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H.A.F.A. Santos, "A Variationally Consistent Force-Based Finite Element Formulation for the Dynamic Analysis of Cracked Beams Under Moving Loads", in P. Iványi, J. Kruis, B.H.V. Topping, (Editors), "Proceedings of the Sixteenth International Conference on Computational Structures Technology", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 14, Paper 15.1, 2026, doi:10.4203/ccc.14.15.1

Keywords: finite element method, force-based formulation, structural dynamics, moving loads, cracked beams, flexibility-based crack modelling.

Abstract

Moving loads can induce dynamic amplifications in beam-like structures that significantly exceed quasi-static predictions, especially in the presence of localized damage. This work extends a recently proposed force-based finite element formulation for beams under moving loads to cracked configurations using a physically consistent flexibility-based crack model. Cracks are represented by Dirac-delta contributions in the bending flexibility, enabling the treatment of concentrated damage without violating positive-definiteness of stiffness. The formulation, derived from a one-field variational principle dual to Hamilton's principle, yields strongly equilibrated and C0-continuous bending moment and shear force fields, which are well suited for design-oriented post-processing. Numerical results for simply-supported Euler-Bernoulli beams in both the frequency and time domains demonstrate the influence of crack location and severity on eigenfrequencies and dynamic response, and confirm the accuracy, robustness, and computational efficiency of the proposed approach.

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Front Page Browse CCC CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Conferences ISSN 2753-3239 CCC: 14 PROCEEDINGS OF THE SIXTEENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: P. Iványi, J. Kruis and B.H.V. Topping Paper 15.1 A Variationally Consistent Force-Based Finite Element Formulation for the Dynamic Analysis of Cracked Beams Under Moving Loads H.A.F.A. Santos Instituto Superior de Engenharia de Lisboa, Polytechnic University of Lisbon, Portugal doi:10.4203/ccc.14.15.1 Full Bibliographic Reference for this paper H.A.F.A. Santos, "A Variationally Consistent Force-Based Finite Element Formulation for the Dynamic Analysis of Cracked Beams Under Moving Loads", in P. Iványi, J. Kruis, B.H.V. Topping, (Editors), "Proceedings of the Sixteenth International Conference on Computational Structures Technology", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 14, Paper 15.1, 2026, doi:10.4203/ccc.14.15.1 Keywords: finite element method, force-based formulation, structural dynamics, moving loads, cracked beams, flexibility-based crack modelling. Abstract Moving loads can induce dynamic amplifications in beam-like structures that significantly exceed quasi-static predictions, especially in the presence of localized damage. This work extends a recently proposed force-based finite element formulation for beams under moving loads to cracked configurations using a physically consistent flexibility-based crack model. Cracks are represented by Dirac-delta contributions in the bending flexibility, enabling the treatment of concentrated damage without violating positive-definiteness of stiffness. The formulation, derived from a one-field variational principle dual to Hamilton's principle, yields strongly equilibrated and C0-continuous bending moment and shear force fields, which are well suited for design-oriented post-processing. Numerical results for simply-supported Euler-Bernoulli beams in both the frequency and time domains demonstrate the influence of crack location and severity on eigenfrequencies and dynamic response, and confirm the accuracy, robustness, and computational efficiency of the proposed approach. download the full-text of this paper (PDF, 14 pages, 456 Kb) go to the previous paper go to the next paper return to the table of contents return to the volume description
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