In this study, the buckling and free vibration of Timoshenko beams resting on variable elastic foundation analyzed by means of a new finite element formulation. The Winkler model has been applied for elastic foundation. A two-node element with four degrees of freedom is suggested for finite element formulation. Displacement and rotational fields are approximated by cubic and quadratic polynomia...

In this paper, a mortar element method is presented for coupling natural boundary element method and finite element method for the Dirichlet exterior problem. Optimal error estimate is obtained and some numerical results are reported.

Based on classical plate theory, standard and spectral finite element methods are extended for vibration and dynamic stability of axially moving thin plates subjected to in-plane forces. The formulation of the standard method earned through Hamilton’s principle is independent of element type. But for solving numerical examples, an isoparametric quadrilateral element is developed using Lagrange ...

Based on classical plate theory, standard and spectral finite element methods are extended for vibration and dynamic stability of axially moving thin plates subjected to in-plane forces. The formulation of the standard method earned through Hamilton’s principle is independent of element type. But for solving numerical examples, an isoparametric quadrilateral element is developed using Lagrange ...

We propose and analyze two locking-free three-field virtual element methods for Biot’s consolidation model in poroelasticity. One is a high-order scheme, the other low-order scheme. For time discretization, we use backward Euler The proposed are well-posed, optimal error estimates of all unknowns obtained fully discrete solutions. generic constants uniformly bounded as Lamé coefficient ? tends ...

In this article, element free Galerkin method is used for static analysis of thin micro/nanoscale plates based on the nonlocal plate theory. The problem is solved for the plates with arbitrary boundary conditions. Since shape functions of the element free Galerkin method do not satisfy the Kronecker’s delta property, the penalty method is used to impose the essential boundary conditions. Discre...