On Natural Boundary Conditions in the Finite-Element Method

1972 ◽  
Vol 39 (4) ◽  
pp. 1149-1150
Author(s):  
R. W. McLay
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
The Finite Element Method ◽  
Natural Boundary ◽  
Natural Boundary Conditions ◽  
Element Method

Physical statement of the problem for a numerical model of soil freezing and heaving taking into account heat and mass transfer

2021 ◽  
pp. 244-256
Author(s):  
Виктор Григорьевич Чеверев ◽  
Евгений Викторович Сафронов ◽  
Алексей Александрович Коротков ◽  
Александр Сергеевич Чернятин
Keyword(s):  
Finite Element Method ◽  
Mass Transfer ◽  
Finite Element ◽  
Numerical Model ◽  
Boundary Conditions ◽  
Heat And Mass Transfer ◽  
Soil Freezing ◽  
The Finite Element Method ◽  
Freezing Front ◽  
Element Method

Существуют два основных подхода решения задачи тепломассопереноса при численном моделировании промерзания грунтов: 1) решение методом конечных разностей с учетом граничных условий (границей, например, является фронт промерзания); 2) решение методом конечных элементов без учета границ модели. Оба подхода имеют существенные недостатки, что оставляет проблему решения задачи для численной модели промерзания грунтов острой и актуальной. В данной работе представлена физическая постановка промерзания, которая позволяет создать численную модель, базирующуюся на решении методом конечных элементов, но при этом отражающую ход фронта промерзания - то есть модель, в которой объединены оба подхода к решению задачи промерзания грунтов. Для подтверждения корректности модели был проделан ряд экспериментов по физическому моделированию промерзания модельного грунта и выполнен сравнительный анализ полученных экспериментальных данных и результатов расчетов на базе представленной численной модели с такими же граничными условиями, как в экспериментах. There are two basic approaches to solving the problem of heat and mass transfer in the numerical modeling of soil freezing: 1) using the finite difference method taking into account boundary conditions (the boundary, for example, is the freezing front); 2) using the finite element method without consideration of model boundaries. Both approaches have significant drawbacks, which leaves the issue of solving the problem for the numerical model of soil freezing acute and up-to-date. This article provides the physical setting of freezing that allows us to create a numerical model based on the solution by the finite element method, but at the same time reflecting the route of the freezing front, i.e. the model that combines both approaches to solving the problem of soil freezing. In order to confirm the correctness of the model, a number of experiments on physical modeling of model soil freezing have been performed, and a comparative analysis of the experimental data obtained and the calculation results based on the provided numerical model with the same boundary conditions as in the experiments was performed.

scholarly journals Calculation of the goffered multilayered composite cylindrical shells by using the finite element method

1999 ◽  
Vol 21 (2) ◽  
pp. 116-128
Author(s):  
Pham Thi Toan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
The Finite Element Method ◽  
Multilayered Composite ◽  
Internal Forces ◽  
External Loads ◽  
Element Method ◽  
Composite Cylindrical Shells

In the present paper, the goffered multilayered composite cylindrical shells is directly calculated by finite element method. Numerical results on displacements, internal forces and moments are obtained for various kinds of external loads and different boundary conditions.

Finite-Element Solution of the Incompressible Lubrication Problem

1969 ◽  
Vol 91 (3) ◽  
pp. 524-533 ◽  
Author(s):  
M. M. Reddi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Minimum Principle ◽  
Test Problems ◽  
Element Solution ◽  
The Finite Element Method ◽  
Natural Boundary ◽  
Flow Computation ◽  
Ritz Procedure ◽  
Natural Boundary Conditions

A minimum principle for the transient incompressible Reynold’s equation, with the natural boundary conditions of prescribed pressure, as well as flow, is presented. The finite element method is introduced as the numerical counterpart of the Rayleigh-Ritz procedure. Flow computation is shown to be a natural corollary of the integral principle. Solutions of several test problems are presented.

Numerical Charaterization of the Shear Behavior of Hetero-Junction Carbon Nanotubes

2013 ◽  
Vol 26 ◽  
pp. 143-151 ◽  
Author(s):  
Sadegh Imani Yengejeh ◽  
Mojtaba Akbarzade ◽  
Andreas Öchsner
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Carbon Nanotubes ◽  
Finite Element ◽  
Boundary Conditions ◽  
Shear Behavior ◽  
The Finite Element Method ◽  
Twisting Angle ◽  
Element Method

In this study, numerous types of straight hetero-junction carbon nanotubes (CNTs) and their fundamental CNTs were investigated by the finite element method (FEM). By applying the FEM, the shear behavior of these hetero-junctions was obtained thorough numerical simulation. The behavior of hetero-junctions and their constituent CNTs were investigated. The investigations revealed that the twisting angle of straight hetero-junction CNTs lies within the range of twisting angle of their fundamental CNTs. In addition, change of boundary conditions did not significantly change the value of obtained twisting angle of hetero-junctions. It was also concluded that the shear behavior of straight hetero-junctions and their constituent CNTs increases by increasing the chiral number of both armchair and zigzag CNTs. The current study provides a better insight towards the prediction of straight hetero-junction CNTs behavior.

scholarly journals Aerodynamical Investigation of The Wings of an Ultralight Aircraft

2018 ◽  
Vol 9 (1) ◽  
pp. 171-174
Author(s):  
Richárd Molnár ◽  
Gergely Dezső
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Complex Task ◽  
The Finite Element Method ◽  
Input Output ◽  
Building Process ◽  
Engineering Work ◽  
Element Method

Abstract Nowadays more and more ultralight aircraft are being built because the building process itself and the acquisition of the necessary documentation is relatively easy. Furthermore, these planes are easier to fly than larger types of aircraft. This article presents the engineering work and documentation that is necessary for the building process. The calculations can be done traditionally on paper which is an extremely complex task. With the innovations and developments in the technical field though, it is possible now to simplify these calculations, the basis of which is the finite element method and aerodynamics simulations. If the finite element method is adequate, the boundary conditions are ideal and input-output settings for the simulations are correct, it is possible to compare the traditional calculations to the modern simulated engineering work, thus the time necessary for achieving precise results becomes significantly shorter.

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.

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