Thermal Behavior of Rectangular Flux Channels With Discretely Specified Contact Flux and Temperature

2015 ◽  
Author(s):  
Masood Razavi ◽  
Yuri S. Muzychka ◽  
Serpil Kocabiyik
Keyword(s):  
Boundary Conditions ◽  
Thermal Behavior ◽  
Least Squares Method ◽  
Separation Of Variables ◽  
Heat Fluxes ◽  
Fourier Series Expansion ◽  
The Finite Element Method ◽  
Commercial Software Package ◽  
Good Agreement

In this paper, an analytical solution for the thermal behavior of rectangular flux channels with discretely specified boundary conditions is presented. The boundary conditions along the source plane can be a combination of contact temperatures, heat fluxes, and/or adiabatic. Convective cooling is applied along the sink plane, and the edges of the channel are assumed adiabatic. The governing equation of the system is the Laplace equation which is solved using the method of separation of variables and the least squares method. The solution is presented in the form of Fourier series expansion. As a case study, a symmetrical flux channel with a combination of five discretely specified boundary conditions, including temperature, heat flux and adiabatic conditions is considered. Temperature profile along the channel is calculated and compared with the Finite Element Method (FEM) using COMSOL commercial software package [1]. A good agreement is observed between the analytical and FEM results.

Unified Solution on Skew Plate Bending with Four Edges Supported under Arbitrary Load

2011 ◽  
Vol 243-249 ◽  
pp. 5994-5998
Author(s):  
Lang Cao ◽  
Xing Jie Xing ◽  
Feng Guang Ge
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fourier Series ◽  
Boundary Conditions ◽  
Engineering Design ◽  
Plate Bending ◽  
The Finite Element Method ◽  
Arbitrary Load ◽  
Skew Plate ◽  
Good Agreement

According to the bending equation and boundary conditions of skew plate in the oblique coordinates system parallel to the edge of the plate, expanding deflection and load into form of Fourier series, the paper derives and obtains unified solution of bending problem for the four-edge-supported skew plate under arbitrary load. Programmed and calculated by mathematica language, the paper also comes with deflections and moments under the condition of any oblique angles, ratios of side length and Poisson ratios. The results of the paper is compared with those by the finite element method in the example, and they’re in good agreement with each other. The paper extends the bending theory of rectangular plate to the skew plate of any angle. The theory being reliable and the result being accurate, the research of the paper can provide reference for engineering design.

scholarly journals Analytical Solution for Free Vibrations of a Moderately Thick Rectangular Plate

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Ivo Senjanović ◽  
Marko Tomić ◽  
Nikola Vladimir ◽  
Dae Seung Cho
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Thick Plate ◽  
Mixed Boundary ◽  
Separation Of Variables ◽  
Equations Of Motion ◽  
Mixed Boundary Conditions ◽  
Free Vibrations ◽  
Force Displacement ◽  
Good Agreement

In the present thick plate vibration theory, governing equations of force-displacement relations and equilibrium of forces are reduced to the system of three partial differential equations of motion with total deflection, which consists of bending and shear contribution, and angles of rotation as the basic unknown functions. The system is starting one for the application of any analytical or numerical method. Most of the analytical methods deal with those three equations, some of them with two (total and bending deflection), and recently a solution based on one equation related to total deflection has been proposed. In this paper, a system of three equations is reduced to one equation with bending deflection acting as a potential function. Method of separation of variables is applied and analytical solution of differential equation is obtained in closed form. Any combination of boundary conditions can be considered. However, the exact solution of boundary value problem is achieved for a plate with two opposite simply supported edges, while for mixed boundary conditions, an approximate solution is derived. Numerical results of illustrative examples are compared with those known in the literature, and very good agreement is achieved.

scholarly journals Free Vibrations of Beam System Structures with Elastic Boundary Conditions and an Internal Elastic Hinge

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Alejandro R. Ratazzi ◽  
Diana V. Bambill ◽  
Carlos A. Rossit
Keyword(s):  
Boundary Conditions ◽  
Dynamic Properties ◽  
Separation Of Variables ◽  
Equations Of Motion ◽  
Free Vibrations ◽  
Exact Expression ◽  
The Finite Element Method ◽  
Bending Vibration ◽  
Elastic Boundary ◽  
Beam System

The study of the dynamic properties of beam structures is extremely important for proper structural design. This present paper deals with the free in-plane vibrations of a system of two orthogonal beam members with an internal elastic hinge. The system is clamped at one end and is elastically connected at the other. Vibrations are analyzed for different boundary conditions at the elastically connected end, including classical conditions such as clamped, simply supported, and free. The beam system is assumed to behave according to the Bernoulli-Euler theory. The governing equations of motion of the structural system in free bending vibration are derived using Hamilton's principle. The exact expression for natural frequencies is obtained using the calculus of variations technique and the method of separation of variables. In the frequency analysis, special attention is paid to the influence of the flexibility and location of the elastic hinge. Results are very similar with those obtained using the finite element method, with values of particular cases of the model available in the literature, and with measurements in an experimental device.

