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

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.

2020 ◽  
Vol 43 (01) ◽  
Author(s):  
THAI PHUONG TRUC

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.


2019 ◽  
Vol 945 ◽  
pp. 857-865
Author(s):  
A.L. Grigorieva ◽  
Y.Y. Grigoriev ◽  
A.I. Khromov

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.


1978 ◽  
Vol 100 (4) ◽  
pp. 660-666 ◽  
Author(s):  
A. L. Salama ◽  
M. Petyt

The finite element method is used to study the free vibration of packets of blades. A packet of six shrouded blades is analyzed, only the tangential vibrations being considered. Results are obtained to establish the effect of certain parameters such as stiffness ratio, mass ratio, the number of blades in the packet, the effect of rotation and the position of the lacing wires. The dynamic response of a packet to periodic loading is also studied. The cases of engine order harmonic excitation and partial admission of gas are considered with reference to a packet of six shrouded blades.


Author(s):  
V. I. Timoshpolsky ◽  
E. I. Marukovich ◽  
I. A. Trusova

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.


2019 ◽  
Vol 275 ◽  
pp. 02015
Author(s):  
Zhenhang ZHAO ◽  
Yuting SHEN ◽  
Xue YAN ◽  
Qiankun SU

In order to study the vertical dynamic characteristics of the composite sleeper ballasted track in tunnels, this paper establishes a dynamic model based on the finite element method, and compares the dynamic response of vehicle, wheel and rail systems, track systems and backfill layer with the type-III concrete sleeper. The research results show that the composite sleeper ballasted tracks’ acceleration of the car body and the wheel-rail force are smaller than that of the type-III sleeper. It can meet the safety of the train and passenger comfort. Because the composite sleeper has good elasticity, The rail displacement and acceleration, the sleeper displacement and acceleration of the composite sleeper are slightly larger than the type-III sleeper ballasted track, but the effect is not great. The composite sleeper has good elasticity and large damping, so that the acceleration of the track bed and the backfill layer is less than that of the type-III sleeper ballasted track. This shows that the composite sleeper has vibration damping characteristics for the track bed and the backfill layer.


Author(s):  
С.А. Пименов ◽  
П.П. Зорков

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.


2013 ◽  
Vol 444-445 ◽  
pp. 1434-1439
Author(s):  
Shan Liu ◽  
Rui Li ◽  
Qian Qian Liu

In recent years, the cases that bridges under the action of debris flow been damaged have increased year by year. In this paper, the dynamic response of the double-column pier under the action of the debris flow are studied. Using the finite element method, considering the action of the upper structures dead load, the analysis of the changes about the displacement and stress of the pier bottom was conducted, as well as the deformation and stress changes in pile foundation.


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