A family of triangular Hermite finite elements complementing the Bogner–Fox–Schmit rectangle

2015 ◽  
Vol 30 (2) ◽  
Author(s):  
Lidia Gileva ◽  
Vladimir Shaidurov ◽  
Boris Dobronets
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Finite Elements ◽  
Polygonal Domain ◽  
The Finite Element Method ◽  
New Family ◽  
Rectangular Element ◽  
Hermite Finite Elements ◽  
Element Method

AbstractThe Bogner-Fox-Schmit rectangular element is one of the simplest elements that provide continuous differentiability of an approximate solution in the framework of the finite element method. However, it can be applied only on a simple domain composed of rectangles whose sides are parallel to two different straight lines.We propose a new family of triangular Hermite elements that involves straight-sided elements and elements with a curved side. Such an element can be used in combination with the Bogner-Fox-Schmit element near the boundary of an arbitrary polygonal domain or a domain with a curved part of the boundary and provides continuous differentiability of an approximate solution in thewhole domain up to the boundary.

THE ROLE OF FINITE ELEMENT METHOD IN CIVIL ENGINEERING

2018 ◽  
Vol 5 (02) ◽  
Author(s):  
Er. Hardik Dhull
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Analytical Method ◽  
Civil Engineering ◽  
The Finite Element Method ◽  
Engineering Problems ◽  
Building Components ◽  
Element Method

The finite element method is a numerical method that is used to find solution of mathematical and engineering problems. It basically deals with partial differential equations. It is very complex for civil engineers to study various structures by using analytical method,so they prefer finite element methods over the analytical methods. As it is an approximate solution, therefore several limitationsare associated in the applicationsin civil engineering due to misinterpretationof analyst. Hence, the main aim of the paper is to study the finite element method in details along with the benefits and limitations of using this method in analysis of building components like beams, frames, trusses, slabs etc.

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.

Rayleigh-Ritz Based Substructure Synthesis for Multiply Supported Structures

1998 ◽  
Vol 122 (1) ◽  
pp. 2-6 ◽  
Author(s):  
C. Morales
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Synthesis Method ◽  
The Finite Element Method ◽  
Compatibility Conditions ◽  
Substructure Synthesis ◽  
Stiffness Matrices ◽  
Element Method

This paper is concerned with the convergence characteristics and application of the Rayleigh-Ritz based substructure synthesis method to structures for which the use of a kinematical procedure taking into account all the compatibility conditions, is not possible. It is demonstrated that the synthesis in this case is characterized by the fact that the mass and stiffness matrices have the embedding property. Consequently, the estimated eigenvalues comply with the inclusion principle, which in turn can be utilized to prove convergence of the approximate solution. The method is applied to a frame and is compared with the finite element method. [S0739-3717(00)00201-4]

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 Approximate solution of the Signorini problem by the finite element method in three-dimensional space

2021 ◽  
Vol 21 (2) ◽  
pp. 203-214
Author(s):  
A.Y. Zolotukhin ◽  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Signorini Problem ◽  
The Finite Element Method ◽  
Three Dimensional Space ◽  
Element Method

The finite element method is usually used for two-dimensional space. The paper investigates the finite element method for solving the Signorini problem in three-dimensional space.

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