scholarly journals Analysis of Structural Concrete Bar Members Based on Secant Stiffness Methods

2020 ◽  
Vol 25 (3) ◽  
pp. 1-16
Author(s):  
Ayad Al-Rumaithi ◽  
Aqeel T. Fadhil ◽  
Ban Fadhil Salman
Keyword(s):  
Numerical Model ◽  
Normal Force ◽  
Axial Strain ◽  
Linear Equations ◽  
Bending Moment ◽  
Structural Concrete ◽  
Concrete Members ◽  
Secant Methods ◽  
Secant Stiffness ◽  
Non Linear Equations

AbstractIn this paper, the behavior of structural concrete linear bar members was studied using numerical model implemented in a computer program written in MATLAB. The numerical model is based on the modified version of the procedure developed by Oukaili. The model is based on real stress-strain diagrams of concrete and steel and their secant modulus of elasticity at different loading stages. The behavior presented by normal force-axial strain and bending moment-curvature relationships is studied by calculating the secant sectional stiffness of the member. Based on secant methods, this methodology can be easily implemented using an iterative procedure to solve non-linear equations. A comparison between numerical and experimental data, illustrated through the strain profiles, stress distribution, normal force-axial strain, and moment-curvature relationships, shows that the numerical model has good numerical accuracy and is capable of predicting the behavior of structural concrete members with different partially prestressing ratios at serviceability and ultimate loading stages.

scholarly journals THE NUMERICAL MODELLING OF TIDES IN A SHALLOW SEMI-ENCLOSED BASIN BY A MODIFIED ELLIPTIC METHOD

2018 ◽  
Vol 21 ◽  
pp. 1-47
Author(s):  
Mulia M. Sidjabat
Keyword(s):  
Numerical Model ◽  
Numerical Modelling ◽  
Boundary Conditions ◽  
Coefficient Of Friction ◽  
Iterative Scheme ◽  
Linear Equations ◽  
Tidal Constituent ◽  
Non Linear ◽  
Non Linear Equations ◽  
Good Agreement

A numerical model which renders possible the numerical solution of the nonlinear tidal equations by obtaining a solution for each individual tidal component is developed. For this purpose, a set of time independent non-linear equations for each tidal constituent is constructed. Each of these sets of equations is interrelated through the non-linear frictional terms, the approximation of which is accomplished by an iterative scheme. The method is tested for several models before it is applied to the real basin (Bight of Abaco). In order to evaluate the model and to construct the boundary conditions along the opening, a series of tidal observations were undertaken. The viability of the method is indicated by the fact that the results of computations using a coefficient of friction r = 0.0034 give good agreement with observations for all components and  over  all stations.

Experimental and numerical assessment of oblique loading quasi-static testing of railway anticlimbers

2020 ◽  
pp. 095440972090899 ◽  
Author(s):  
C Moreno ◽  
S Reid ◽  
T Williams
Keyword(s):  
Numerical Model ◽  
Normal Force ◽  
Bending Moment ◽  
Test Machine ◽  
Test Results ◽  
Compression Tests ◽  
Railway Vehicles ◽  
Static Testing ◽  
Numerical Assessment ◽  
Oblique Loading

An oblique loading angle test was devised in order to subject the anticlimbers of railway vehicles to a predetermined perpendicular load as well as a predetermined bending moment. The motivation for this type of test was the Standard and industry requirements for anticlimbing devices to prevent overriding and resist a determined perpendicular force while dissipating energy. Anticlimbing units, based on shrinking circular deformation tubes, were subjected to compression tests. The oblique loading was applied by placing the anticlimbing unit on a plate at an angle to the centreline of the unit. A numerical model was validated against the test results, in order to infer the bending moment subjected to the anticlimber unit. The bending moment on the anticlimbers was expected to be fully determined by the perpendicular force and the length of the tube. The predicted bending moment measured by the validated numerical model was smaller than anticipated and was potentially unpredictable. The discrepancy was caused by the irregular distribution of the normal force at the interface of the test machine and the anticlimber head. As a result, the devised angle test was proved unsuitable to induce a consistent and predictable bending moment on the anticlimber units of railway vehicles.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

scholarly journals Framework for Reconstruction of Pseudo Quad Polarimetric Imagery from General Compact Polarimetry

2021 ◽  
Vol 13 (3) ◽  
pp. 530
Author(s):  
Junjun Yin ◽  
Jian Yang
Keyword(s):  
Linear Equations ◽  
Estimation Method ◽  
Data Sets ◽  
Reconstruction Procedure ◽  
Component Decomposition ◽  
Reconstruction Methods ◽  
Sar Imagery ◽  
Key Aspects ◽  
Non Linear Equations ◽  
Reconstruction Model

