Article

Element free Galerkin method for beams on elastic foundation

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Abstract

This paper presents the analysis of elastically supported beams using the element free Galerkin method (EFGM). The elastic support can be provided in the form of a load-bearing medium such as soil, distributed continuously along the length of the beam. This type of supports can be found in a variety of engineering problems, for example in the case of actual foundations or in the case of railroad track. The main difficulty in the analysis of the soil foundation interaction lies in the determination of the contact pressure. Any constitutive models may be used for simulating the action of the soil media. The finite element method has been used to model the beams on elastic foundations by representing continuity of the soil medium. However, the computations involved are more and has limited practical applications. In this paper, an attempt has been made to provide a simple but sufficiently accurate model for beams on elastic foundations using the meshfree technique, called as element free Galerkin method which does not rely on mesh. The formulation for the beams on elastic foundation is given for the governing equation which treats the soil in the form of rows of closely spaced independent elastic springs. The EFGM presented in the paper employs generalized moving least square approximants to approximate the function and transformation method for imposing the essential boundary conditions. Numerical examples are provided to study the convergence with various loading and boundary conditions. The results of the proposed method are compared with analytical solutions.

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... (24) and (25) and get the weak form as in Eq. (30). There are several technique suggested by different researchers in this regard [37,39]. For the present work a method suggested by Sunitha et al. [39] is used for imposing essential boundary conditions. ...
... There are several technique suggested by different researchers in this regard [37,39]. For the present work a method suggested by Sunitha et al. [39] is used for imposing essential boundary conditions. From Eq. (14) and its first derivative with respect to x, a relation between nodal valuesd, and nodal parameters d, can be written aŝ ...
... A. Gupta, C.O.Arun / Computers and Structures 194 (2018) [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] ...
Article
This paper proposes a probabilistic approach for the solution of elastic buckling of columns, involving uncertainties, using stochastic element free Galerkin method. In the present work, modulus of elasticity is modeled as a homogeneous random field. Karhunen-Loeve expansion and shape function method are used to represent random field and their effectiveness is compared in modeling the same in a computationally viable manner. Both Gaussian and non-Gaussian field are considered for the present study. The stochastic eigenvalue problem is solved for first and second moment characteristics of buckling load, using perturbation analysis. Numerical examples of columns with different boundary conditions are solved. Monte Carlo simulation is used as a validation tool. The obtained results are found in good agreement with those obtained by Monte Carlo simulation.
... Rieker et al. [Rieker, Lin and Trethewey (1996)] investigated the relationship between the model accuracy and the number of elements used to discretize a structure for a moving load analysis, and provided guidance for the development of suitable meshes. Sunitha et al. [Sunitha, Dodagoudar and Rao (2007) ;Dodagoudar, Rao and Sunitha (2015)] proposed a simple but sufficiently accurate model for beams on elastic foundation using a mesh-free technique, called the element-free Galerkin method, that did not rely on any mesh. Correa et al. [Correa, Costa and Simoes (2018)] presented the FE modeling of a rail resting on a Winkler-Coulomb foundation and subjected to a moving concentrated load. ...
Article
One of mesh free methods, element free Galerkin method, is presented to analyze the finite beam on elastic foundation. The shape functions are constructed by using the moving least square interpolation based on a set of nodes that are arbitrarily distributed in specified domain. Discrete system equations are derived from the variation form of system equations. Numerical examples of finite beam on elastic foundation are given by establishing Matlab code. The results of this paper demonstrate the effectiveness of the proposed method with small errors compared to analytical solutions. Keywords: mesh free method, element free Galerkin method, moving least square, finite beam, elastic foundation.
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