scholarly journals Calculation of V-shaped overlaps

2021 ◽  
pp. 11-15
Author(s):  
В.А. Манухин
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress State ◽  
Reference Solution ◽  
Normal Stresses ◽  
The Finite Element Method ◽  
Approximate Methods ◽  
The Dead ◽  
The Difference ◽  
Strength And Stiffness

В статье приводится краткое описание и сравнение двух приближенных методик учета килеватости V-образных перекрытий при расчетах их прочности и жесткости. В обеих методиках килеватость учитывается введением добавочной жесткости центральной продольной балки, при этом само перекрытие рассматривается как плоское. Отличие методик заключается в различном подходе к оценке добавочной жесткости центральной балки и учете зависимости добавочной жесткости от угла килеватости, соотношения размеров перекрытия, наличия распора продольных кромок перекрытия. Расчеты по обеим методикам сравниваются с «эталонным» решением, полученным методом конечных элементов. Для простейшего V-образного перекрытия с одной продольной центральной балкой исследовано влияние на результаты вычислений угла килеватости и распора продольных кромок перекрытия. Показано, что оба приближенных подхода дают в целом надежные оценки прогиба перекрытия и напряженного состояния в середине пролета центральной балки, однако наибольшие нормальные напряжения в опорных сечениях центральной балки ими существенно занижаются. The article provides a brief description and comparison of two approximate methods for taking into account the dead-rise angle of V-shaped overlaps when calculating their strength and stiffness. In both methods, the dead-rise angle is taken into account by introducing additional rigidity of the Central longitudinal beam, while the overlap itself is considered as flat. The difference between the methods is a different approach to assessing the additional stiffness of the central beam and taking into account the dependence of the additional stiffness on the dead-rise angle angle, the ratio of the overlap size, and the presence of a emphasis of the longitudinal edges of the overlap. Calculations using both methods are compared with the "reference" solution obtained by the finite element method. For the simplest V-shaped floor with a single longitudinal central beam, the influence of the dead-rise angle and the spacer of the longitudinal edges of the floor on the results of calculations is studied. It is shown that both approximate approaches give generally reliable estimates of the overlap deflection and the stress state in the middle of the central beam span, but they significantly underestimate the maximum normal stresses in the support sections of the central beam.

scholarly journals The Search of Spatial Functions of Pressure in Adjustable Hydrostaticradial Bearing

2015 ◽  
Vol 9 (1) ◽  
pp. 23-26 ◽  
Author(s):  
Dmytro Fedorynenko ◽  
Sergiy Boyko ◽  
Serhii Sapon
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Deformation ◽  
Tangential Direction ◽  
The Finite Element Method ◽  
Radial Bearing ◽  
Operational Characteristics ◽  
Service Conditions ◽  
The Difference ◽  
Element Method

Abstract The analysis of spatial functions of pressure considering the geometrical deviations and the elastic deformation of conjugate surace have been considered. The analysis of spatial functions of pressure is performed by the finite element method. The difference of the size of pressure in a tangential direction of a pocket of a support under various service conditions has been investigated. A recommendation for improving of operational characteristics in regulated hydrostatic radial bearing has been developed.

scholarly journals Application of a new vector mode solver to optical fiber-based plasmonic sensors

2016 ◽  
Vol 30 (07) ◽  
pp. 1650075 ◽  
Author(s):  
V. A. Popescu ◽  
N. N. Puscas ◽  
G. Perrone
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Method ◽  
Distilled Water ◽  
The Finite Element Method ◽  
Plasmonic Sensor ◽  
Plasmonic Sensors ◽  
Vector Mode ◽  
Hankel Functions ◽  
The Difference

Our analytical method uses a linear combination of the Hankel functions [Formula: see text] and [Formula: see text] to represent the field in the gold region of a fiber-based plasmonic sensor. This method is applied for different structures made from three, four and five layers. When the analyte is distilled water, the difference between the resonant wavelengths calculated with the finite element method and the analytical method is very small (0.00 nm for three layers, 0.19 nm for four layers and 0.07 nm for five layers with two gold layers). The important characteristics of the Bessel and Hankel functions at the loss matching point are analyzed.

