A mixed finite element formulation for timoshenko beam on winkler foundation

Ergüven, M.E.; Gedikli, Abdullah

doi:10.1007/s00466-003-0420-9

Cited by 19 publications

(3 citation statements)

References 38 publications

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“…Reports of other approaches, such as relaxation techniques22, iterative methods23–26, integral transform techniques27, matrix method28–32, and initial condition methods33, can be found in the literature. Other recent developments included the Green's function approach34, 35, finite element methods36–39, and boundary integral equation methods40. In particular, Yin41, 42 has developed a Timoshenko beam model for the analysis of interaction action between a reinforced structure and the soil.…”

Section: Beams On An Elastic Foundationmentioning

confidence: 99%

Beams and plates on elastic foundations: a review

Wang

Tham

Cheung

2005

Progress Structural Eng Maths

165

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The interaction action between structures and supporting soil media is of fundamental importance in foundation design and it has always attracted the attention of both researchers and engineers. This paper reviews the state-of-the-art in this field, highlighting the key areas of development, including the modelling of the soil media and various analytical as well as numerical approaches in analysing the interaction action between the foundation and soil.

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Section: Beams On An Elastic Foundationmentioning

confidence: 99%

Beams and plates on elastic foundations: a review

Wang

Tham

Cheung

2005

Progress Structural Eng Maths

165

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“…A discrete method such as the Finite Element Method (FEM) is the first to address the problem numerically [1][2][3]. The Differential Quadrature Method (DQM) is also employed for the solution to similar engineering problems involving beam vibrations and foundations [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

A Discrete Model for Nonlinear Vibration of Beams Resting on Various Types of Elastic Foundations

Khnaijar

Benamar

2017

Advances in Acoustics and Vibration

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This paper presents a discrete physical model to approach the problem of nonlinear vibrations of beams resting on elastic foundations. The model consists of a beam made of several small bars, evenly spaced. The bending stiffness is modeled by spiral springs, and the Winkler soil stiffness is modeled using linear vertical springs. Concentrated masses, presenting the inertia of the beam, are located at the bar ends. Finally, the nonlinear effect is presented by the axial forces in the bars, assumed to behave as longitudinal springs, due to the change in their length induced by the Pythagorean Theorem. This model has the advantage of simplifying parametric studies, because of its discrete nature, allowing any modification in the mass matrix, the stiffness matrix, and the nonlinearity tensor to be made separately. Therefore, once the model is established, various practical applications may be performed without the need of going through all the formulation again. The study of the nonlinear behavior makes the solution of the movement equation rise in complexity. By considering this discrete model and using the linearization method, one can achieve an idealized approach to this nonlinear problem and obtain quite easily approximate solutions.

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“…Zhaohua and Cook [34] showed that in a certain case, only one beam-foundation element derived based on the exact displacement interpolation functions yielded results as precise as those obtained with eighty beam-foundation elements derived based on the assumed Hermite displacement interpolation functions. Due to some desirable features of the force method recognized in the framework of structural analysis [42,43], several researchers [15,44,45] have developed the beam-foundation elements based on mixed and force-based finite element formulations using the assumed displacement and force interpolation functions. Although a drastic improvement in the model accuracy was gained in these unconventional beam-foundation elements, an approximate nature was still inherent in their element stiffness matrices.…”

Section: Introductionmentioning

confidence: 99%

Force‐based derivation of exact stiffness matrix for beams onWinkler‐Pasternak foundation

et al. 2013

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Key wordsBeam elements, Winkler-Pasternak foundation, finite element, force-based formulation, virtual force principle, soil-structure interaction, natural stiffness matrix.In this paper, the exact element stiffness matrix for a beam on Winkler-Pasternak foundation and the fixed-end force vector due to a linearly distributed load are alternatively derived based on the virtual force principle. The exact element flexibility matrix is at the core of the derivation of the exact element stiffness matrix and is formulated based on the exact force interpolation functions. The virtual force principle is employed to reveal the governing differential compatibility equations as well as the associated end-boundary compatibility conditions. The exact force interpolation functions of the beam-foundation system are derived based on the analytical solution of the governing differential compatibility equations of the problem for all combinations of foundation parameters and beam rigidity. This feature is unique to this paper. The matrix virtual force equation is employed to obtain the exact element flexibility matrix using the exact force interpolation functions. The so-called "natural" element stiffness matrix is obtained by inverting the exact element flexibility matrix.Three numerical examples confirm the accuracy and the efficiency of the natural beam element on Winkler-Pasternak foundation and show the deficiency of the widely used Winkler foundation model.

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A mixed finite element formulation for timoshenko beam on winkler foundation

Cited by 19 publications

References 38 publications

Beams and plates on elastic foundations: a review

Beams and plates on elastic foundations: a review

A Discrete Model for Nonlinear Vibration of Beams Resting on Various Types of Elastic Foundations

Force‐based derivation of exact stiffness matrix for beams onWinkler‐Pasternak foundation

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