Abstract
The convergence of numerical solution based on two nodded beam finite element require considerable number of iterations and time; and is also plagued with shear locking. To address these deficiencies a three nodded beam element is proposed in this study to simulate the behavior of beams on elastic foundation. The analytical formulation of the model and development of shape functions are achieved with assumption of Winkler hypothesis for beam on elastic foundation A Matlab programme was developed to determine the combined beam and foundation stiffness as well as the load vector. The proposed model reliably simulates the deformations and stress resultants of beam on elastic foundation under general loading conditions. The result showed faster convergence devoid of shear locking. The maximum deflection and bending moment differ from the classical solution by about 5 percent.
Highlights
Recent environmental changes have resulted in frequent flooding of towns and cities, hurricanes, tsunamis, landslides and earthquakes etc around the world with attendant damages to infrastructure, causing economic damages as well as displacement of persons
Most structures subject to these kinds of loading rely on raft and pile foundations for which the fundamental principle of analysis is based on the beam of elastic foundation
The results of the computations of the maximum deflection according to the various models as a function of the number of finite elements used are presented in Table 1 and plotted in Figure. 3. These results show that the value of end deflection obtained for the two nodded Euler-Bernoulli beam element is several orders of magnitude less than the theoretical value of 0.01895147m
Summary
Recent environmental changes have resulted in frequent flooding of towns and cities, hurricanes, tsunamis, landslides and earthquakes etc around the world with attendant damages to infrastructure, causing economic damages as well as displacement of persons. Most structures subject to these kinds of loading rely on raft and pile foundations for which the fundamental principle of analysis is based on the beam of elastic foundation. To reduce the economic impact of failures and collapses on investment, there is need for continuous improvement in solutions for the analysis and design of beams of elastic foundation. For other more realistic cases, the finite element method provides better solutions [9]. These numerous studies have shown that the stiffness of the beam and elasticity of the foundation depend largely on the modulus of the foundation soil which is modeled as a great number of springs such that the foundation reaction is directly proportional to local deflection of the beam
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