Reduction and recovering method of frame structures into a single degree of freedom system

Abstract eng:
The work in this paper proposes a new method for reducing MDOF (Multi Degree of Freedom) system of frame structures into SDOF (Single Degree of Freedom) system and recovering back the results of dynamic analysis from the SDOF to the MDOF system. In most of the dynamic condensation methods, the reduction of MDOF into an SDOF system is usually done by means of modal analysis. As a result, simplification against the MDOF is made forward-wise and not reversible. In other words, after the responses of SDOF sytem evaluated by the modal and dynamic analyses, then it is not possible to recover back the responses of the other condensed degree of freedoms accurately. In this paper, a new method to reduce MDOF system of frame structures into strains field is introduced. In this Strain Reduction Method, displacement and rotational DOFs of all nodal points in the frame structures except an arbitrarily selected representative node are transformed into their strains field before the reduction process. By adopting previous authors’ work in improving the dynamic reduction method, small order in magnitude of strains field can be separated as secondary DOFs, hence leaving the representative node as an SDOF system. After conducting dynamic analysis to the SDOF system, the time historical responses of the SDOF system can be used to recover back the time historical responses in the MDOF system of frame structures within negligible error.

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