An improved formulation of the Element-Free Galerkin Method (EFGM) is presented in this paper. The major shortcoming of the conventional EFGM has been that, due to the use of Moving Least-Squares (MLS) approximation, ...
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An improved formulation of the Element-Free Galerkin Method (EFGM) is presented in this paper. The major shortcoming of the conventional EFGM has been that, due to the use of Moving Least-Squares (MLS) approximation, it does not allow the explicit prescription of boundary conditions. Lagrange multipliers have been employed to circumvent this problem undermining the attractiveness of the method. The proposed EFGM formulation eliminates this shortcoming through the use of a set of MLS interpolants that employ singular weight functions. The validity, accuracy and efficiency of the present formulation are demonstrated through the solution of a variety of example problems. (C) 1997 by John Wiley & Sons, Ltd.
An independent refinement and integration procedure is developed to couple together independently modelled (global and local) regions in a single analysis. The finite element models can have different levels of refine...
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An independent refinement and integration procedure is developed to couple together independently modelled (global and local) regions in a single analysis. The finite element models can have different levels of refinement and the nodes along the interface between them need not coincide with one another. A spline interpolation function that satisfies the linear isotropic plate-bending differential equation is used to relate the local model interface nodal displacements to the global model interface displacements. The proposed independent refinement and integration procedure is validated by applying it to problems involving in-plane and out-of-plane deformations.
conventionally, solid finite elements have been looked upon as just generalizations of two-dimensional finite elements. In this article we trace their development starting from the days of their inception. Keeping in ...
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conventionally, solid finite elements have been looked upon as just generalizations of two-dimensional finite elements. In this article we trace their development starting from the days of their inception. Keeping in tune with our perceptions on developing finite elements, without taking recourse to any extra variational techniques, we discuss a few of the techniques which have been applied to solid finite elements. Finally we critically examine our own work on formulating solid finite elements based on the solutions to the Navier equations.
Charge simulation and boundary element techniques typically solve for discretized charge densities on or within domain boundaries by satisfying, in general, the Cauchy condition for a discrete number of collocation po...
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Charge simulation and boundary element techniques typically solve for discretized charge densities on or within domain boundaries by satisfying, in general, the Cauchy condition for a discrete number of collocation points. No constraint is imposed upon the approximation except at these locations, and the boundary conditions may not be met at other points along the boundary. We propose to process the Fredholm integral equation relating potential to an unknown source density function by the Galerkin weighted residual technique. In essence, this allows us to optimally satisfy the Dirichlet condition over the entire conductor surface. Solving the resulting equations requires evaluation of a second surface integration over weakly singular kernels, and the increased accuracy comes at some computational expense. The singularity issue is addressed analytically for 2-D problems and semi-analytically for axi-symmetric problems. We describe how the integrals are evaluated for both the standard and Galerkin Boundary element functions using zero, first, and second order interpolation functions. We demonstrate that the Galerkin solution is superior to the standard collocation procedure for some canonical problems, including one in which analytical charge density becomes singular.
This paper presents a comprehensive discussion of the approximation of the n‐dimensional wave f(X) using the sampled values of the output wave obtained by exciting a series of time‐invariant linear circuits by the w...
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This paper presents a comprehensive discussion of the approximation of the n‐dimensional wave f(X) using the sampled values of the output wave obtained by exciting a series of time‐invariant linear circuits by the wave f(X). It is assumed that the approximate wave h(X) of f(X) is given by the sum of sample values of the output wave multiplied by certain n‐dimensional waves. For simplicity, n‐dimensional waves to be multiplied with the sample values are called the interpolation functions. The set of sample points treated in this paper is defined as a subset obtained by sampling periodically the vertices of the n‐dimensional parallelepipeds placed periodically in the space Rn. Such a set of sampling points includes the most of the typical arrangements of the sampling points, such as the hexagonal and the octagonal lattices on the two‐dimensional space. It is assumed that the sample values contain statistically independent errors such as the observation error and/or the quantization error. Moreover, it is assumed that the interpolation functions have the supports which are parallel‐translations of each other. First, it is assumed that the functional forms of these interpolation functions may be different. Further, a set of n‐dimensional waves is considered where the corresponding spectrum has the weighted p‐norms smaller than the prescribed positive constant. The standard deviations of the difference between f(X) and their approximations are considered. As the measure of the approximation error, the upper limit of the standard deviation obtained by varying the original waves over the given set of waves is adopted. In the following sections it is shown that the interpolation functions minimizing the forementioned measure of error can be expressed as the parallel‐translations of a finite number of functions. Further, in special cases, the interpolation functions have the discrete orthogonality. Since the measure of error is a convex function of the interpolati
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