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.

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 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.

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.

scholarly journals Analysis of the stressed-strained state of the foundation-shell at interaction with the elastic-plastic medium

2021 ◽  
pp. 105-112
Author(s):  
Maksym Vabishchevich ◽  
Gherman Zatyliuk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Bearing Capacity ◽  
The Finite Element Method ◽  
Plastic Medium ◽  
Soil Base ◽  
Elastic Plastic ◽  
The Impact ◽  
Element Method

On the basis of modern numerical implementations of the finite element method the article presents the justification of the adequacy of the method of solving the problems of structures straining in their contact interaction with the elastic-plastic nonlinear soil medium. Compatible calculations of structures and nonlinear bases, which are described by modern mechanical and soil models within one problem is a significant technical problem. The solution of the assigned tasks is possible only within the framework of numerical methods, the most common of which is the finite element method (FEM). The construction of the computational finite element model raises many complex questions that require additional detailed study. In addition, the compliance with the state building norms and regulations is an important factor for further practical use. The use of numerical methods in the calculation of machines and structures, taking into account their interaction with the elastic-plastic medium is largely determined by the complexity or even impossibility of analytical calculation due to the complexity of structural schemes, heterogeneity of material features, uneven soil layers, implementation of step-by-step work execution technologies and so on. The combination of the latest achievements in the field of structural mechanics and soil mechanics is a promising direction for the development of effective approaches to building discrete models of space systems “structure-nonlinear base” for solving applied problems. The use of the developed method allows to significantly specify the structures stress state interacting with the soil base, and to significantly specify the impact on the calculated level of the base bearing capacity. Only the simultaneous consideration of the nonlinear resistance of the soil base together with the plasticity and the structure destruction in the numerical simulation of the foundation-shell load provided good agreement with the natural experiment data as to the type of the boundary state and the bearing capacity level.

COMPARISION AND STUDY OF NUMERICAL METHODS FOR DYNAMIC RESPONSE EVALUATION OF SDOF

2020 ◽  
Vol 43 (01) ◽  
Author(s):  
THAI PHUONG TRUC
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Dynamic Response ◽  
Field Analysis ◽  
Full Detail ◽  
The Finite Element Method ◽  
Senior Year ◽  
Acceleration Method ◽  
Element Method

Written for senior-year undergraduates and first-year graduate students with solid backgrounds in differential and integral calculus, this paper is oriented toward engineers and applied mathematicians. Consequently, this paper should be useful to senior-year undergraduates the finite element method [1]. The scaled direct approach is adopted for this purpose and each step in the finite element solution process is given in full detail. For this reason, all students must be exposed to (and indeed should master). This paper provides the general framework for the development of nearly all (nonstructural) finite element models. The finite element method of analysis is a very powerful, modern computational tool. Applications range from deformation and stress analysis of automotive, aircraft, building, and bridge structures to field analysis of beat flux, fluid flow, magnetic flux, seepage, and other flow problems. This paper presents study and comparison of numerical methods which are used for evaluation of dynamic response. A Single Degree of Freedom (SDF)-linear problem is solved by means of Newmark’s Average acceleration method [2], Linear acceleration method [2], Central Difference method [6,7] with the help of MATLAB. The advantages, disadvantages, relative precision and applicability of these numerical methods are discussed throughout the analysis.

scholarly journals Nonlinear problem of structural deformation in interaction with elastoplastic medium

2020 ◽  
pp. 48-63
Author(s):  
Ivan Solodei ◽  
Eduard Petrenko ◽  
Gherman Zatyliuk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Structural Deformation ◽  
Spatial Problem ◽  
The Finite Element Method ◽  
Arbitrary Boundary ◽  
Soil Medium ◽  
Elastic Plastic ◽  
Element Method

The use of numerical methods in the calculation of machines and structures, taking into account their interaction with the elastic-plastic medium is largely determined by the complexity or even impossibility of analytical calculation due to the complexity of structural schemes, heterogeneity of material features, uneven soil layers, implementation of step-by-step work execution technologies and so on. Compatible calculations of structures and nonlinear basis, which are described by modern mechanical and soil models in one problem is a significant technical problem. And neither the existing “problem-oriented” software packages, nor the “universal” ones - do not fully contain such models. The tasks solution is possible only within the framework of numerical methods, the most common of which is the finite element method (FEM). The construction of the calculated finite element model raises many complex questions that require additional detailed study. In addition, the compliance with the state building norms and regulations is an important factor for further practical use. The combination of the latest achievements in the field of structural mechanics and soil mechanics is a promising direction for the development of effective approaches for building discrete models of spatial systems “structure-nonlinear base” for solving applied problems. On the basis of modern numerical implementations of the finite element method the article presents the theoretical foundations of the analysis of deformation processes of machines and structures in their contact interaction with the elastic-plastic nonlinear soil medium within the three-dimensional spatial problem taking into account the previous stress state and load history. The methodology of construction of computational models of joint deformation and mutual influence of rigid structures and essentially plastic external medium is developed, new special heterogeneous finite elements of SAFEM of general form with variable geometrical and physical-mechanical parameters and arbitrary boundary conditions for approximation of arrays of hardly connected reinforced soils are developed.

scholarly journals The accuracy of numerical methods for the analysis of electrostatic fields

2021 ◽  
Vol 7 (1) ◽  
pp. 59-70
Author(s):  
Vladimir N. Taran ◽  
Maxim V. Shevlyugin ◽  
Aleksey V. Shandybin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Analytical Solution ◽  
Electromagnetic Fields ◽  
The Finite Element Method ◽  
Electrostatic Fields ◽  
Improve Accuracy ◽  
Real Objects ◽  
Element Method

Aim: Estimation of the accuracy of the numerical method relative to the analytical solution. Methods: This article reports on studies of the accuracy of numerical calculations based on the finite element method. The variational scheme of the method is considered. Results: The dependences of errors on the number of simplexes used are obtained and analyzed. The authors noted ways to further improve accuracy. Conclusion: The article gives recommendations on the possible application of the finite element method in solving problems of calculating the electromagnetic fields of real objects.

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