Element-Free Galerkin Method for Reinforced Timoshenko Beam on Elastic Foundation
The aim of this paper is to present an efficient and reliable computational technique for the analysis of soil structure interaction problems. In this paper a reinforced Timoshenko beam resting on an elastic foundation subjected to distributed load and point load have been analysed by means of Element-Free Galerkin method (EFGM). This is one of the efficient mesh-free methods which needs only nodal data and does not need any nodal connectivity, which provides an advantage over the FEM. Its shape function is constructed by Moving least square approximation. Galerkin weak form is used to develop the discretized system of equations. EFGM poses difficulties in enforcing essential boundary conditions. To overcome this difficulty Lagrange Multiplier is used. The results presented in this paper are checked for validity, convergence and accuracy of numerical solutions and compared with the exact analytical solutions. The granular fill, soft soil, and geosynthetic reinforcements are considered as linear elastic materials. The geosynthetic reinforcements are modeled as cable elements fully bonded with the surrounding soil, thus neglecting any slip between the reinforcement and the soil.
KeywordsTimoshenko beam Winkler springs Element-free galerkin method Geosynthetic shear stiffness Tension modulus
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