Modelling of ballraceway contacts in a slewing bearing with non-linear springs

2011 ◽  
Vol 225 (4) ◽  
pp. 827-831 ◽  
Author(s):  
X H Gao ◽  
X D Huang ◽  
H Wang ◽  
J Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Contact Area ◽  
The Finite Element Method ◽  
Simple Method ◽  
Slewing Bearing ◽  
Combined Loads ◽  
Non Linear ◽  
The Difference ◽  
Supporting Structures

During the operation, a slewing bearing is always subjected to a set of combined loads. It is the source of deformation of ballraceway contacts, rings, and even supporting structures. In practice, deformation of rings and supporting structures is often neglected for simplification, that is, they are supposed to be ideally stiff. To take elasticity of rings and supporting (fixed) structures into consideration, the finite-element method (FEM) is applied. Due to hundreds of contact pairs and the difference in the scale of contact area and rings or supporting structures, it is difficult to simultaneously model both local ballraceway contacts and the global slewing rings in a slewing bearing. The article developed a simple method to solve the problem, where the contacts are replaced by non-linear springs.

scholarly journals УЗАГАЛЬНЕННЯ МОДЕЛІ ФОЛЬКЕРСЕНА НА ВИПАДОК ОСЬОВОЇ СИМЕТРІЇ

2021 ◽  
pp. 78-89
Author(s):  
К. П. Барахов
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Stress State ◽  
Boundary Conditions ◽  
Classical Model ◽  
The Finite Element Method ◽  
Premature Failure ◽  
One Dimensional ◽  
Element Method

Thin-walled structures may contain defects as cracks and holes that are leftovers of the material the construction, is made of or they occur during the operation as a result of, for example, mechanical damage. The presence of holes in the plate causes a concentration of stresses at the boundary of the holes and ultimately leads to premature failure of the structural element. Repair of local damage of modern aircraft structures can be made by creating overlays that are glued to the main structure. The overlay takes on part of the load, unloading the damaged area. This method of repair provides tightness and aerodynamic efficiency to the structure. The calculation of the stress state of such glued structures is usually performed by using the finite element method. The classic models of the stress state of overlapped joints are one-dimensional. That is, the change of the stress state along only one coordinate is considered. At the same time, the connections of a rectangular form are also considered. The purpose of this work is to create a mathematical model of the stress state of circular axisymmetric adhesive joints and to build an appropriate analytical solution to the problem. It is assumed that the bending of the plates is absent; the deformation of the plates is even by thickness. The adhesive layer works only on the shift. The main plate and the overlay are considered isotropic. The solution is built on polar coordinates. The stress state of the connection depends only on the radial coordinate, i.e. one-dimensional. The solution is obtained in analytical form. This mathematical model is a generalization of the classical model of the adhesive connection of Volkersen to a circular or annular region and is considered for the first time. Boundary conditions are met exactly. The satisfaction of marginal conditions, as well as boundary conditions, leads to a system of linear equations with respect to the unknown coefficients of the obtained solutions. The model problem is solved and the numerical results are compared with the results of calculations performed by using the finite element method. It is shown that the proposed model has sufficient accuracy for engineering problems and can be used to solve problems of the design of aerospace structures.

scholarly journals Comparative analysis of finite element formulations at plane loading of an elastic body

2020 ◽  
Vol 16 (2) ◽  
pp. 139-145
Author(s):  
Natalia A. Gureeva ◽  
Anatoly P. Nikolaev ◽  
Vladislav N. Yushkin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Body ◽  
Stiffness Matrix ◽  
Strain State ◽  
Mixed Formulation ◽  
The Finite Element Method ◽  
Displacement Method ◽  
Internal Forces ◽  
The Difference

