The Strain of a Plane Sampleat the Homogeneous Field of the Strain Rates under the Plane Strain Conditions

2019 ◽  
Vol 945 ◽  
pp. 857-865
Author(s):  
A.L. Grigorieva ◽  
Y.Y. Grigoriev ◽  
A.I. Khromov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Strip Thickness ◽  
Homogeneous Field ◽  
Strain Rates ◽  
The Finite Element Method ◽  
Strain Fields ◽  
Strain Tensors ◽  
The Continuum

In this paper, we obtained analytical solutions of the fields of strain tensors under uniaxial tension of a rigidplasticstrip underthe conditions of a plane stress state.The topicalityof the construction of these solutions is connected with significant difficulties in determining the strain fields by numerical methods (for example, the finite element method).In the construction of these solutions, the change in the geometric characteristics of the strip (thickness, width) was taken into account, which led to the solution of the nonlinear problem of the continuum mechanics.

scholarly journals Application of classical numerical methods in the calculation of solidification modes of a continuous ingot

2020 ◽  
pp. 41-47
Author(s):  
V. I. Timoshpolsky ◽  
E. I. Marukovich ◽  
I. A. Trusova
Keyword(s):  
Experimental Data ◽  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Continuous Casting ◽  
Computational Analysis ◽  
The Finite Element Method ◽  
Casting Technology ◽  
Continuous Ingot ◽  
Continuously Cast

This paper presents approaches to the computational analysis of solidification and cooling processes of continuously cast billets in order to improve and develop technological modes in the conditions of modern continuous casting machines using FEM.The application of modern numerical methods for solidification and cooling of workpieces on continuous casting machines is considered. The use of the finite element method is justified when using computational and experimental data for the development and improvement of casting technology.

Development of software based on NX Open for assessing the reliability of REA designs

2018 ◽  
Author(s):  
С.А. Пименов ◽  
П.П. Зорков
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Statistical Modelling ◽  
Probabilistic Methods ◽  
The Finite Element Method ◽  
Random Loading ◽  
Random Load ◽  
Wide Range ◽  
Element Method

Рассматриваются основные алгоритмы и численные методы решения задач оценки надежности конструкций радиоэлектронной аппаратуры. Алгоритмы реализованы в виде расчетного программного обеспечения АРКОН для проведения оценки надежности конструкций в условиях случайного нагружения с применением численных методов: метода конечных элементов и метода статистического моделирования. The paper deals with the development of new software which allows us to use probabilistic methods for evaluating the reliability of CEA designs. The main algorithms and numerical methods for solving problems of reliability assessment of REA structures are considered. The reason for conducting the study was the presence of the lag in development of the program-technical complexes aimed at assessment of the strength reliability in relation to the tasks being solved. At the moment, analytical methods for estimating the probability of failure-free operation have been developed. Their implementation requires the existence of a law for the distribution of random load parameters and the system itself. This method is deprived of the method of statistical modelling with the calculation of stresses using the finite element method. The algorithms are implemented in the form of computational software for assessing the reliability of structures under random loading conditions. To implement this method, an open CAE was chosen — a system with the ability to program its own modules — the NX Open system. The developed software is displayed on the NX panel in the form of a special icon tray Reliability. The developed software is intended for analysis of the strength of reliability of CEA structures with random loading. The software does not have domestic or foreign alternatives. The main advantages are universality (the ability to perform calculations for a wide range of designs, taking into account the statistical nature of the initial data), the reliability of the estimated estimates, confirmed by the use of modern numerical methods: the finite element method and the statistical modelling method.

scholarly journals The methods of numerical mechanics for the improvement of machine-tools

2020 ◽  
Vol 10 (2) ◽  
pp. 133-144
Author(s):  
Attila Szilágyi ◽  
Dániel Kiss
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
General Problem ◽  
Machine Tools ◽  
The Finite Element Method ◽  
Element Method

This paper gives a brief summary on the mechanical and thermal applicability of the finite element method (FEM) from the field of designing procedure of machine tools. The solutions of certain problems, as examples, are also demonstrated. First the summary of such phenomena is performed, where the application of numerical methods is inevitable. Through the brief summary of the general problem of elasticity, the justification of the numerical methods is demonstrated. Finally, examples are set to demonstrate the applicability of the numerical methods and the achieved results, which demonstrate the efficiency of the FEM applied for the development of machine tools. Among several numerical methods the FEM is focused on in this paper.

scholarly journals The implementation of the boundary element method to the Helmholtz equation of acoustics

2021 ◽  
pp. 13-19
Author(s):  
Sergey Sivak ◽  
Mihail Royak ◽  
Ilya Stupakov ◽  
Aleksandr Aleksashin ◽  
Ekaterina Voznjuk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Numerical Methods ◽  
Helmholtz Equation ◽  
Boundary Value Problems ◽  
Boundary Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Element Method

