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An extended beam theory for smart materials applications part I: Extended beam models, duality theory, and finite element simulations

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Abstract

An extended theory for elastic and plastic beam problems is studied. By introducing new dependent and independent variables, the standard Timoshenko beam model is extended to take account of shear variation in the lateral direction. The dynamic governing equations are established via Hamilton's principle, and existence and uniqueness results for the solution of the static problem are proved. Using the theory of convex analysis, the duality theory for the extended beam model is developed. Moreover, the extended theory for rigid-perfectly plastic beams is also established. Based on the extended model, a finite-element method is proposed and numerical results are obtained indicating the usefulness of the extended theory in applications.

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Communicated by R. Triggiani

The work of the first author was supported in part by National Science Foundation under Grant DMS9400565.

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Gao, D.Y., Russell, D.L. An extended beam theory for smart materials applications part I: Extended beam models, duality theory, and finite element simulations. Appl Math Optim 34, 279–298 (1996). https://doi.org/10.1007/BF01182627

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  • DOI: https://doi.org/10.1007/BF01182627

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