Approximate solution methods in mechanics analysis of a class of nonlinear seepage problems by a finite-element method

1992 ◽  
Vol 58 (1) ◽  
pp. 60-64
Author(s):  
V. S. Voloshin ◽  
A. A. Glushchenko ◽  
E. G. Sheshukov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Mechanics Analysis ◽  
Solution Methods ◽  
Element Method

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]

Two-Scale Algorithm for Computing the Approximation of the Displacement in Periodic Perforated Structure of Composites

2011 ◽  
Vol 374-377 ◽  
pp. 1226-1229
Author(s):  
Ming Xiang Deng ◽  
Yong Ping Feng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Higher Order ◽  
New Method ◽  
Approximation Solution ◽  
Scale Method ◽  
Small Periodic ◽  
Element Method

By means of two-scale method, the approximation solution of the displacement for structure of composites with small periodic perforated configuration is built, and the algorithm corresponding to two-scale finite element method is presented. One new method of higher order for computing approximate solution of the displacement in periodic perforated composites is given.

Fractal Finite-Element Method for Evaluating Sensitivities of Fracture Parameters for Multiple Cracked Systems

2008 ◽  
Author(s):  
R. M. Reddy ◽  
B. N. Rao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Material Derivative ◽  
Probabilistic Fracture Mechanics ◽  
Linear Elastic ◽  
Fracture Parameters ◽  
Mechanics Analysis ◽  
Cracked Structures ◽  
Element Method

The sensitivities of fracture parameters in cracked structures provide useful information for the prediction of stability and arrest of a single crack, the growth pattern analysis of a system of interacting cracks, configurational stability analysis of evolving cracks, probabilistic fracture mechanics analysis and universal size effect model. In the case of multiple crack systems, for example, sensitivities of fracture parameters at one crack tip due to the growth of any other crack must be calculated to determine the strength of the interaction. In probabilistic fracture mechanics analysis of linear-elastic cracked structures, the first and second order reliability methods require accurate estimates of fracture parameters, their sensitivities. This paper presents a new fractal finite element method based continuum shape sensitivity analysis for evaluating sensitivities of fracture parameters in a homogeneous, isotropic, and two dimensional linear-elastic multiple cracked system subject to mixed-mode loading conditions. The method is based on the material derivative concept of continuum mechanics, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the proposed method to calculate the sensitivity of fracture parameters. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations predict the first-order sensitivity of fracture parameters, more efficiently and accurately than the finite-difference method.

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