dc.description.abstract |
Soils do not behave as elastic solids, but elasticity theory is widely used to compute
stresses and displacements in soil profiles. Different subgrade models have been
proposed by many researchers for problems of beams and plates on elastic foundations.
The most common and simplest model is the single-parameter model proposed by
Winkler. However, because of its inherent shortcomings, researchers have subsequently
proposed improved models involving multiple parameters. Though these relatively more
recent models present improvements, they still have their own drawbacks associated with
the nature of the simplifying assumptions they make. Worku suggested improved
continuum-based models, with the objective of improvement of such models.
The main objective of this research is to implement, calibrate and validate the improved
continuum-based Winkler-Type and Pasternak-Type models of Worku for the analysis of
beams and strip plates using the Finite Difference Method. This demanded the
determination of the governing ODEs integrating the beam-soil behavior. The ODEs are
then transformed into a set of algebraic equations with parameters defined at regular
intervals along the domain of the problem. This transformation is achieved by
approximating the derivatives of a continuous function by a combination of discrete
values of the variables at selected points in the domain with appropriate boundary
conditions. The algebraic equations obtained are then written in matrix form.
The basic parameters of interest in this study are beam/strip deformation (deflection) and
internal forces. Comparisons are also made with selected existing models.
MATLAB software is used to provide fast and time saving method of solution for the
matrices of algebraic equations. A FE-based softwares PLAXIS 3D and PlAXIS 2D are
used for the calibration and validation purposes of beams and strip plates respectively
The calibration factors for both models are established from comparative numerical FD -
FE studies and are recommended to be used for practical use. It is found that, the
calibrated formulas are efficient for the analysis of beams and strip plates on elastic
foundations. |
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