The Finite Element Method–A Basic Introduction for Engineers (K. C. Rockey, H. R. Evans, D. W. Griffiths, and D. A. Nethercot) and Finite Elements: An Introduction for Engineers (R. K. Livesley)

SIAM Review ◽  
1985 ◽  
Vol 27 (2) ◽  
pp. 286-288
Author(s):  
David S. Malkus
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
The Finite Element Method ◽  
Element Method

Teaching Electromagnetics through Finite Elements. Part I: The Rationale

1988 ◽  
Vol 25 (1) ◽  
pp. 33-49 ◽  
Author(s):  
S. Ratnajeevan H. Hoole
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Special Solution ◽  
The Finite Element Method ◽  
Solution Methods ◽  
Element Method

The rationale for teaching undergraduate electromagnetics partly through the finite element method, is put forward. Properly presented, the finite element method, easily within the ken of the engineering undergraduate, promotes clarity and helps to replace large portions of syllabi devoted to special solution methods, with problems of industrial magnitude and character.

A Numerical Solution of the Elastohydrodynamic Lubrication Problem Using Finite Elements

1972 ◽  
Vol 14 (4) ◽  
pp. 229-237 ◽  
Author(s):  
C. Taylor ◽  
J. F. O'Callaghan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Numerical Solution ◽  
Elastohydrodynamic Lubrication ◽  
The Finite Element Method ◽  
Galerkin Approach ◽  
Recent Developments ◽  
Element Method ◽  
Isoparametric Elements

This paper comprises a report on recent developments in the application of the finite element method in the analysis of elastohydrodynamic lubrication (e.h.l.) problems. The basic formulation is effected, using the Galerkin approach and the domain under investigation is discretized using isoparametric elements. The techniques used to locate the inlet and outlet boundaries and those employed during successive iterations are illustrated by application to particular examples.

Transient Dynamic Analysis of Rotors Using the Combined Methodologies of Finite Elements and Transfer Matrix

1988 ◽  
Vol 55 (2) ◽  
pp. 448-452 ◽  
Author(s):  
R. Subbiah ◽  
A. S. Kumar ◽  
T. S. Sankar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Transfer Matrix ◽  
Computational Effort ◽  
The Finite Element Method ◽  
Transient Dynamic Analysis ◽  
New Approach ◽  
System Properties ◽  
Element Method

A new approach is proposed to predict the dynamic behavior of rotor-bearing systems in time domain using the combined methodologies of finite elements and transfer matrices. This approach makes use of the finite element method to model symmetric shafts and then transforms the system properties to transfer matrix mode. The formulation provides flexibility to include both linear and nonlinear system models, often encountered in rotor dynamic applications. Few example rotor cases had been studied and the results were compared with those obtained using finite element method. This establishes that considerable savings in computational effort can be achieved without losing any accuracy.

Development of the CAPP Code Based on the Finite Element Method for the Analysis of VHTR Cores

2008 ◽  
Author(s):  
Hyun Chul Lee ◽  
Chang Keun Jo ◽  
Jae Man Noh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Cross Sections ◽  
Linear Mapping ◽  
The Finite Element Method ◽  
Parametric Mapping ◽  
Numerical Tests ◽  
Neutron Diffusion Equation ◽  
Element Method

In this study, we developed a neutron diffusion equation solver based on the finite element method for CAPP code. Three types of triangular finite elements and five types of rectangular depending on the order of the shape functions were implemented for 2-D application. Ten types of triangular prismatic finite elements and seventeen types of rectangular prismatic finite elements were also implemented for 3-D application. Two types of polynomial mapping from the master finite element to a real finite element were adopted for flexibility in dealing with complex geometry. They are linear mapping and iso-parametric mapping. In linear mapping, only the vertex nodes are used as the mapping points. In iso-parametric mapping, all the nodal points in the finite element are used as the mapping points, which enables the real finite elements to have curved surfaces. For the treatment of spatial dependency of cross-sections in the finite elements, three types of polynomial expansion of the cross-sections in the finite elements were implemented. They are constant, linear, and iso-parametric cross-section expansions. The power method with the Wielandt acceleration technique was adopted as the outer iteration algorithm. The BiCGSTAB algorithm with the ILU (Incomplete LU) decomposition preconditioner was used as the linear equation solver in the inner iteration. The neutron diffusion equation solver developed in this study was verified against two well known benchmark problems, IAEA PWR benchmark problem and OECD/NEA PBMR400 benchmark problem. Results of numerical tests showed that the solution converged to the reference solution as the finite elements are refined and as the order of the finite elements increases. Numerical tests also showed that the higher order finite element method is much efficient than lower order finite element method or finite difference method.

scholarly journals INVESTIGATION OF THE CARRYING CAPACITY OF REINFORCED CONCRETE SLABS WITH CRACKS AFTER THEIR REINFORCEMENT WITH COMPOSITE FABRICS BY THE FINITE ELEMENT METHOD USING THE PRINS COMPUTER COMPLEX

2019 ◽  
Vol 45 (4) ◽  
pp. 142-152 ◽  
Author(s):  
V. P. Agapov ◽  
K. R. Aydemirov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Reinforced Concrete ◽  
Finite Elements ◽  
Concrete Slabs ◽  
The Finite Element Method ◽  
Design Scheme ◽  
Reinforced Concrete Slabs ◽  
Composite Fabrics ◽  
Element Method

