Mathematical Modelling of Thin-Walled Cold-Rolled Cross-Section

2014 ◽  
Vol 617 ◽  
pp. 171-174 ◽  
Author(s):  
Jakub Flodr ◽  
Martin Krejsa ◽  
David Mikolášek ◽  
Oldrich Sucharda ◽  
Libor Žídek
Keyword(s):  
Mathematical Model ◽  
Static Analysis ◽  
Cross Section ◽  
Wind Engineering ◽  
Thin Wall ◽  
Software Applications ◽  
Extreme Loads ◽  
Load Carrying ◽  
Cold Rolled ◽  
The Mathematical Model

The purpose of the paper is to perform a static analysis of a thin-wall cold-rolled steel cross-section of a trapezoidal sheet by means of a mathematical model developed in ANSYS, commercially available software applications. The trapezoidal sheets are used typically as an external cladding which covers the structures of steel halls. Investigating into behaviour of the trapezoidal sheets subjected to extreme loads represents an urgent issue in wind engineering. A physical tension test has been performed in order to verify and confirm the mathematical model. Experiments have been performed to prove results of the static analysis into the behaviour of a load-carrying structure formed by a thin-wall cross-section.

Development of a Mathematical Model for a Workpiece Heating and Cooling in a Protective Medium while Treatment under Pressure

2021 ◽  
Vol 410 ◽  
pp. 115-122
Author(s):  
Victoria V. Devyatiarova ◽  
Eugenia E. Balakhnina ◽  
Lilya M. Valeeva
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Arbitrary Shape ◽  
Thermal Conductivity Coefficient ◽  
Regression Equations ◽  
Heating And Cooling ◽  
Temperature Problem ◽  
Protective Medium ◽  
Computer Calculations ◽  
The Mathematical Model

The paper reviews and develops the mathematical model of plastic flow during the hot-forming processes. A flat non-stationary temperature problem for a cross-section of a long solid (rolled product) of arbitrary shape with different heat transfer conditions along the perimeter of the cross-section was considered. Equations for calculation of the thermal conductivity coefficient and heat capacity of tungsten billets were obtained in the temperature range of 700 - 1500°C, based on the literature data. Analytical dependences in form of regression equations were obtained, allowing for computer calculations of physical specifications of 11x11 mm VA grade tungsten billets in form of temperature functions with accuracy sufficient for practical calculations.

scholarly journals Bore formation, evolution and disintegration into solitons in shallow inhomogeneous channels

2003 ◽  
Vol 10 (4/5) ◽  
pp. 407-424 ◽  
Author(s):  
J.-G. Caputo ◽  
Y. A. Stepanyants
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Vries Equation ◽  
Spatial Inhomogeneity ◽  
Hydraulic Jumps ◽  
Variable Depth ◽  
Nonlinear Surface Waves ◽  
Nonlinear Surface ◽  
The Mathematical Model ◽  
Riemann Waves

Abstract. The propagation of nonlinear surface waves in channels of smoothly variable in space cross section is studied theoretically and by means of numerical computations. The mathematical model describing wave evolution is based on the generalized Korteweg-de Vries equation with additional terms due to spatial inhomogeneity and energy dissipation. Specifically we consider channels of variable depth and width. The breaking of Riemann waves and the disintegration of hydraulic jumps into trains of solitons have been examined. The results obtained can be useful in particular for the understanding some peculiarities of bore (mascaret) formation, viscous evolution and disintegration into solitons in inhomogeneous channels or rivers.

scholarly journals The mathematical model and numerical approach based on ENO schemes for the flows in variable cross-section channels with combustion

2016 ◽  
pp. 1-20
Author(s):  
Ekaterina Vladimirovna Borovik ◽  
Mikhail Mikhailovich Krasnov ◽  
Yuri Germanovich Rykov ◽  
Dmitriy Konstantinovich Shalyga
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Numerical Approach ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Eno Schemes ◽  
The Mathematical Model

scholarly journals FINDING THE LINEAR DEPENDENCE OF THE CROSS-SECTION PROFILE FOR A UNIFORM FEEDING OF BREAD MATERIAL IN THE THRESHING PROCESS

