scholarly journals The New Approach to Analysis of Thin Isotropic Symmetrical Plates

2020 ◽  
Vol 10 (17) ◽  
pp. 5931
Author(s):  
Mykhaylo Delyavskyy ◽  
Krystian Rosiński
Keyword(s):  
Present Method ◽  
Automatic Differentiation ◽  
Linear Equations ◽  
High Accuracy ◽  
Rectangular Plates ◽  
System Of Linear Equations ◽  
New Approach ◽  
Summation Convention ◽  
Analytical Formulae ◽  
Einstein Summation Convention

A new approach to solve plate constructions using combined analytical and numerical methods has been developed in this paper. It is based on an exact solution of an equilibrium equation. The proposed mathematical model is implemented as a computer program in which known analytical formulae are rewritten as wrapper functions of two arguments. Partial derivatives are calculated using automatic differentiation. A solution of a system of linear equations is substituted to these functions and evaluated using the Einstein summation convention. The calculated results are presented and compared to other analytical and numerical ones. The boundary conditions are satisfied with high accuracy. The effectiveness of the present method is illustrated by examples of rectangular plates. The model can be extended with the ability to solve plates of any shape.

A Hybrid Analytical and Finite Element Method for Mid-Frequency Vibration Analysis of Plate Structures with Discontinuities

2017 ◽  
Vol 17 (04) ◽  
pp. 1750052 ◽  
Author(s):  
Yongbin Ma ◽  
Yahui Zhang ◽  
Bo Ping Wang
Keyword(s):  
Finite Element ◽  
Vibration Analysis ◽  
Present Method ◽  
High Efficiency ◽  
Main Idea ◽  
High Accuracy ◽  
Symplectic Method ◽  
Rectangular Plates ◽  
Fe Method ◽  
Plate Structures

A hybrid analytical and numerical method is presented for the mid-frequency vibration analysis of a class of plate structures with discontinuities based on the concept of structural partitioning. The type of structures considered includes rectangular plates with internal property discontinuity, homogeneous but non-rectangular plates, or built-up structures composed of rectangular homogenous plates with complex joints. Compared with the conventional finite element (FE) method, the present method has the advantage of high accuracy and high efficiency in the analysis of mid-frequency vibration of the structures of concern. The main idea of the proposed approach is to divide the whole structure into uniform rectangular plate regions and other non-rectangular regions. The vibration behavior of the rectangular regions is accurately and efficiently described by analytical wave solutions so that the FE modeling for these regions is not necessary. The other non-rectangular regions are modeled by the conventional FE method. The analytical waves used to describe the rectangular regions are obtained by the symplectic method, thereby avoiding the limitation of the conventional analytical method in dealing with plates having two opposite edges simply supported. By enforcing the displacement continuity and force equilibrium at the connection interfaces, the dynamic coupling is established between the rectangular regions described in terms of the analytical waves and the regions modeled by FEs. Furthermore, the hybrid solution formulation for the mid-frequency vibration of the entire structure is proposed. The high accuracy and efficiency of the present method are demonstrated by several numerical examples, with the effect of element size of the FE regions investigated. Finally, the applicability of the proposed method is analyzed.

FUZZY CENTRE BASED SOLUTION OF FUZZY COMPLEX LINEAR SYSTEM OF EQUATIONS

2013 ◽  
Vol 21 (04) ◽  
pp. 629-642 ◽  
Author(s):  
DIPTIRANJAN BEHERA ◽  
S. CHAKRAVERTY
Keyword(s):  
Linear Time ◽  
Linear Equations ◽  
Electric Circuit ◽  
System Of Linear Equations ◽  
New Approach ◽  
Linear System Of Equations ◽  
Linear Time Invariant ◽  
Complex Linear ◽  
Time Invariant ◽  
Good Agreement

A new approach to solve Fuzzy Complex System of Linear Equations (FCSLE) based on fuzzy complex centre procedure is presented here. Few theorems related to the investigation are stated and proved. Finally the presented procedure is used to analyze an example problem of linear time invariant electric circuit with complex crisp coefficient and fuzzy complex sources. The results obtained are also compared with the known solutions and are found to be in good agreement.