The aim of the work - comparison of the results of determining the parameters of the stress-strain state of plane-loaded elastic bodies based on the finite element method in the formulation of the displacement method and in the mixed formulation. Methods. Algorithms of the finite element method in various formulations have been developed and applied. Results. In the Cartesian coordinate system, to determine the stress-strain state of an elastic body under plane loading, a finite element of a quadrangular shape is used in two formulations: in the formulation of the method of displacements with nodal unknowns in the form of displacements and their derivatives, and in a mixed formulation with nodal unknowns in the form of displacements and stresses. The approximation of displacements through the nodal unknowns when obtaining the stiffness matrix of the finite element was carried out using the form function, whose elements were adopted Hermite polynomials of the third degree. Upon receipt of the deformation matrix, the displacements and stresses of the internal points of the finite element were approximated through nodal unknowns using bilinear functions. The stiffness matrix of the quadrangular finite element in the formulation of the displacement method is obtained on the basis of a functional based on the difference between the actual workings of external and internal forces under loading of a solid. The matrix of deformation of the finite element was formed on the basis of a mixed functional obtained from the proposed functional by repla-cing the actual work of internal forces with the difference between the total and additional work of internal forces when loading the body. The calculation example shows a significant advantage of using a finite element in a mixed formulation.

METHODOLOGY FOR CALCULATING THE STRESS STATE OF THE PILLAR FOR THE SALVAGE CHAMBER IN THE PRESENCE OF AN ADJACENT MINED OUT LONGWALL

2021 ◽  
Vol 4 (1) ◽  
pp. 364-374
Author(s):  
I. A. Ermakova ◽  
◽  
V. A. Fedusov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress State ◽  
Quantitative Assessment ◽  
Underground Mines ◽  
The Finite Element Method ◽  
Load Factors ◽  
Relevant Task ◽  
Mining Conditions ◽  
Edge Part

Analysis of salvage operations at the underground mines of JSC SUEK-Kuzbass has shown that they can have different locations relative to the previously mined out adjacent longwall, which has a significant impact on the duration of salvage operations. If there is a previously mined out adjacent longwall next to the salvage chamber, the duration of salvage operations increases significantly, in contrast to the case when the salvage chamber is located within a pillar, outside the zone affected by the previously mined out longwall. In this regard, the calculation of the stress state of the pillar for the salvage chamber in the presence of an ad-jacent previously mined out longwall is a relevant task. The paper presents a methodology for quantitative assessment of the stress affecting the pillar for the salvage chamber, based on the use of the finite element method. An example of calculating the stress on the pillar for the sal-vage chamber in the presence of an adjacent mined out longwall for specific geological and mining conditions is considered. It has been established that the presence of a previously mined out adjacent longwall causes additional load on the specified pillar. The highest load factors are observed in the edge part of the pillar near the ventilation gateroad.

Interference Fit Stress Concentrations with Full Chamfered Hub

2013 ◽  
Vol 572 ◽  
pp. 209-212 ◽  
Author(s):  
Juan Carlos Pérez-Cerdán ◽  
Miguel Lorenzo ◽  
Carmen Blanco
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress State ◽  
Quantitative Determination ◽  
Numerical Simulations ◽  
Not Given ◽  
The Finite Element Method ◽  
Stress Concentrations ◽  
Interference Fit

Quantitative determination of stress concentrations factors (SCF) in interference fits joints is highly relevant since they are not given by the theory of pressure cylinders commonly used for designing them. We study the capability of using a full chamfered hub as a geometrical design for reducing SCF. Stresses distributions and stresses concentrations factors are analyzed as a function of parameters that define the hub geometry with the aim of optimizing the design of proposed modified hubs. To achieve this goal, diverse numerical simulations by means of the finite element method (FEM) were carried out in order to quantitatively estimate the stress state existing at hub-shaft interface.

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