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]

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.

A MODIFIED TRIANGULATION ALGORITHM TAILORED FOR THE SMOOTHED FINITE ELEMENT METHOD (S-FEM)

2013 ◽  
Vol 11 (01) ◽  
pp. 1350069 ◽  
Author(s):  
Y. LI ◽  
M. LI ◽  
G. R. LIU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
The Finite Element Method ◽  
Advancing Front ◽  
Stiffness Matrices ◽  
Smoothed Finite Element Method ◽  
Complicated Geometry ◽  
Discrete Domains ◽  
Volume Method ◽  
Element Method

Meshing is one of the key tasks in using the finite element method (FEM), the smoothed finite element method (S-FEM), finite volume method (FVM), and many other discrete numerical methods. Linear triangular (T3) mesh is one of the most widely used mesh, because it can be generated and refined automatically for discrete domains of complicated geometry, and hence save significantly the time for model creation. This paper presents a modified triangulation algorithm based on the advancing front technique to provide a comprehensive linear triangular mesh generator with six connectivity lists, including element–node (Ele–N) connectivity, element–edge (Ele–Eg) connectivity, edge–node (Eg–N) connectivity, edge–element (Eg–Ele) connectivity, node–edge (N–Eg) connectivity and node–element (N–Ele) connectivity. These six connectivity lists are generated along the way when the T3 elements are created, and hence it is done in a most efficient fashion. The connectivity is recorded in the usual counter-clockwise convention for convenient utilization in various S-FEM models for effective analyses. In addition, an algorithm is developed for renumbering the nodes in the T3 mesh to obtain a minimized bandwidth of stiffness matrices for both FEM and S-FEM models.

The Finite-Element Method—Part II

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Integration ◽  
Gaussian Quadrature ◽  
The Finite Element Method ◽  
Gaussian Quadrature Formula ◽  
Stiffness Matrices ◽  
Minimum Number ◽  
Element Technique ◽  
Element Method

Numerical integration is an important part of the finite-element technique. As seen in Section 6.5 of Chap. 6, volume integrations as well as surface integrations should be carried out in order to represent the elemental stiffness equations in a simple matrix form. In deriving the variational principle, it is implicitly assumed that these integrations are exact. However, exact integrations of the terms included in the element matrices are not always possible. In the finite-element method, further approximations are made in the procedure for integration, which is summarized in this section. Numerical integration requires, in general, that the integrand be evaluated at a finite number of points, called Integration points, within the integration limits. The number of integration points can be reduced, while achieving the same degree of accuracy, by determining the locations of integration points selectively. In evaluating integration in the stiffness matrices, it is necessary to use an integration formula that requires the least number of integrand evaluations. Since the Gaussian quadrature is known to require the minimum number of integration points, we use the Gaussian quadrature formula almost exclusively to carry out the numerical integrations.

scholarly journals Modal analysis of damaged structures by the modified finite element method

1998 ◽  
Vol 20 (1) ◽  
pp. 29-46 ◽  
Author(s):  
Nguyen Cao Menh ◽  
Nguyen Tien Khiem ◽  
Dao Nhu Mai ◽  
Nguyen Viet Khoa
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Standard Procedure ◽  
Frame Structures ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Stiffness Matrices ◽  
Flexible Supports ◽  
Cubic Polynomial ◽  
Element Method

The classical 3D beam element has been modified and developed as a new finite element for vibration analysis of frame structures with flexible connections and cracked members. The mass and stiffness matrices of the modified elements are established basing on a new form of shape functions, which are obtained in investigating a beam with flexible supports and crack modeled through equivalent springs. These shape functions remain the cubic polynomial form and contain flexible connection (or crack) parameters. They do not change standard procedure of the finite element method (FEM). Therefore, the presented method is easy for engineers in application and allows to analyze Eigen-parameters of structures as functions of the connection (or crack) parameters. The proposed approach has been applied to calculate natural frequencies and mode shape of typical frame structures in presented examples.

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.