A new approach to (s, S) inventory systems

1993 ◽  
Vol 30 (4) ◽  
pp. 898-912 ◽  
Author(s):  
Jian-Qiang Hu ◽  
Soracha Nananukul ◽  
Wei-Bo Gong
Keyword(s):  
Infinite System ◽  
Linear Equations ◽  
Inventory Systems ◽  
Inventory Level ◽  
Maclaurin Series ◽  
System Of Linear Equations ◽  
New Approach ◽  
Recursive Procedures ◽  
Recursive Equations ◽  
Infinite Linear

In this paper, we consider period review (s, S) inventory systems with independent and identically distributed continuous demands and full backlogging. Using an approach recently proposed by Gong and Hu (1992), we derive an infinite system of linear equations for all moments of inventory level. Based on this infinite system, we develop two algorithms to calculate the moments of the inventory level. In the first one, we solve a finite system of linear equations whose solution converges to the moments as its dimension goes to infinity. In the second one, we in fact obtain the power series of the moments with respect to s and S. Both algorithms are based on some very simple recursive procedures. To show their efficiency and speed, we provide some numerical examples for the first algorithm.(s, S) INVENTORY SYSTEMS; DYNAMIC RECURSIVE EQUATIONS; INFINITE LINEAR EQUATIONS; MACLAURIN SERIES

The eigenvalue problem for infinite systems of linear equations

1977 ◽  
Vol 82 (2) ◽  
pp. 269-273 ◽  
Author(s):  
F. P. Sayer
Keyword(s):  
Eigenvalue Problem ◽  
Infinite System ◽  
Linear Equations ◽  
Theoretical Work ◽  
Rectangular Plates ◽  
System Of Linear Equations ◽  
Usual Procedure ◽  
Systems Of Linear Equations ◽  
Image Position

Given an infinite system of linear equationswhere the aij depend on a parameter λ, the eigenvalue problem is to determine values of λ for which xj (j = 1, 2, …) are not all zero. This problem (Taylor (3) and Vaughan (4)) can arise in the vibration of rectangular plates. Little theoretical work, however, appears to have been done concerning the existence and determination of the eigenvalues. The usual procedure (see (3) and (4)) is to consider a truncated or reduced system of N equations and find the values of λ for which the determinant of the N × N matrix [aij] vanishes. If a particular λ tends to a constant value as N is increased then this value is assumed to be an eigenvalue. The question therefore arises as to what happens if no limit exists. Can we assert that there are no eigenvalues? By constructing an appropriate example we show that the non-existence of a limit does not imply the non-existence of eigenvalues. In order to construct our example we first establish a result concerning the Legendre polynomials.

A new approach to (s, S) inventory systems

1993 ◽  
Vol 30 (04) ◽  
pp. 898-912
Author(s):  
Jian-Qiang Hu ◽  
Soracha Nananukul ◽  
Wei-Bo Gong
Keyword(s):  
Infinite System ◽  
Linear Equations ◽  
Inventory Systems ◽  
Inventory Level ◽  
Maclaurin Series ◽  
System Of Linear Equations ◽  
New Approach ◽  
Recursive Procedures ◽  
Recursive Equations ◽  
Infinite Linear

In this paper, we consider period review (s, S) inventory systems with independent and identically distributed continuous demands and full backlogging. Using an approach recently proposed by Gong and Hu (1992), we derive an infinite system of linear equations for all moments of inventory level. Based on this infinite system, we develop two algorithms to calculate the moments of the inventory level. In the first one, we solve a finite system of linear equations whose solution converges to the moments as its dimension goes to infinity. In the second one, we in fact obtain the power series of the moments with respect to s and S. Both algorithms are based on some very simple recursive procedures. To show their efficiency and speed, we provide some numerical examples for the first algorithm. (s, S) INVENTORY SYSTEMS; DYNAMIC RECURSIVE EQUATIONS; INFINITE LINEAR EQUATIONS; MACLAURIN SERIES

scholarly journals Interval Approach to Magnetotelluric Data Processing

2021 ◽  
Vol 2096 (1) ◽  
pp. 012127
Author(s):  
A A Lavrukhin ◽  
A S Tukanova
Keyword(s):  
Data Processing ◽  
Computational Algorithm ◽  
Least Squares Method ◽  
Linear Equations ◽  
Reference Method ◽  
Impedance Tensor ◽  
System Of Linear Equations ◽  
Magnetotelluric Data ◽  
New Approach ◽  
Interval Approach

Abstract The article presents a new approach to estimate the frequency characteristics of the impedance tensor for processing magnetotelluric data. The approach is based on the applying of interval analysis methods when solving a system of linear equations. As a reference method, to compare with, a combined robust algorithm is used (with discarding data by the coherence criterion, median estimating, and weighting least squares method). This algorithm is compared with the results of the proposed interval computational algorithm that is based on the method of J. Rohn, implemented in the intvalpy Python library. Computational experiments on the data processing were performed using natural magnetotelluric field data. The interval approach can be successfully applied to the processing of magnetotelluric data.

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