scholarly journals Eigenfunction Convergence of the Rayleigh-Ritz-Meirovitch Method and the FEM

2007 ◽  
Vol 14 (6) ◽  
pp. 417-428 ◽  
Author(s):  
C.A. Morales ◽  
R. Goncalves
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Linear Combination ◽  
Ritz Method ◽  
Structural Response ◽  
Characteristic Functions ◽  
Natural Mode ◽  
The Finite Element Method ◽  
Definition Of ◽  
General Response

Eigenfunction convergence characteristics of the finite element method and the Rayleigh-Ritz method with quasicomparison functions (RRMM) are compared. The RRMM has previously proved to be superior in comparing eigenvalue convergence characteristics. The importance of studying natural mode convergence is associated to the fact that the general response of a structure is a linear combination of these characteristic functions; in other words, accurate structural response attainment demands accurate structural modes in the analysis. It is shown that in this case the RRMM also produces superior results. A refined definition of quasicomparison functions is advanced.

Definition of the Temperature and Heat Flux in Micromilling of Hardened Steel Using the Finite Element Method

2014 ◽  
Vol 39 (10) ◽  
pp. 7229-7239 ◽  
Author(s):  
Sergio Luiz Moni Ribeiro Filho ◽  
Marcelo Oliveira Gomes ◽  
Carlos Henrique Lauro ◽  
Lincoln Cardoso Brandão
Keyword(s):  
Finite Element Method ◽  
Heat Flux ◽  
Finite Element ◽  
Hardened Steel ◽  
The Finite Element Method ◽  
Definition Of ◽  
Element Method

scholarly journals Design and Structural Analysis of a SWATH type vessel using the Finite Element Method and its response to Slamming events

2020 ◽  
Vol 14 (27) ◽  
pp. 55-66
Author(s):  
Hugo Leonardo Murcia Gallo ◽  
Richard Lionel Luco Salman ◽  
David Ignacio Fuentes Montaña
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Speed ◽  
Load Condition ◽  
Structural Response ◽  
Water Area ◽  
The Finite Element Method ◽  
Short Period ◽  
Classification Society ◽  
Element Method

The main objective of this study is to analyze the structural response of a boat during a slamming event using the Finite Element Method in a Small Water Area Twin Hull (SWATH) type boat.  In the mentioned load condition, the acceptance criteria established by a classification society must be fulfilled, taking into account the areas where this event affects the structure such as the junction deck, the pontoons and other structural members established by the standard, all this generated by the high pressure loads in the ship's structure in a very short period of time being an element of study in this type of vessels, as long as they are within the range of high speed vessels. Among the main results of this study were the deformations and stresses in the structure obtained under the reference parameters of the classification society.

scholarly journals INFORMATIZATION OF CONSTRUCTION MANAGEMENT AS A BASIS FOR PREVENTING MAN-MADE ACCIDENTS

2021 ◽  
Vol 4 (4) ◽  
pp. 11-31
Author(s):  
S. Koryagina
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
The Finite Element Method ◽  
Calculation Results ◽  
Definition Of ◽  
Deep Pits ◽  
Geotechnical Problems ◽  
Seismic Impacts ◽  
Base Structure ◽  
Element Method

the article presents the principles and algorithms of the finite element method in solving geotechnical prob-lems taking into account seismic impacts for determining the stress-strain state of structures and slope stabil-ity, implemented in the Midas GTS NX software package. GTS NX allows you to perform calculations of various types of geotechnical problems and solve complex geotechnical problems in a single software envi-ronment. GTS NX covers the entire range of engineering and geotechnical projects, including calculations of the "base-structure" system, deep pits with various mounting options, tunnels of complex shape, consolida-tion and filtration calculations, as well as calculations for dynamic actions and stability calculations. At the same time, all types of calculations in GTS NX can be performed both in 2D and in 3D. The author does not claim to be the author of the finite element method, but he cannot do without pointing out the basic equa-tions, as this affects the definition of the boundaries of use, the formulation of algorithms for constructing calculation schemes and the analysis of calculation results.

The Finite-Element Method—Part I

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Ritz Method ◽  
Approximate Solutions ◽  
Plane Elasticity ◽  
Heat Transfer Analysis ◽  
Deformation Analysis ◽  
The Finite Element Method ◽  
Element Method

The concept of the finite-element procedure may be dated back to 1943 when Courant approximated the warping function linearly in each of an assemblage of triangular elements to the St. Venant torsion problem and proceeded to formulate the problem using the principle of minimum potential energy. Similar ideas were used later by several investigators to obtain the approximate solutions to certain boundary-value problems. It was Clough who first introduced the term “finite elements” in the study of plane elasticity problems. The equivalence of this method with the well-known Ritz method was established at a later date, which made it possible to extend the applications to a broad spectrum of problems for which a variational formulation is possible. Since then numerous studies have been reported on the theory and applications of the finite-element method. In this and next chapters the finite-element formulations necessary for the deformation analysis of metal-forming processes are presented. For hot forming processes, heat transfer analysis should also be carried out as well as deformation analysis. Discretization for temperature calculations and coupling of heat transfer and deformation are discussed in Chap. 12. More detailed descriptions of the method in general and the solution techniques can be found in References [3-5], in addition to the books on the finite-element method listed in Chap. 1. The path to the solution of a problem formulated in finite-element form is described in Chap. 1 (Section 1.2). Discretization of a problem consists of the following steps: (1) describing the element, (2) setting up the element equation, and (3) assembling the element equations. Numerical analysis techniques are then applied for obtaining the solution of the global equations. The basis of the element equations and the assembling into global equations is derived in Chap. 5. The solution satisfying eq. (5.20) is obtained from the admissible velocity fields that are constructed by introducing the shape function in such a way that a continuous velocity field over each element can be denned uniquely in terms of velocities of associated nodal points.

