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Direct stiffness method
About: Direct stiffness method is a research topic. Over the lifetime, 2584 publications have been published within this topic receiving 53131 citations.
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TL;DR: In this paper, the authors derived the finite element of a beam with an arbitrary number of transverse cracks, where each crack is replaced by a corresponding linear rotational spring connecting two adjacent elastic parts.
31 citations
TL;DR: In this paper, the authors examined several basic issues related to the properties of the interface stiffness, especially the determination of the interfaces stiffness in particular directions (i.e., the commonly used scalar form of interface stiffness).
31 citations
TL;DR: In this article, a train-track-bridge model was proposed by combining the direct stiffness method (DSM) and the mode superposition method (MSM) for analysis of the train track-bridge interaction.
Abstract: In this study, a track-bridge model was proposed by combining the direct stiffness method (DSM) and the mode superposition method (MSM) for analysis of the train-track-bridge interaction. The tracks were modeled by applying DSM, which can effectively display the nonlinear contact spring and the dynamic behavior of the tracks. The bridge was modeled by applying MSM, a method that can efficiently show dynamic behavior with a small number of modes. The analysis model was built based on a previously proposed train-track analysis model. Consequently, the train, track, and bridge were modeled as a coupled system that was interconnected by nonlinear Hertzian springs between the train and track, and springs and dampers between the track and bridge. Thus, the convergence is greatly improved as a result of the stabilization of the analytical system. Using the proposed train-bridge-track interaction analysis model, the impacts of the vertical displacements of the bridge resulting from thermal load on the dyn...
31 citations
TL;DR: In this paper, a method for locating and estimating structural damage in two and three-dimensional analytical models of buildings is presented, where damage is defined in terms of changes in elements stiffness.
31 citations
TL;DR: In this article, a joint matrix for internally generated moments and a moment matrix for externally applied moments is derived for planar frames that are allowed to buckle both in and out of plane.
Abstract: Conventional element assembly process based on the initial configuration of structures does not necessarily imply the satisfaction of compatibility conditions in the deformed state. This may result in a violation to the rule that all physical relations should be specified for deformed structures in a buckling analysis. Based on an exact consideration of the interelement compatibility for structural members, one can derive a joint matrix for internally generated moments and a moment matrix for externally applied moments, in addition to the elastic and geometric stiffness matrices commonly used in nonlinear analysis. To highlight the linking between the fundamental mechanics equations and their finite element counterparts, the present derivation will be made only for planar frames that are allowed to buckle both in and out of plane. The validity of the present procedure is confirmed in the numerical examples.
31 citations