Open Access
ARTICLE
V. Panchore1, R. Ganguli2, S. N. Omkar3
CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.4, pp. 215-237, 2015, DOI:10.3970/cmes.2015.108.215
Abstract A rotating Timoshenko beam free vibration problem is solved using the meshless local Petrov-Galerkin method. A locking-free shape function formulation is introduced with an improved radial basis function interpolation and the governing differential equations of the Timoshenko beam are used instead of the alternative formulation used by Cho and Atluri (2001). The locking-free approximation overcomes the problem of ill conditioning associated with the normal approximation. The radial basis functions satisfy the Kronercker delta property and make it easier to apply the essential boundary conditions. The mass matrix and the stiffness matrix are derived for the meshless local Petrov-Galerkin method. Results… More >
Open Access
ARTICLE
Annamaria Mazzia1, Giorgio Pini1, Flavio Sartoretto2
CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.4, pp. 239-262, 2015, DOI:10.3970/cmes.2015.108.239
Abstract Meshless Local Petrov Galerkin (MLPG) methods are pure meshless techniques for solving Partial Differential Equations (PDE). MLPG techniques are nowadays used for solving a huge number of complex, real–life problems. While MLPG aims to approximate the solution of a given differential problem, its “dual” Direct MLPG (DMLPG) technique relies upon approximating linear functionals. Assume adaptive methods are to be implemented. When using a mesh–based method, inserting and/or deleting a node implies complex adjustment of connections. Meshless methods are more apt to implement adaptivity, since they does not require such adjustments. Nevertheless, ad–hoc insertion and/or deletion algorithms must be devised, in… More >
Open Access
ARTICLE
F. Bulut1,2, Ö. Oruç3, A. Esen3
CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.4, pp. 263-284, 2015, DOI:10.3970/cmes.2015.108.263
Abstract In this paper, time fractional one dimensional coupled KdV and coupled modified KdV equations are solved numerically by Haar wavelet method. Proposed method is new in the sense that it doesn’t use fractional order Haar operational matrices. In the proposed method L1 discretization formula is used for time discretization where fractional derivatives are Caputo derivative and spatial discretization is made by Haar wavelets. L2 and L∞ error norms for various initial and boundary conditions are used for testing accuracy of the proposed method when exact solutions are known. Numerical results which produced by the proposed method for the problems under… More >
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