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Coupled Systems Mechanics Volume 10, Number 1, February 2021 , pages 79-102 DOI: https://doi.org/10.12989/csm.2021.10.1.079 |
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Linearized instability analysis of frame structures under nonconservative loads: Static and dynamic approach |
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Emina Hajdo, Rosa Adela Mejia-Nava, Ismar Imamovic
and Adnan Ibrahimbegovic
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| Abstract | ||
| In this paper we deal with instability problems of structures under nonconservative loading. It is shown that such class of problems should be analyzed in dynamics framework. Next to analytic solutions, provided for several simple problems, we show how to obtain the numerical solutions to more complex problems in efficient manner by using the finite element method. In particular, the numerical solution is obtained by using a modified Euler-Bernoulli beam finite element that includes the von Karman (virtual) strain in order to capture linearized instabilities (or Euler buckling). We next generalize the numerical solution to instability problems that include shear deformation by using the Timoshenko beam finite element. The proposed numerical beam models are validated against the corresponding analytic solutions. | ||
| Key Words | ||
| instability problems; non-conservative load; Euler-Bernoulli beam; von Karman strain; Timoshenko beam; shear deformation | ||
| Address | ||
| Emina Hajdo: Faculty of Civil Engineering, University of Sarajevo, Patriotske lige 30, Sarajevo, BiH, Bosnia and Herzegovina Rosa Adela Mejia-Nava: Universite de Technologie Compiegne, Laboratoire Roberval de Mecanique, Rue du Dr Schweitzer, 60200 Compiegne, France Ismar Imamovic: Faculty of Civil Engineering, University of Sarajevo, Patriotske lige 30, Sarajevo, BiH, Bosnia and Herzegovina Adnan Ibrahimbegovic: Universite de Technologie Compiegne, Laboratoire Roberval de Mecanique, Rue du Dr Schweitzer, 60200 Compiegne, France; Institut Universitaire de France, France | ||
