Keywords: flexural-torsional analysis, dynamic analysis, nonlinear analysis, prismatic beams, beams of variable cross section, non-uniform torsion, boundary element method..

In this paper, the geometrically nonlinear flexural-torsional dynamic analysis of beams of uniform or variable stiffness is reviewed. As far as prismatic beams are concerned, the most general case is examined by considering arbitrary thin- or thick-walled cross sections possessing no axis of symmetry. Additionally, when it comes to cross sectional variability, the frequently encountered case of beams of arbitrary doubly symmetric cross section having symmetric and smooth variation law is also examined. In any case, the beam may undergo moderately large deflections and twisting rotations, under the most general boundary conditions. The beam is subjected to arbitrarily distributed or concentrated transverse loading, which can be applied to any arbitrary point of the lateral surface of the beam; to bending moments, as well as to twisting and/or axial loading. Four boundary value problems are formulated and solved using the analog equation method (AEM), which is a boundary element method (BEM) based technique. Application of the boundary element technique yields a system of nonlinear coupled differential-algebraic equations of motion, which can be solved iteratively using any efficient solver. The torsional warping function, the geometric constants of the cross sections, and the stress components on any arbitrary point of the beam are evaluated employing a pure BEM approach, i.e. only boundary discretization of the cross section is used. In order to illustrate the application of the developed model numerical, examples are presented and discussed. Finally, the paper closes with some concluding remarks and future perspectives.

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