Finite Elements in Time and Space

1969 ◽  
Vol 73 (708) ◽  
pp. 1041-1044 ◽  
Author(s):  
J. H. Argyris ◽  
D. W. Scharpf
Keyword(s):  
Finite Elements ◽  
Linear Equations ◽  
Time Integration ◽  
Fixed Time ◽  
Time Interval ◽  
Structural Elements ◽  
Dynamic Problems ◽  
System Of Linear Equations ◽  
Interpolation Procedure ◽  
Variational Statement

The present paper seeks to apply the ideas of discretisation to time dependent phenomena. As a suitable variational statement we may use Hamilton's principle. In practise this means that the time is discretised into a set of finite elements which are taken to be the same for all structural elements. A finite element in time consists simply of a fixed time interval. In our present discussion we detail in particular the case when at the beginning and end of the time interval the generalised displacements and velocities are given. For dynamic problems this is the minimum of information required, but the technique may easily be extended to account for additional “timewise degrees of freedoms”. Introducing an appropriate interpolation procedure we may obtain the displacement and velocity at any instant of time. It is then possible to carry out in the variational statement the time integration explicitly and to obtain hence a system of linear equations. The method is extremely simple, since the time interpolation of all structural freedoms of an element in space is the same. We also demonstrate that the general case of a multi-degree of freedoms system can be made to depend on the matrices which describe the unidimensional motion of a mass point.

scholarly journals MODELING SINGLE BARRETTES AS ELASTIC SUPPORT BY CCT

2018 ◽  
Vol 30 (2) ◽  
Author(s):  
Mahmoud El Gendy ◽  
Hassan Ibrahim ◽  
Ibrahim El Arabi
Keyword(s):  
Finite Elements ◽  
Stiffness Matrix ◽  
Linear Equations ◽  
Vertical Direction ◽  
The Finite Element Method ◽  
System Of Linear Equations ◽  
Heavy Load ◽  
Vertical Displacements ◽  
Surrounding Soil ◽  
Coefficient Technique

Classical analyses of barrette foundation taking into account full interactions between barrette and the surrounding soil leads to a huge barrette stiffness matrix. Consequently, a large system of linear equations must be solved, especially for analyzing barrette group and barrette raft. To overcome this problem, a Composed Coefficient Technique (CCT) is developed for analyzing barrette. In the analysis, the elasticity of the barrette body is considered using the finite element method, while that of the soil elements is considered using flexibility coefficients. The compatibility between the vertical displacements of the barrette and the soil settlements at the soil-barrette interface is taken in the vertical direction only. This assumption is that the external load on the barrette head, which is expected to be heavy load, is applied in the vertical direction. For comparative examinations, the barrette elasticity is determined using either 1D or 3D finite elements. A series of examinations is carried out to verify the application for analyzing barrette by CCT. It was found that, treating the barrette as an elastic body and representing the barrette by either 1D or 3D finite elements, gives nearly the same results.

Analysis of the busy period for the M/M/c queue: an algorithmic approach

2001 ◽  
Vol 38 (01) ◽  
pp. 209-222
Author(s):  
J. R. Artalejo ◽  
M. J. Lopez-Herrero
Keyword(s):  
Busy Period ◽  
Queueing System ◽  
Linear Equations ◽  
Time Interval ◽  
System Of Linear Equations ◽  
Recursive Procedure ◽  
Algorithmic Approach ◽  
Period Distribution ◽  
Algorithmic Analysis ◽  
Number Of Customers

This paper presents an algorithmic analysis of the busy period for the M/M/c queueing system. By setting the busy period equal to the time interval during which at least one server is busy, we develop a first step analysis which gives the Laplace-Stieltjes transform of the busy period as the solution of a finite system of linear equations. This approach is useful in obtaining a suitable recursive procedure for computing the moments of the length of a busy period and the number of customers served during it. The maximum entropy formalism is then used to analyse what is the influence of a given set of moments on the distribution of the busy period and to estimate the true busy period distribution. Our study supplements a recent work of Daley and Servi (1998) and other studies where the busy period of a multiserver queue follows a different definition, i.e., a busy period is the time interval during which all servers are engaged.

Incompressibility in Dynamic Relaxation

1987 ◽  
Vol 54 (3) ◽  
pp. 539-544 ◽  
Author(s):  
S. A. Silling
Keyword(s):  
Solid Mechanics ◽  
Linear Equations ◽  
Time Integration ◽  
Natural State ◽  
System Of Linear Equations ◽  
Dynamic Relaxation ◽  
Explicit Time Integration ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Incompressibility Constraint

A method is described for enforcing the incompressibility constraint in large-deformation solid mechanics computations using dynamic relaxation. The method is well-suited to explicit time-integration schemes because it does not require the solution of a system of linear equations. It is based on an analogy with thermoelasticity involving manipulation of the natural state of a solid.