Bifurcation of Elastic-Plastic Circular Cylindrical Shells Under Internal Pressure

1979 ◽  
Vol 46 (4) ◽  
pp. 889-894 ◽  
Author(s):  
C.-C. Chu
Keyword(s):  
Internal Pressure ◽  
Critical Pressure ◽  
Separation Of Variables ◽  
Cylindrical Shells ◽  
Maximum Pressure ◽  
Thin Shells ◽  
The Finite Element Method ◽  
Elastic Plastic ◽  
Analytical Results ◽  
Good Agreement

The bifurcation of long elastic-plastic cylindrical shells subject to internal pressure is investigated. It is assumed that the end conditions are such that plane strain conditions prevail. For thin shells, simple approximate bifurcation criteria are obtained analytically. The finite-element method is then employed, in conjunction with separation of variables, to obtain the bifurcation conditions for cylindrical shells with arbitrary thickness to radius ratios. For sufficiently thin shells, the numerical and the analytical results are in good agreement for the critical pressure at bifurcation. The numerical and analytical results both indicate that, for sufficiently thin shells, a variety of bifurcation modes are available virtually simultaneously at this critical pressure. However, for thicker shells, the numerical results reveal that there is a single preferred bifurcation mode. The mode number associated with this preferred bifurcation mode depends on the thickness to radius ratio. The possibility of bifurcation occurring before the attainment of the maximum pressure is also explored. For the specific cases investigated here, bifurcation always occurs after the maximum pressure point.

Optimal Damper Location for Mid-High Frequency Vibration Control on Built-Up Structures: Case Study Using VA One

2011 ◽  
Vol 105-107 ◽  
pp. 705-709
Author(s):  
Asan G.A. Muthalif
Keyword(s):  
High Frequency ◽  
Energy Analysis ◽  
Statistical Energy Analysis ◽  
Simulation Studies ◽  
The Finite Element Method ◽  
Hybrid Modelling ◽  
High Frequencies ◽  
Modelling Method ◽  
Good Agreement

This paper presents a guide to identify optimal damper location to reduce vibration on built-up structures. The guide is derived from simulation studies carried out on a set of benchmark models. Optimization is carried out using genetic algorithm. Optimal location is found using found using Generic algorithm and the hybrid method. The hybrid modelling method combines the finite element method (FEM) and Statistical energy analysis (SEA) to provide an efficient response predication for mid-high frequencies. The guide to find optimal damper location is tested on a fuselage model of Boeing 737. The fuselage model is developed using VA One software. Good agreement is seen for the optimal locations using the simple guide and result from VA One.

scholarly journals Computation of Stray Losses in Transformer Bushing Regions Considering Harmonics in the Load Current

2020 ◽  
Vol 10 (10) ◽  
pp. 3527
Author(s):  
Sohail Khan ◽  
Serguei Maximov ◽  
Rafael Escarela-Perez ◽  
Juan Carlos Olivares-Galvan ◽  
Enrique Melgoza-Vazquez ◽  
...  
Keyword(s):  
Differential Equation ◽  
Finite Element ◽  
Electromagnetic Field ◽  
Boundary Conditions ◽  
Eddy Current ◽  
Special Functions ◽  
Separation Of Variables ◽  
Practical Implementation ◽  
Load Current ◽  
Good Agreement

The presence of harmonics in the load current considerably increases stray losses in electric transformers. In this research paper, a new model for computing the electromagnetic field (EMF) and eddy current (EC) losses in transformer tank covers is derived considering harmonics. Maxwell’s equations are solved with their corresponding boundary conditions. The differential equation thus obtained is solved using the method of separation of variables. The obtained expressions do not require the use of special functions, accommodating them for practical implementation in the industry. The obtained formulas are evaluated for different spectrum contents of the load current and losses. The results are in good agreement with simulations carried out using the Altair Flux finite element (FE) software.