Introduction: To solve the Helmholtz equation is important for the branches of engineering that require the simulation of wave phenomenon. Numerical methods allow effectiveness’ enhancing of the related computations. Methods: To find a numerical solution of the Helmholtz equation one may apply the boundary element method. Only the surface mesh constructed for the boundary of the three-dimensional domain of interest must be supplied to make the computations possible. This method’s trait makes it possible toconduct numerical experiments in the regions which are external in relation to some Euclidian three-dimensional subdomain bounded in the three-dimensional space. The later also provides the opportunity of not using additional geometric techniques to consider the infinitely distant boundary. However, it’s only possible to use the boundary element methods either for the homogeneous domains or for the domains composed out of adjacent homogeneous subdomains. Results: The implementation of the boundary elementmethod was committed in the program complex named Quasar. The discrepancy between the analytic solution approximation and the numerical results computed through the boundary element method for internal and external boundary value problems was analyzed. The results computed via the finite element method for the model boundary value problems are also provided for the purpose of the comparative analysis done between these two approaches. Practical relevance: The method gives an opportunityto solve the Helmholtz equation in an unbounded region which is a significant advantage over the numerical methods requiring the volume discretization of computational domains in general and over the finite element method in particular. Discussion: It is planned to make a coupling of the two methods for the purpose of providing the opportunity to conduct the computations in the complex regions with unbounded homogeneous subdomain and subdomains with substantial inhomogeneity inside.

Structural Analysis

2017 ◽  
pp. 124-219
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Numerical Methods ◽  
Three Dimensional ◽  
Wind Engineering ◽  
The Finite Element Method ◽  
Material Models ◽  
Three Dimensional Models ◽  
Base Connections

This chapter develops the components required for successful modelling of temporary structures. It presents the principles, methods and the associated limitations that currently are seen as the state-of-the-art in structural analysis using the Finite Element Method. Material models of steel, aluminium and bamboo are presented with an emphasis on linear and multilinear models for steel and the Ramberg-Osgood model for aluminium. Models are presented for braces, props, beam-to-column connections, top connections, base connections and column-to-column connections based on the latest theoretical and experimental procedures developed by the authors and co-workers. Examples of two and three dimensional models are then developed for access scaffolds, bridge falsework and bamboo scaffolds. Finally, the chapter presents information on the effects of ground modelling and on advanced wind engineering using complex numerical methods.

Teaching Undergraduate Numerical Methods Through a Practical Multibody Dynamics Project

2011 ◽  
Author(s):  
Alfonso Callejo ◽  
Javier Garci´a de Jalo´n
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Multibody Dynamics ◽  
Mechanical Engineering ◽  
Practical Training ◽  
The Finite Element Method ◽  
The Many ◽  
Short Time ◽  
Element Method

Among the many different approaches to teach engineering subjects, the project-based methodology turns out to be one of the most effective ones. In the field of undergraduate numerical methods, it can overcome some of its inherent difficulties. This paper considers a particular context: a general 90-hour numerical methods subject in an Industrial-Mechanical Engineering degree. The methods are applied to mechanical engineering problems such as matrix structural analysis, finite element method, multibody systems (MBS), harmonic analysis, or optimization. The article suggests how an appropriate formulation and a practical MATLAB™-based project make up a good approach for a short-time practical training on multibody dynamics (MBD) within that subject. The keys to the theoretical lessons and an example of the project are explained thoroughly. The mechanical project has to be rich in numerical methods. MBD and the finite element method fulfill this requirement. The former is chosen in this article. The students know the basics, but they have to learn everything about MBD in very little time. This experience can be useful in other educational contexts. After explaining the approach, some sample assignment exercises are described, as well as a possible way to assess the work of the students. The result of this approach is a reasonable achievement-time tradeoff shown in the solid skills acquired by the students and proven by the experience of the last few years.

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.

scholarly journals Application of Direct Integration Methods in the solution of a nonlinear beam problem

2021 ◽  
Vol 7 (1) ◽  
pp. e3002
Author(s):  
Raul Carreira Rufato ◽  
Santos Alberto Enriquez-Remigio ◽  
Tobias Souza Morais
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Dynamic Response ◽  
Dynamic Problem ◽  
Direct Integration ◽  
The Finite Element Method ◽  
Integration Methods ◽  
Nonlinear Beam ◽  
Fortran Language

This work applies different numerical methods involved in the solution of a nonlinear clamped beam problem. The methodology used in the discretization of the dynamic problem is based on the Finite Element Method (FEM), followed by mode superposition, where a localized nonlinearity is applied at the free end of the beam. The solution of the nonlinear problem is performed by five different integration methods. The solution code is implemented in FORTRAN language, validated with ANSYS and the dynamic response and the graphs are obtained with the help of MATLAB software. The work shows the convergence of the implemented methods with various validation problems.

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