In this paper, a novel complex potential function for the solution of the flexure-torsion problem in De Saint Venant beams is proposed, considering the simultaneous presence of external shear and torsion excitations. By defining a fictitious vector field and taking advantage of a hydrodynamic analogy, the proposed complex potential function allows the stress vector field and the unitary twist rotation of the cross-section to be determined at once, and, therefore, returns the complete solution of the problem. The proposed approach is well-suited for domains having boundary singularities. A numerical application, implemented by using the Complex Variable Boundary Element Method (CVBEM), is reported for an elliptical cross-section to show the validity of the proposed complex potential. Finally, two singularity problems are analyzed, considering an L-shaped and an epicycloid-shaped cross-section.

Complex potential by hydrodynamic analogy for the determination of flexure-torsion induced stresses in de Saint Venant beams with boundary singularities

BARONE, GIORGIO;LO IACONO, FRANCESCO;NAVARRA, GIACOMO CAMILLO
2013

Abstract

In this paper, a novel complex potential function for the solution of the flexure-torsion problem in De Saint Venant beams is proposed, considering the simultaneous presence of external shear and torsion excitations. By defining a fictitious vector field and taking advantage of a hydrodynamic analogy, the proposed complex potential function allows the stress vector field and the unitary twist rotation of the cross-section to be determined at once, and, therefore, returns the complete solution of the problem. The proposed approach is well-suited for domains having boundary singularities. A numerical application, implemented by using the Complex Variable Boundary Element Method (CVBEM), is reported for an elliptical cross-section to show the validity of the proposed complex potential. Finally, two singularity problems are analyzed, considering an L-shaped and an epicycloid-shaped cross-section.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11387/44526
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