This paper presents element-free Galerkin (EFG) method as a computational technique that can effectively avoid the disadvantage of mesh entanglement. The present method is used to analyze the static defelection of beams. The moving least squares (MLS) approximation has been used for constructing the shape function based on a set of nodes arbitrarily distributed in the analysis domain.

This paper introduces a computational strategy to collaboratively develop the Galerkin Finite Volume Method (GFVM) as one of the most straightforward and efficient explicit numerical methods to solve structural problems encountering material nonlinearity in a small limited area, while the remainder of the domain represents a linear elastic behavior. In this regard, the Element Free Galerkin method (EFG), which is remarkably robust and accurate, but presumably more expensive, has locally been employed as a nonlinear sub-model to cover the shortcomings of the GFVM in the elastoplastic analysis. Since the formulations of these two methods are fundamentally different, the iterative zonal coupling has been accomplished using overlapping Multi-Grid (MG) patches with a non-matching interface and Iterative Global/Local (IGL) approach. The main property of such an algorithm is its non-intrusiveness, which means the complex nonlinear EFG solver is locally utilized over an elastic global GFVM without any geometric modification. This method is verified and investigated with available analytical and numerical solutions which gave quiet promising results showing the robustness and accuracy of the method. The Moving Least-Square approximation (MLS) has widely been applied on transfer level due to the non-conforming interface at the patch edges, and easily allows us to attach complex geometries with different mesh patterns. The new type of Quasi-Newtonian accelerator is adopted on the global material constitutive matrices and its convergence property and accuracy is compared with dynamic Aitken accelerators for two-dimensional problems in MATLAB. Finally, various accelerator types and mapping strategies are also concerned in the examination.

In this paper, we propose an efficient implementation of the ChebyshevGalerkin method for  rst order Volterra and Fredholm integro-differentialequations of the second kind. Some numerical examples are presented toshow the accuracy of the method.

In this paper, first, the von Karman nonlinear theory of plate is used to present the differential equations of large deformation of thin plates in terms of the in-plane forces and out-of-plane displacement and moment sum. Then, the Galerkin integrated formulation of problem is presented. The independent variable of this equation includes the displacement u, v, w and the moment sum M. As a basic step of the Galerkin method all variables are independent in terms of the basic functions which are given in area coordinate system and the generalized coordinates. The integrated equations for each problem are solved by Newton-Raphson to drive the generalized coordinates. Several examples are solved including isocel and right-angled triangular plates under uniform distributed load and compared with results obtained by other researchers.

In this paper we analyze the interaction of water waves with a permeable barrier which is slightly perturbed from its vertical position within the framework of linearised water wave theory. The barrier is placed in water of finite depth. Two different kinds of barriers are examined, namely, (I) a partially immersed barrier and (II) a submerged bottom standing barrier. The governing boundary value problem involving the velocity potential function is split into two boundary value problems involving the zeroth order as well as the first order velocity potential functions by using a simplified perturbation technique. The zeroth order reflection and transmission coefficients which are due to a vertical permeable barrier are evaluated by solving a Fredholm integral equation of second kind numerically by using a one term Galerkin approximation. Green’ s theorem is applied to evaluate the first order reflection and transmission coefficients. The first order transmission coefficient vanishes irrespective of the shape of the barrier. The numerical values for the first order reflection coefficient are determined by choosing some appropriate shape functions. The numerical results for the zeroth order reflection coefficient which stand for the case of a vertical barrier are validated against the known results for both the permeable and impermeable barriers. The first order reflection curves are also compared by making the porosity constant to be zero with those available in the literature for an impermeable nearly vertical barrier.