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This paper discusses a new approach for displacement-based topology optimization of continuum. Topology optimization of continuum can be performed with the optimization of material distribution. This optimization problem will incl...
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This paper discusses a new approach for displacement-based topology optimization of continuum. Topology optimization of continuum can be performed with the optimization of material distribution. This optimization problem will include a large number of design variables, and it may require a high computational cost, especially for computation of gradient components with respect to an objective function and determination of an appropriate updating increment. A conventional approximate optimization technique may not be effective for this problem because it is a very large-scale problem.
From this viewpoint, a new optimization technique, which is based on a successive approximation algorithm, is proposed. The proposed method consists of two main processes: (1) a linear approximation for determination of an updating direction, and (2) a nonlinear approximation for determining a scale coefficient of the updating vector. The first approximation is performed using the perturbation-based finite element analysis, and the second approximation is performed using the Kriging Method.
In order to investigate effectiveness of the proposed method, it is applied to some typical examples for topology optimization problem. From the numerical results, effectiveness and validity of the proposed method are discussed.
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In this paper, we suggested an successive approximation method and Pade approximants method for the solution of the non-linear differential equation. First we calculate power series of the given equation system then transform it i...
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In this paper, we suggested an successive approximation method and Pade approximants method for the solution of the non-linear differential equation. First we calculate power series of the given equation system then transform it into Pade (approximants) series form, which give an arbitrary order for solving differential equation numerically. We compare our results with the result obtained by successive method for the non-linear equation. (C) 2002 Elsevier Inc. All rights reserved. [References: 7]
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This paper is devoted tot he study of approximation of the solution for the differential equation whose coefficients are almost period functions. To this end the authors establish the estimation of the solution of general linear d...
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This paper is devoted tot he study of approximation of the solution for the differential equation whose coefficients are almost period functions. To this end the authors establish the estimation of the solution of general linear differential equation for infinite interval case. For finite interval case, this equation was investigated by G. Tamarkin applying the Picard method of successive approximation.
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In this paper we investigate and compare the variational iteration method and the successive approximations method for solving a class of nonlinear differential equations. We prove that these two methods are equivalent for solving...
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In this paper we investigate and compare the variational iteration method and the successive approximations method for solving a class of nonlinear differential equations. We prove that these two methods are equivalent for solving these types of equations.
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In this paper, we investigate a modification of the principle contraction mapping for the one defined in the E-Banach space. Also, we suggested an approximation method for the solution of the nonlinear operator equation. (C) 2000 ...
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In this paper, we investigate a modification of the principle contraction mapping for the one defined in the E-Banach space. Also, we suggested an approximation method for the solution of the nonlinear operator equation. (C) 2000 Elsevier Science Inc. All rights reserved. [References: 6]
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In this paper, it is proved the existence of a transmutation operator between two schrodinger equations with perturbed exactly solvable potential. An explicit formula for the solution of nucleus function by using Varsha and Jafari...
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In this paper, it is proved the existence of a transmutation operator between two schrodinger equations with perturbed exactly solvable potential. An explicit formula for the solution of nucleus function by using Varsha and Jafari's method is also provided.
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In this paper, we reconstruct the He's iterative scheme in order to show that the He's variational iteration method can be handled without using the correction functional and restricted variations. We apply the Laplace transform t...
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In this paper, we reconstruct the He's iterative scheme in order to show that the He's variational iteration method can be handled without using the correction functional and restricted variations. We apply the Laplace transform to determine the general Lagrange multiplier without invoking variational theory. We conclude with an interesting comparison between the two methods of successive approximations and the He's variational iteration.
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In this paper we shall deal in greater detail with the special class of boundary value problems for which the differential equation and boundary conditions are linear and boundary conditions are based on three points. We will find...
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In this paper we shall deal in greater detail with the special class of boundary value problems for which the differential equation and boundary conditions are linear and boundary conditions are based on three points. We will find a Fredholm integral equation for a multipoint boundary value problem. Then, using two methods, we shall construct the approximations for the unique solution. (C) 2002 Elsevier Science Inc. All rights reserved. [References: 6]
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In this work, we consider the axisymmetric boundary-value problem of thermoplasticity for the laminated shells made of isotropic and orthotropic materials subjected to heating and loading. The equations of the plastic flow theory ...
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In this work, we consider the axisymmetric boundary-value problem of thermoplasticity for the laminated shells made of isotropic and orthotropic materials subjected to heating and loading. The equations of the plastic flow theory with isotropic hardening and the R. Hill flow theory are used. A method of successive approximations is developed to solve the problem. The components of stress-strain state of two laminated shells under loading and heating are obtained and represented graphically.
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We present a novel method for the design of finite impulse response (FIR) filters with discrete coefficients that belong in the sum of powers-of-two (POT) space. The importance of this class of filters cannot be overstated, given ...
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We present a novel method for the design of finite impulse response (FIR) filters with discrete coefficients that belong in the sum of powers-of-two (POT) space. The importance of this class of filters cannot be overstated, given the ever-increasing number of applications for which a specific hardware implementation is needed. Filters that have coefficients that belong to such a class are also referred to as multiplierless filters, given that the operations performed by the filter can all be implemented by using appropriately designed shifts of the input data, making them a perfect choice whenever implementation simplicity and processing speed are the ultimate goal. To produce such a design, we employ a vector successive approximation technique successfully used in data compression that has a very low computational complexity, the Matching Pursuits Generalized BitPlanes algorithm (MPGBP). We derive optimality conditions for the approximation dictionary. We compare filters obtained with the proposed method with those derived in previous works. Based on this comparative analysis, we show that this new and powerful way of producing the filters' coefficients is also among the simplest available in the literature.
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