Objectives. The finite element method for cracked reinforced concrete slabs analysis after they were reinforced with composite fabrics in order to determine the residual safety factor is considered. Method. The method is based on the use of algorithms for calculating of structures with the account of the geometrical and physical nonlinearities, implemented in the PRINS program. These algorithms assume the use of the same calculation scheme in the process of the problem solving. However, the specifics of the assigned problem is that the design sсheme of the structure before the appearance of defects in it and after its amplification with the help of composite materials should change. Result. Taking into account this circumstance, the algorithms of nonlinear calculation of structures under the PRINS program were supplemented with an option that allows changing the parameters of the design scheme in the process of through calculation. To study the bearing capacity of reinforced concrete slabs, multilayer finite elements are used, for each of which a specific package of materials is specified. Modernization of the design scheme in this case comes down to replacing one package of materials with another. An example of calculation of a slab with a crack reinforced with composite fabric is given. Conclusion. It is shown that the use of a tunable design scheme can significantly improve the accuracy of calculations. In this case, the final result depends on what stage of the formation of defects in the slab its strengthening is realized. The special  multilayered finite elements of a quadrangular shape are used in calculations. The elements consist of four simple triangles, for which most of the matrix characteristics are calculated in a closed form. This is especially important when carrying out nonlinear calculations that require repeated computations of these characteristics. 

scholarly journals Design General Cam Profiles Based on Finite Element Method

2021 ◽  
Vol 11 (13) ◽  
pp. 6052
Author(s):  
Thi Thanh Nga Nguyen ◽  
Thang Xuan Duong ◽  
Van-Sy Nguyen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
General Framework ◽  
The Finite Element Method ◽  
Nonlinear System Of Equations ◽  
Numerical Stabilization ◽  
Cam Profile ◽  
Element Method

This paper presents a general framework to design a cam profile using the finite element method from given displacements of the follower. The arbitrarily complex cam profile is described by Lagrangian finite elements, which are formed by the connectivity of nodes. In order to obtain the desired profile, a penalty-type functional that enforces the prescribed displacement of the follower is proposed. Additionally, in order to ensure convexity of the functional, a numerical stabilization scheme is used. The nodal positions are then obtained by solving a nonlinear system of equations resulting from minimizing the total functional. The geometrical accuracy of the cam profile can be controlled by the number of finite elements. A case study is considered to illustrate the flexibility, accuracy, and robustness of the proposed approach.

The Use of the Finite Element Method for Ensuring Efficient and Safe Extraction of Minerals

2017 ◽  
Vol 743 ◽  
pp. 411-416
Author(s):  
Dmitriy Ilyukhin ◽  
Vladimir Gusev
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rock Mass ◽  
Finite Elements ◽  
Mineral Resources ◽  
Finite Elements Method ◽  
The Finite Element Method ◽  
Fracture Zones ◽  
Efficient Extraction ◽  
Element Method

The development of mineral resources requires predicting its possible impact on the undermined rock mass. The aim of this work is to ensure safe and efficient extraction and minimization of losses. This article considers the problem of formation of water conducting fracture zones in terms of its predictability using the finite elements method.

SCALED BOUNDARY FINITE ELEMENT METHOD FOR ACOUSTICS

2006 ◽  
Vol 14 (04) ◽  
pp. 489-506 ◽  
Author(s):  
L. LEHMANN ◽  
S. LANGER ◽  
D. CLASEN
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Sound Propagation ◽  
Sound Field ◽  
Radiation Condition ◽  
The Finite Element Method ◽  
Scaled Boundary Finite Element ◽  
Element Method

When studying unbounded wave propagation phenomena, the Sommerfeld radiation condition has to be fulfilled. The artificial boundary of a domain discretized using standard finite elements produces errors. It reflects spurious energy back into the domain. The scaled boundary finite element method (SBFEM) overcomes this problem. It unites the concept of geometric similarity with the standard approach of finite elements assembly. Here, the SBFEM for acoustical problems and its coupling with the finite element method for an elastic structure is presented. The achieved numerical algorithm is best suited to study the sound propagation in an unbounded domain or interaction phenomena of a vibrating structure and an unbounded acoustical domain. The SBFEM is applied to study the sound transmission through a separating component, and for the determination of the sound field around a sound insulating wall. The results are compared with a hybrid algorithm of Finite and Boundary Elements or with the Boundary Element Method, respectively.

scholarly journals CALCULATION OF THE CENTRIFULAL PUMP CRITICAL FREQUENCIES BASED ON ITS DISCRETE MATHEMATICAL MODEL

2021 ◽  
pp. 43-52
Author(s):  
A. Y. Verbovoy ◽  
M. L. Sieryk ◽  
I. V. Pavlenko ◽  
A. A. Rudenko
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Discrete Model ◽  
Three Dimensional ◽  
Beam Model ◽  
The Finite Element Method ◽  
Functional Software ◽  
Discrete Mathematical Model ◽  
Element Method

Calculations of the centrifugal machines critical frequencies of the rotors are currently carried out on the basis of the finite element method using multi-functional software as same as ANSYS and other similar, that work with finite elements of the three-dimensional type, as well as some specialized computer programs working with the beam-type finite elements. Anyway, the finite element method is used. But in this case an user needs a lot of time for prepation of the initial data. Therefore, this article presents a calculation of the critical frequencies of the rotor of a centrifugal fuel pump of a liquid-propellant engine based on its discrete model. This calculation also includes an algorithm of results clarification. This model has been verificated by comparing the critical frequencies obtained in calculations based on the finite element beam model and discrete model with using the algorithm of results clarification and without it.

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