2020 ◽  
Author(s):  
I.R. Antypas ◽  
◽  
T.P. Savostina
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Numerical Model ◽  
Cross Section ◽  
Reliability Optimization ◽  
Profile Line ◽  
Section Profile ◽  
The Cross ◽  
Cross Section Profile ◽  
The Mathematical Model

The use of advanced methods and technologies of threshing and separation allows you to predict and minimize losses. The results of reliability optimization of the cross-section profile of the transporting device and its influence on threshing and separation have not yet been studied. To solve this problem, the article modeled a mathematical numerical model that allows you to describe the function of the cut profile line in a General way. The mathematical model is solved using experimental data.

Study on the Curve Reconstructing in the Process of Blade Repairing

2013 ◽  
Vol 819 ◽  
pp. 86-90
Author(s):  
Tao Wang ◽  
Yi Liu Liu ◽  
Jie Tang ◽  
Hao Wang ◽  
Li Wen Wang
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Working Conditions ◽  
Future Research ◽  
Data Points ◽  
Mathematical Equations ◽  
Working Performance ◽  
Section Curve ◽  
The Mathematical Model ◽  
Very High

the aero-blades are often easy to be damaged because of the severe working conditions, and the invading of out objects. Repairing is preferred to replacing with a new one due to the very high expense. The mathematical model of cross section curve is very important to the process of repairing the blade and to the analysis for the working performance of repaired blade. The method of remodeling the curve of cross section is studied including scanning the broken blade, denoising the data points, analyzing the points of cross section and dividing them into four assembles, and fitting them with adaptive mathematical equations. Lastly, the future research plans are given.

New Method for Static Analysis of Frame Structures Considered Floor Deformation

2014 ◽  
Vol 501-504 ◽  
pp. 518-522
Author(s):  
Hua Zhang ◽  
Li Huang
Keyword(s):  
Mathematical Model ◽  
Numerical Solution ◽  
State Space ◽  
Static Analysis ◽  
Frame Structure ◽  
Frame Structures ◽  
Internal Forces ◽  
State Method ◽  
The Mathematical Model ◽  
Computation Work

The piecewise continuum technique was used for the frame structure and a series-parallel system was taken for the mathematical model for the structure in which the deformation of floor slab had to be considered, and its state space equations were derived. Then the numerical solution of deformations and internal forces were obtained by using of state method. It is shown that the method of this paper has the advantages of less computation work and high precision.

Static Analysis of Tensegrity Structures

2005 ◽  
Vol 127 (2) ◽  
pp. 257-268 ◽  
Author(s):  
Carl D. Crane ◽  
Joseph Duffy ◽  
Julio C. Correa
Keyword(s):  
Mathematical Model ◽  
Static Analysis ◽  
Virtual Work ◽  
Numerical Results ◽  
Equilibrium Equations ◽  
Arbitrary Length ◽  
Verification Method ◽  
Tensegrity Structure ◽  
The Mathematical Model ◽  
External Loads

Two problems are addressed in this paper. First, the mathematical model to perform the static analysis of an antiprism tensegrity structure subjected to a wide variety of external loads is presented. The virtual work approach is used to deduce the equilibrium equations and a method based on Newton’s Third Law is used to verify the numerical results. Two numerical examples are provided to demonstrate the use of the mathematical model, as well as the verification method. The second problem deals with the development of a mathematical model to perform the static analysis of a prestressed antiprism tensegrity structure subjected to an arbitrary length reduction of its connecting ties. Again, a virtual work approach is used to deduce the equilibrium equations and the numerical results are verified using a Newtonian approach. One example is provided to illustrate the mathematical model.

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