scholarly journals Matrix Method Development for Structural Analysis of Euler Bernoulli Beams with Finite Difference Method

2016 ◽  
Vol 16 (3) ◽  
pp. 693-710
Author(s):  
Abdurrahman Sahin
Keyword(s):  
Structural Analysis ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Matrix Method ◽  
Method Development

Interpolating matrix method: A finite difference method for arbitrary arrangement of mesh points

1988 ◽  
Vol 75 (2) ◽  
pp. 444-468 ◽  
Author(s):  
Seiichi Koshizuka ◽  
Yoshiaki Oka ◽  
Yasumasa Togo ◽  
Shunsuke Kondo
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Matrix Method

Fractional Chebyshev Finite Difference Method for Solving the Fractional-Order Delay BVPs

2015 ◽  
Vol 12 (06) ◽  
pp. 1550033 ◽  
Author(s):  
M. M. Khader
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Fractional Order ◽  
Difference Method ◽  
Matrix Method ◽  
Fractional Derivatives ◽  
Numerical Technique ◽  
Operational Matrix ◽  
Operational Matrix Method ◽  
Chebyshev Finite Difference Method

In this paper, we implement an efficient numerical technique which we call fractional Chebyshev finite difference method (FChFDM). The fractional derivatives are presented in terms of Caputo sense. The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a nonuniform finite difference scheme. The error bound for the fractional derivatives is introduced. We used the introduced technique to solve numerically the fractional-order delay BVPs. The application of the proposed method to introduced problem leads to algebraic systems which can be solved by an appropriate numerical method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

Discussion on Commonly Methods for Analysis of Drill String Acoustic Spectral Characteristics

2012 ◽  
Vol 226-228 ◽  
pp. 466-469 ◽  
Author(s):  
Yong Wang Liu ◽  
Zhi Chuan Guan ◽  
Guan Shan Zhao ◽  
Zhi Qiang Long
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Transfer Matrix ◽  
Numerical Algorithm ◽  
Difference Method ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Spectral Characteristics ◽  
Drill String ◽  
Impulse Function

Finite difference method and transfer matrix method were used to get spectrum response curve of unit impulse function signal to research the spectrum characteristics of acoustic traveling though the drill string. Similarities and differences of the two methods were discussed through analysis of spectrum curve get from the two approaches. The results show that: The distribution of band-pass and band-stop get by the two calculating methods is basically the same, some transmission coefficient of finite difference method is less than 1, is not completely transmission phenomenon. Analysis of the reason for this is that the transfer matrix method is an analytic method, finite difference method is a numerical algorithm. From the calculation precision of speaking, analytic algorithm is higher than that of numerical algorithm. But to verify the reliability of two methods needs based on laboratory experiment or field test.

Adjoint Aerodynamic Design Optimization for Blades in Multistage Turbomachines—Part I: Methodology and Verification

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
D. X. Wang ◽  
L. He
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Design Optimization ◽  
Difference Method ◽  
Method Development ◽  
Adjoint Method ◽  
Flow Characteristics ◽  
Compressor Stage ◽  
Flow Domain ◽  
Domain Conservation

The adjoint method for blade design optimization will be described in this two-part paper. The main objective is to develop the capability of carrying out aerodynamic blading shape design optimization in a multistage turbomachinery environment. To this end, an adjoint mixing-plane treatment has been proposed. In the first part, the numerical elements pertinent to the present approach will be described. Attention is paid to the exactly opposite propagation of the adjoint characteristics against the physical flow characteristics, providing a simple and consistent guidance in the adjoint method development and applications. The adjoint mixing-plane treatment is formulated to have the two fundamental features of its counterpart in the physical flow domain: conservation and nonreflectiveness across the interface. The adjoint solver is verified by comparing gradient results with a direct finite difference method and through a 2D inverse design. The adjoint mixing-plane treatment is verified by comparing gradient results against those by the finite difference method for a 2D compressor stage. The redesign of the 2D compressor stage further demonstrates the validity of the adjoint mixing-plane treatment and the benefit of using it in a multi-bladerow environment.

Analysis of continuous curved girder-slab bridges

1989 ◽  
Vol 16 (6) ◽  
pp. 895-901 ◽  
Author(s):  
Abul K. Azad ◽  
Mohammed H. Baluch ◽  
Aejaz Ali
Keyword(s):  
Structural Analysis ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Static Analysis ◽  
Difference Method ◽  
Series Solution ◽  
Curved Beams ◽  
Radial Line ◽  
Horizontally Curved ◽  
Flexible Supports

A static analysis of horizontally curved, continuous multigirder slab type bridge decks has been proposed using finite difference method in conjunction with the method of consistent deformation. The deck is idealized as a curved thin plate supported by flexible supports having both vertical and rotational flexibility. The proposed Levy-type series solution requires generation of linear equilibrium difference equations only along the central radial line of the deck, thus obviating the need of a large computational molecule. The simple repetitive algorithm for this method of analysis is an advantage in computer programming. Key words: bridges (curved), beams (curved), structural analysis, computation, concrete, steels, moments.

scholarly journals WO-GRID METHOD OF STRUCTURAL ANALYSIS BASED ON DISCRETE HAAR BASIS. PART 1: ONE-DIMENSIONAL PROBLEMS

2017 ◽  
Vol 13 (4) ◽  
pp. 128-139
Author(s):  
Marina L. Mozgaleva ◽  
Pavel A. Akimov
Keyword(s):  
Structural Analysis ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Grid Method ◽  
Algebraic Equations ◽  
Initial State ◽  
One Dimensional ◽  
Haar Basis ◽  
Linear Algebraic Equations

The distinctive paper is devoted to the two-grid method of structural analysis based on discrete Haar basis (in particular, the simplest one-dimensional problems are under consideration). A brief review of publications of recent years of Russian and foreign specialists devoted to the current trends in the use of wavelet analysis in construction mechanics is given. Approximations of the mesh functions in discrete Haar bases of zero and first levels are described (the mesh function is represented as the sum in which one term is its approximation of the first level, and the second term is so-called complement (up to the initial state) on the grid of the first level). Projectors are constructed for the spaces of vector functions of the original grid to the space of their approximation on the first-level grid and its complement (the detailing component) to the initial state. Basic scheme of the two-grid method is presented. This method allows solution of boundary problems of structural mechanics with the use of matrix operators of significantly smaller dimension. It should be noted that discrete analogue of the initial operator equation (defined on a given interval) is a system of linear algebraic equations (SLAE) constructed within finite difference method (FDM) or the finite element method (FEM). Next, the transition to the resolving SLAE is done. Block Gauss method is used for its direct solution (forward-backward algorithm is realized). We consider a numerical solution of the boundary problem of bending of the Bernoulli beam lying on an elastic foundation (within Winkler model) as a practically important one-dimensional sample. There is good consistency of the results obtained by the proposed method and by standard finite difference method.

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