Analysis of the busy period for the M/M/c queue: an algorithmic approach

2001 ◽  
Vol 38 (1) ◽  
pp. 209-222 ◽  
Author(s):  
J. R. Artalejo ◽  
M. J. Lopez-Herrero
Keyword(s):  
Busy Period ◽  
Queueing System ◽  
Linear Equations ◽  
Time Interval ◽  
System Of Linear Equations ◽  
Recursive Procedure ◽  
Algorithmic Approach ◽  
Period Distribution ◽  
Algorithmic Analysis ◽  
Number Of Customers

This paper presents an algorithmic analysis of the busy period for the M/M/c queueing system. By setting the busy period equal to the time interval during which at least one server is busy, we develop a first step analysis which gives the Laplace-Stieltjes transform of the busy period as the solution of a finite system of linear equations. This approach is useful in obtaining a suitable recursive procedure for computing the moments of the length of a busy period and the number of customers served during it. The maximum entropy formalism is then used to analyse what is the influence of a given set of moments on the distribution of the busy period and to estimate the true busy period distribution. Our study supplements a recent work of Daley and Servi (1998) and other studies where the busy period of a multiserver queue follows a different definition, i.e., a busy period is the time interval during which all servers are engaged.

Utilization of remote sensing for estimation of scale of cutting and growing of forest zones

2017 ◽  
Vol 920 (2) ◽  
pp. 57-60
Author(s):  
F.E. Guliyeva
Keyword(s):  
Remote Sensing ◽  
Fixed Time ◽  
Time Interval ◽  
Time Points ◽  
Average Value ◽  
Time Period ◽  
Remote Estimation ◽  
The Given ◽  
Forest Cutting

The study of results of relevant works on remote sensing of forests has shown that the known methods of remote estimation of forest cuts and growth don’t allow to calculate the objective average value of forests cut volume during the fixed time period. The existing mathematical estimates are not monotonous and make it possible to estimate primitively the scale of cutting by computing the ratio of data in two fixed time points. In the article the extreme properties of the considered estimates for deforestation and reforestation models are researched. The extreme features of integrated averaged values of given estimates upon limitations applied on variables, characterizing the deforestation and reforestation processes are studied. The integrated parameter, making it possible to calculate the averaged value of estimates of forest cutting, computed for all fixed time period with a fixed step is suggested. It is shown mathematically that the given estimate has a monotonous feature in regard of value of given time interval and make it possible to evaluate objectively the scales of forest cutting.

scholarly journals Approximate solution of system of equations arising in interior-point methods for bound-constrained optimization

2021 ◽  
Author(s):  
David Ek ◽  
Anders Forsgren
Keyword(s):  
Approximate Solution ◽  
Interior Point ◽  
Interior Point Methods ◽  
Linear Equations ◽  
Approximate Solutions ◽  
System Of Nonlinear Equations ◽  
Intermediate Step ◽  
System Of Linear Equations ◽  
Constrained Nonlinear Optimization ◽  
Asymptotic Error

AbstractThe focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton’s method. There is a trade-off between solving Newton systems directly, which give high quality solutions, and solving many approximate Newton systems which are computationally less expensive but give lower quality solutions. We propose partial and full approximate solutions to the Newton systems. The specific approximate solution depends on estimates of the active and inactive constraints at the solution. These sets are at each iteration estimated by basic heuristics. The partial approximate solutions are computationally inexpensive, whereas a system of linear equations needs to be solved for the full approximate solution. The size of the system is determined by the estimate of the inactive constraints at the solution. In addition, we motivate and suggest two Newton-like approaches which are based on an intermediate step that consists of the partial approximate solutions. The theoretical setting is introduced and asymptotic error bounds are given. We also give numerical results to investigate the performance of the approximate solutions within and beyond the theoretical framework.

scholarly journals Numerical approximation for the solution of linear sixth order boundary value problems by cubic B-spline

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
A. Khalid ◽  
M. N. Naeem ◽  
P. Agarwal ◽  
A. Ghaffar ◽  
Z. Ullah ◽  
...  
Keyword(s):  
Numerical Approximation ◽  
Analytic Solution ◽  
Linear Equations ◽  
Computational Cost ◽  
Spline Method ◽  
System Of Linear Equations ◽  
Approximation Solution ◽  
B Spline ◽  
Novel Technique ◽  
Derivatives Of

AbstractIn the current paper, authors proposed a computational model based on the cubic B-spline method to solve linear 6th order BVPs arising in astrophysics. The prescribed method transforms the boundary problem to a system of linear equations. The algorithm we are going to develop in this paper is not only simply the approximation solution of the 6th order BVPs using cubic B-spline, but it also describes the estimated derivatives of 1st order to 6th order of the analytic solution at the same time. This novel technique has lesser computational cost than numerous other techniques and is second order convergent. To show the efficiency of the proposed method, four numerical examples have been tested. The results are described using error tables and graphs and are compared with the results existing in the literature.

scholarly journals Optimal control of robotic systems using finite elements for time integration of covariant control equations

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Juan Antonio Rojas-Quintero ◽  
Jorge Villalobos-Chin ◽  
Victor Santibanez
Keyword(s):  
Optimal Control ◽  
Finite Elements ◽  
Time Integration ◽  
Robotic Systems
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