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Geomechanics and Engineering
  Volume 24, Number 4, February25 2021 , pages 371-388

Nonlinear flexibility-based beam element on Winkler-Pasternak foundation
Worathep Sae-Long, Suchart Limkatanyu, Chayanon Hansapinyo, Woraphot Prachasaree, Jaroon Rungamornrat and Minho Kwon

    A novel flexibility-based beam-foundation model for inelastic analyses of beams resting on foundation is presented in this paper. To model the deformability of supporting foundation media, the Winkler-Pasternak foundation model is adopted. Following the derivation of basic equations of the problem (strong form), the flexibility-based finite beam-foundation element (weak form) is formulated within the framework of the matrix virtual force principle. Through equilibrated force shape functions, the internal force fields are related to the element force degrees of freedom. Tonti's diagrams are adopted to present both strong and weak forms of the problem. Three numerical simulations are employed to assess validity and to show effectiveness of the proposed flexibility-based beam-foundation model. The first two simulations focus on elastic beam-foundation systems while the last simulation emphasizes on an inelastic beam-foundation system. The influences of the adopted foundation model to represent the underlying foundation medium are also discussed.
Key Words
    flexibility-based formulation; beam element; Winkler-Pasternak foundation; soil-structure interaction; virtual force principle; finite element; nonlinear analysis
Worathep Sae-Long: Department of Civil Engineering, School of Engineering, University of Phayao, Phayao 56000, Thailand

Suchart Limkatanyu and Woraphot Prachasaree: Department of Civil Engineering, Faculty of Engineering, Prince of Songkla University, Songkhla 90110, Thailand

Chayanon Hansapinyo: Excellence Center in Infrastructure and Transportation Engingeering (ExCITE),Department of Civil Engineering, Chiang Mai University, Chiang Mai 50200, Thailand

Jaroon Rungamornrat: Applied Mechanics and Structures Research Unit, Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand

Minho Kwon: Department of Civil Engineering, ERI, Gyeongsang National University, Jinju 660-701, South Korea

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