Natural stiffness matrix for beams on Winkler foundation: exact force-based derivation

Suchart Limkatanyu, Kittisak Kuntiyawichai, Enrico Spacone and Minho Kwon

Abstract

This paper presents an alternative way to derive the exact element stiffness matrix for a beam on Winkler foundation and the fixed-end force vector due to a linearly distributed load. The element flexibility matrix is derived first and forms the core of the exact element stiffness matrix. The governing differential compatibility of the problem is derived using the virtual force principle and solved to obtain the exact moment interpolation functions. The matrix virtual force equation is employed to obtain the exact element flexibility matrix using the exact moment interpolation functions. The so-called \"natural\" element stiffness matrix is obtained by inverting the exact element flexibility matrix. Two numerical examples are used to verify the accuracy and the efficiency of the natural beam element on Winkler foundation.

Key Words

beam elements; winkler foundation; finite element; flexibility-based formulation; virtual force principle; soil-structure interaction; natural stiffness matrix

Address

Suchart Limkatanyu: Department of Civil Engineering, Faculty of Engineering, Prince of Songkla University, Songkhla, 90110, Thailand Kittisak Kuntiyawichai: Department of Civil Engineering, Faculty of Engineering, Ubonratchathani University, Ubonratchathani, Thailand Enrico Spacone: Department of PRICOS, Faculty of Architecture, University \"G. D\'Annunzio\", Pescara, Italy Minho Kwon: Department of Civil Engineering, ERI, Gyeongsang National University, Jinju, Korea

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