Pseudo quad polarimetric (quad-pol) image reconstruction from the hybrid dual-pol (or compact polarimetric (CP)) synthetic aperture radar (SAR) imagery is a category of important techniques for radar polarimetric applications. There are three key aspects concerned in the literature for the reconstruction methods, i.e., the scattering symmetric assumption, the reconstruction model, and the solving approach of the unknowns. Since CP measurements depend on the CP mode configurations, different reconstruction procedures were designed when the transmit wave varies, which means the reconstruction procedures were not unified. In this study, we propose a unified reconstruction framework for the general CP mode, which is applicable to the mode with an arbitrary transmitted ellipse wave. The unified reconstruction procedure is based on the formalized CP descriptors. The general CP symmetric scattering model-based three-component decomposition method is also employed to fit the reconstruction model parameter. Finally, a least squares (LS) estimation method, which was proposed for the linear π/4 CP data, is extended for the arbitrary CP mode to estimate the solution of the system of non-linear equations. Validation is carried out based on polarimetric data sets from both RADARSAT-2 (C-band) and ALOS-2/PALSAR (L-band), to compare the performances of reconstruction models, methods, and CP modes.

scholarly journals Striated Tire Yaw Marks—Modeling and Validation

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4309
Author(s):  
Wojciech Wach ◽  
Jakub Zębala
Keyword(s):  
Vehicle Dynamics ◽  
Linear Equations ◽  
Tire Model ◽  
Vehicle Accidents ◽  
The Road ◽  
Variable Curvature ◽  
Macro Scale ◽  
On The Road ◽  
Multi Body ◽  
Non Linear Equations

Tire yaw marks deposited on the road surface carry a lot of information of paramount importance for the analysis of vehicle accidents. They can be used: (a) in a macro-scale for establishing the vehicle’s positions and orientation as well as an estimation of the vehicle’s speed at the start of yawing; (b) in a micro-scale for inferring among others things the braking or acceleration status of the wheels from the topology of the striations forming the mark. A mathematical model of how the striations will appear has been developed. The model is universal, i.e., it applies to a tire moving along any trajectory with variable curvature, and it takes into account the forces and torques which are calculated by solving a system of non-linear equations of vehicle dynamics. It was validated in the program developed by the author, in which the vehicle is represented by a 36 degree of freedom multi-body system with the TMeasy tire model. The mark-creating model shows good compliance with experimental data. It gives a deep view of the nature of striated yaw marks’ formation and can be applied in any program for the simulation of vehicle dynamics with any level of simplification.

scholarly journals Compartmental Learning versus Joint Learning in Engineering Education

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 662
Author(s):  
María Jesús Santos ◽  
Alejandro Medina ◽  
José Miguel Mateos Roco ◽  
Araceli Queiruga-Dios
Keyword(s):  
Engineering Students ◽  
Chemical Engineering ◽  
Linear Equations ◽  
Mathematical Software ◽  
Mathematical Concepts ◽  
Joint Learning ◽  
The University ◽  
Academic Year ◽  
Non Linear Equations ◽  
Mathematics And Physics

Sophomore students from the Chemical Engineering undergraduate Degree at the University of Salamanca are involved in a Mathematics course during the third semester and in an Engineering Thermodynamics course during the fourth one. When they participate in the latter they are already familiar with mathematical software and mathematical concepts about numerical methods, including non-linear equations, interpolation or differential equations. We have focused this study on the way engineering students learn Mathematics and Engineering Thermodynamics. As students use to learn each matter separately and do not associate Mathematics and Physics, they separate each matter into different and independent compartments. We have proposed an experience to increase the interrelationship between different subjects, to promote transversal skills, and to make the subjects closer to real work. The satisfactory results of the experience are exposed in this work. Moreover, we have analyzed the results obtained in both courses during the academic year 2018–2019. We found that there is a relation between both courses and student’s final marks do not depend on the course.

Partially Invariant Solutions for Two-dimensional Ideal MHD Equations

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1219-1229 ◽  
Author(s):  
D.-A. Becker ◽  
E. W. Richter
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Mhd Equations ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
First Order ◽  
Partially Invariant Solutions ◽  
Quasilinear Systems ◽  
Ideal Mhd ◽  
Non Linear Equations

AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

scholarly journals A derivative free globally convergent method and its deformations

2021 ◽  
Author(s):  
Manoj Kumar Singh ◽  
Arvind K. Singh
Keyword(s):  
Difference Operator ◽  
Linear Equations ◽  
Numerical Test ◽  
Test Functions ◽  
Globally Convergent ◽  
Forward Difference ◽  
Derivative Free ◽  
Fractal Patterns ◽  
Convergent Method ◽  
Non Linear Equations

AbstractThe motive of the present work is to introduce and investigate the quadratically convergent Newton’s like method for solving the non-linear equations. We have studied some new properties of a Newton’s like method with examples and obtained a derivative-free globally convergent Newton’s like method using forward difference operator and bisection method. Finally, we have used various numerical test functions along with their fractal patterns to show the utility of the proposed method. These patterns support the numerical results and explain the compactness regarding the convergence, divergence and stability of the methods to different roots.

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