlinear flexural - torsional analysis of Timoshenko beam-columns of arbitrary simply or multiply connected constant cross section, undergoing moderate large deflections under general boundary conditions. The beam-column is subjected to the combined action of an arbitrarily distributed or concentrated axial and transverse loading as well as to bending and twisting moments. To account for shear deformations, the concept of shear deformation coefficients is used. Seven boundary value problems are formulated with respect to the transverse displacements, to the axial displacement, to the angle of twist (which is assumed to be small), to the primary warping function and to two stress functions and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique yields a system of nonlinear equations from which the transverse and axial displacements as well as the angle of twist are computed by an iterative process. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress 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 influence of both the shear deformation effect and the variableness of the axial loading are remarkable.

## Keywords

E. . Sapountzakis and J. . Dourakopoulos, "Flexural - torsional nonlinear analysis of timoshenko beam-column of arbitrary cross section by bem," Computers, Materials & Continua, vol. 18, no.2, pp. 121–154, 2010.

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