AN IMPROVED RAYLEIGH–RITZ SUBSTRUCTURE SYNTHESIS METHOD ADOPTING MIXED COORDINATES

2003 ◽  
Vol 03 (04) ◽  
pp. 541-565
Author(s):  
MARIO SCHEBLE ◽  
AGUSTÍN G. RAUSCHERT ◽  
JOSÉ CONVERTI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Condition Number ◽  
Free Choice ◽  
Synthesis Method ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Substructure Synthesis ◽  
Generalized Coordinates ◽  
Mixed Coordinates

This paper presents an improvement of the Rayleigh–Ritz substructure synthesis method that retains all the advantages of the more elaborate existing versions. The displacement field in each component is represented by a set of simple non-admissible shape functions (generalized coordinates). These are subject to a transformation to mixed coordinates (physical and internal). The physical coordinates are defined where necessary to impose boundary conditions and geometrical compatibility. The internal coordinates are chosen in order to optimize the condition number of the matrices involved. Such a change of coordinates makes possible the use of the convenient assembling procedure of the Finite Element Method. The procedure, done in a systematic manner, leaves no free choice to the user and leads to an optimal numerical behavior. Several examples of applications are presented.

scholarly journals An approximate solution of the filtration problem of a system of the dams by the finite element method

2015 ◽  
Vol 1 (1) ◽  
pp. 21-26
Author(s):  
Ngo Van Luoc ◽  
Ta Hong Quang ◽  
Le Kim Luat
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Viet Nam ◽  
The Finite Element Method ◽  
Filtration Problem ◽  
Hoa Binh ◽  
Element Method

Using the finite element method we construct an algorithm for solving the filtration problem of a system of dams. The program based on  this algorithm is coded in FORTRAN for the EC-1022 and MINSK-32. This program is used for solving the filtration problem of Hoa Binh dam in Viet Nam.

Non-Linear Dynamic Analysis of Cylindrical Shells Subjected to a Flowing Fluid

2000 ◽  
Author(s):  
A. A. Lakis ◽  
A. Selmane ◽  
C. Dupuis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Empty Shell ◽  
The Finite Element Method ◽  
Linear Dynamic ◽  
Stiffness Matrices ◽  
Non Linear ◽  
Element Method

Abstract A theory is presented to predict the influence of non-linearities associated with the wall of the shell and with the fluid flow on the dynamic of elastic, thin, orthotropic open and closed cylindrical shells submerged and subjected to an internal and external fluid. The open shells are assumed to be freely simply-supported along their curved edges and to have arbitrary straight edge boundary conditions. The method developed is a hybrid of thin shell theory, fluid theory and the finite element method. The solution is divided into four parts. In part one, the displacement functions are obtained from Sanders’ linear shell theory and the mass and linear stiffness matrices for the empty shell are obtained by the finite element procedure. In part two, the modal coefficients derived from the Sanders-Koiter non-linear theory of thin shells are obtained for these displacement functions. Expressions for the second and third order non-linear stiffness matrices of the empty shell are then determined through the finite element method. In part three a fluid finite element is developed, the model requires the use of a linear operator for the velocity potential and a linear boundary condition of impermeability. With the non-linear dynamic pressure, we develop in the fourth part three non-linear matrices for the fluid. The non-linear equation of motion is then solved by the fourth-order Runge-Kutta numerical method. The linear and non-linear natural frequency variations are determined as a function of shell amplitudes for different cases.

Load-induced stiffness matrix of plates

2002 ◽  
Vol 29 (1) ◽  
pp. 181-184 ◽  
Author(s):  
Shi-Jun Zhou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Closed Form Solutions ◽  
Stiffness Matrices ◽  
Support Conditions ◽  
Stiffening Effect ◽  
Element Method

In this paper, a rectangular plate element for the finite-element method, which takes into consideration the stiffening effect of dead loads, is proposed. The element stiffness matrices that include the effect of dead loads are derived. The effect of dead loads on dynamic behaviors of plates is analyzed using the finite-element method. It is shown that the stiffness of plates increases when the effect of dead loads is included in the calculation and that the effect is more significant for plates with a smaller stiffness. The validity of the proposed procedure is confirmed by numerical examples. Although the finite-element results obtained are in agreement with the approximate closed-form solutions, the proposed method based on a finite-element formulation is more easily applied to practical structures under various support conditions and various types of dead loads.Key words: load-induced stiffness matrix of plate, stiffening effect of dead loads.

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