A Three-Dimensional Inverse Problem of Estimating the Surface Thermal Behavior of the Working Roll in Rolling Process

1998 ◽  
Vol 122 (1) ◽  
pp. 76-82 ◽  
Author(s):  
Pao-Tung Hsu ◽  
Yue-Tzu Yang ◽  
Cha’o-Kuang Chen
Keyword(s):  
Boundary Conditions ◽  
Thermal Behavior ◽  
Measurement Errors ◽  
Inverse Analysis ◽  
Least Squares Method ◽  
Finite Difference Methods ◽  
Three Dimensional ◽  
Rolling Process ◽  
Initial Guess ◽  
The Matrix

A three-dimensional inverse analysis utilizes a different perspective to estimate the surface thermal behavior of the working roll in rolling process. The inverse analysis is based on the temperature reading taken inside the roll at several different locations. At the beginning of the study, finite-difference methods are employed to discretize the problem domain and then a linear inverse model is constructed to identify the boundary conditions. The present approach is to rearrange the matrix forms of the differential governing equations and estimate the surface unknown conditions of the working roll. Then, the linear least-squares method is adopted to find the solution. The advantages of this proposed inverse analysis method are that no prior information is needed regarding the functional form of the unknown quantities, no initial guess need be used and the numbers of iterations for calculation process is limited to one. The results show that only few measuring points are sufficient to estimate the boundary conditions when measurement errors are neglected. When measurement errors are considered, more measuring points are needed in order to increase the congruence of the estimated results to exact solutions. [S1087-1357(00)70201-2]

Analysis of the Contact Deformation of Tread Blocks

1992 ◽  
Vol 20 (4) ◽  
pp. 230-253 ◽  
Author(s):  
T. Akasaka ◽  
K. Kabe ◽  
M. Koishi ◽  
M. Kuwashima
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Deformation Behavior ◽  
Contact Deformation ◽  
The Finite Element Method ◽  
The Road ◽  
Loss Of Contact ◽  
Tread Rubber ◽  
Good Agreement ◽  
Rubber Block

Abstract The deformation behavior of a tire in contact with the roadway is complicated, in particular, under the traction and braking conditions. A tread rubber block in contact with the road undergoes compression and shearing forces. These forces may cause the loss of contact at the edges of the block. Theoretical analysis based on the energy method is presented on the contact deformation of a tread rubber block subjected to compressive and shearing forces. Experimental work and numerical calculation by means of the finite element method are conducted to verify the predicted results. Good agreement is obtained among these analytical, numerical, and experimental results.

scholarly journals Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models

2020 ◽  
Vol 66 (4) ◽  
pp. 773-793 ◽  
Author(s):  
Arman Shojaei ◽  
Alexander Hermann ◽  
Pablo Seleson ◽  
Christian J. Cyron
Keyword(s):  
Boundary Conditions ◽  
Materials Science ◽  
Unbounded Domains ◽  
Diffusion Models ◽  
Absorbing Boundary Conditions ◽  
The Finite Element Method ◽  
Absorbing Boundary ◽  
Diffusion Type ◽  
2D And 3D ◽  
Accuracy And Stability

Abstract Diffusion-type problems in (nearly) unbounded domains play important roles in various fields of fluid dynamics, biology, and materials science. The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) suitable for classical (local) as well as nonlocal peridynamic (PD) diffusion models. The main focus of the present study is on the PD diffusion formulation. The majority of the PD diffusion models proposed so far are applied to bounded domains only. In this study, we propose an effective way to handle unbounded domains both with PD and classical diffusion models. For the former, we employ a meshfree discretization, whereas for the latter the finite element method (FEM) is employed. The proposed ABCs are time-dependent and Dirichlet-type, making the approach easy to implement in the available models. The performance of the approach, in terms of accuracy and stability, is illustrated by numerical examples in 1D, 2D, and 3D.

Automatic identification system data-driven model for analysis of ship domain near bridge-waters

2021 ◽  
pp. 1-22
Author(s):  
Lei Jinyu ◽  
Liu Lei ◽  
Chu Xiumin ◽  
He Wei ◽  
Liu Xinglong ◽  
...  
Keyword(s):  
Least Squares Method ◽  
Automatic Identification ◽  
Identification System ◽  
Collision Risk ◽  
Automatic Identification System ◽  
Domain Models ◽  
System Data ◽  
Quantification Model ◽  
Highly Correlated

Abstract The ship safety domain plays a significant role in collision risk assessment. However, few studies take the practical considerations of implementing this method in the vicinity of bridge-waters into account. Therefore, historical automatic identification system data is utilised to construct and analyse ship domains considering ship–ship and ship–bridge collisions. A method for determining the closest boundary is proposed, and the boundary of the ship domain is fitted by the least squares method. The ship domains near bridge-waters are constructed as ellipse models, the characteristics of which are discussed. Novel fuzzy quaternion ship domain models are established respectively for inland ships and bridge piers, which would assist in the construction of a risk quantification model and the calculation of a grid ship collision index. A case study is carried out on the multi-bridge waterway of the Yangtze River in Wuhan, China. The results show that the size of the ship domain is highly correlated with the ship's speed and length, and analysis of collision risk can reflect the real situation near bridge-waters, which is helpful to demonstrate the application of the ship domain in quantifying the collision risk and to characterise the collision risk distribution near bridge-waters.

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