The Definition of a Critical Deflection of Compressed Rods with the Creep by the Method of Bubnov-Galerkin

2018 ◽  
Vol 931 ◽  
pp. 127-132
Author(s):  
Batyr M. Yazyev ◽  
Serdar B. Yazyev ◽  
Anatoly P. Grinev ◽  
Elena A. Britikova
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Difference Method ◽  
Stability Problem ◽  
The Finite Element Method ◽  
The Difference ◽  
The Stability ◽  
Definition Of ◽  
The Galerkin Method

The comparison of the numerical methods: the finite element method, the Galerkin Method, the difference method is considered for the study of the stability of the rods. The dependence of the solution of the stability problem on the parameters of the discretization of these numerical methods is studied. It is shown that the mathematical models are sufficiently accurate to analyze the stability of the rods of constant and variable sections.

Finite Element Assessment of Difficult Pipelines at Bends

2014 ◽  
Vol 567 ◽  
pp. 253-258
Author(s):  
Zahiraniza Mustaffa ◽  
Thar M. Badri Albarody ◽  
Azrulfirdaus Muhamad Roshdi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Distribution ◽  
Equivalent Stress ◽  
Structural Response ◽  
The Finite Element Method ◽  
Pipe Bend ◽  
Dead End ◽  
Numerical Assessment ◽  
Different Depths

This paper presents numerical assessment of difficult pipelines at bends using the finite element method (FEM). Difficult pipelines are those that are unable to be inspected using a pig inspection tool. These unpiggable pipes, especially at the bend sections, exhibit difficulties to be piggable for several reasons, thus they are exposed to hazards that can neither be inspected nor controlled. The structural response of the bends is then required to be investigated. This paper aims at simulating the structural response of bends caused by internal corrosions using the ANSYS FEM software. Circular pitting corrosion at different depths and diameters were applied to simulate the stress distribution for three pipe models, namely standard 90° pipe bend, miter bend and unbarred full-bore tees pipe bend near dead end. The results of different corrosion equivalent stress distribution were compared and the most reliable type of bend was reported.

Finite Element Analysis of the Relationship between Clasp Dimensions and Flexibility

1990 ◽  
Vol 69 (10) ◽  
pp. 1664-1668 ◽  
Author(s):  
Y. Yuasa ◽  
Y. Sato ◽  
S. Ohkawa ◽  
T. Nagasawa ◽  
H. Tsuru
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Simple Formula ◽  
Parameter Study ◽  
Stiffness Parameter ◽  
Shape Parameters ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Definition Of ◽  
The Relationship

A parameter study with use of the finite element method was conducted for examination of the relationships between the shape parameters of a clasp (width and thickness at the base and tip of the clasp) and its displacement or stress. By synthesis of these relationships, a simple formula defining the clasp tip displacement in terms of clasp dimensions ("displacement formula") was obtained. A stiffness parameter "Fd" (the load producing a 1-mm displacement of the clasp tip) was proposed, and a formula defining Fd in terms of shape parameters was derived from the displacement formula. Fd would be a practical parameter for the definition of clasp retention, and the present formulae appear to be useful tools for investigation of the retention of removable partial dentures.

scholarly journals Structural Response of a Reciprocating Compressor's Discharge Tube Subjected to Model and Data Uncertainties

2018 ◽  
Vol 23 (No 3, September 2018) ◽  
pp. 385-391
Author(s):  
Filipe Fontanela ◽  
Olavo Mecias da Silva ◽  
Thiago Antonio Fiorentin ◽  
Arcanjo Lenzi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stochastic Models ◽  
Structural Response ◽  
Model Parameters ◽  
Manufacturing Processes ◽  
The Finite Element Method ◽  
Physical Processes ◽  
Parameter Uncertainties ◽  
Deterministic Framework

The analysis of the dynamical responses of compressor components are typically evaluated by using mathematicalmechanical models, and many decisions are given based on numerical simulations. Such an investigation is usually performed in a deterministic framework that cannot consider the uncertainties of the numerical model. These uncertainties are present in a numerical investigation due to the variability of the model parameters, caused by the limitations of the manufacturing processes, as well as simplifications and/or lack of knowledge to describe complex physical processes accurately. In order to quantify the sensitivity of the model parameters and the epistemic uncertainties of a discharge tube’s structural numerical response—solved by the finite element method—two stochastic models are constructed, and their results are simultaneously analysed. The dynamical responses obtained from both stochastic models identify the robustness limits of the structural response when it is subjected to parameter uncertainties as well as model sensitivity by separating each contribution in the estimated dynamical structural response.

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