scholarly journals Identification of Flexural Rigidity in a Kirchhoff Plates Model Using a Convex Objective and Continuous Newton Method

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
B. Jadamba ◽  
R. Kahler ◽  
A. A. Khan ◽  
F. Raciti ◽  
B. Winkler
Keyword(s):  
Inverse Problem ◽  
Newton Method ◽  
Fourth Order ◽  
Flexural Rigidity ◽  
Numerical Study ◽  
Variable Parameter ◽  
Kirchhoff Plates ◽  
Estimation Problems ◽  
Output Least Squares ◽  
Continuous Newton Method

This work provides a detailed theoretical and numerical study of the inverse problem of identifying flexural rigidity in Kirchhoff plate models. From a mathematical standpoint, this inverse problem requires estimating a variable coefficient in a fourth-order boundary value problem. This inverse problem and related estimation problems associated with general plates and shell models have been investigated by numerous researchers through an optimization framework using the output least-squares (OLSs) formulation. OLS yields a nonconvex framework and hence it is suitable for investigating only the local behavior of the solution. In this work, we propose a new convex framework for the inverse problem of identifying a variable parameter in a fourth-order inverse problem. Existence results, optimality conditions, and discretization issues are discussed in detail. The discrete inverse problem is solved by using a continuous Newton method. Numerical results show the feasibility of the proposed framework.

scholarly journals Numerical study of time-fractional fourth-order differential equations with variable coefficients

2011 ◽  
Vol 23 (1) ◽  
pp. 91-98 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Nasir-Uddin Khan ◽  
Muhammad Ayaz ◽  
Amir Mahmood ◽  
Noor Fatima
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Numerical Study ◽  
Variable Coefficients

scholarly journals Numerical Study on Phase-Fitted and Amplification-Fitted Diagonally Implicit Two Derivative Runge-Kutta Method for Periodic IVPS

2021 ◽  
Vol 50 (6) ◽  
pp. 1799-1814
Author(s):  
Norazak Senu ◽  
Nur Amirah Ahmad ◽  
Zarina Bibi Ibrahim ◽  
Mohamed Othman
Keyword(s):  
Fourth Order ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Numerical Study ◽  
Kutta Method ◽  
Initial Value ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.

An efficient fourth order weighted-Newton method for systems of nonlinear equations

2012 ◽  
Vol 62 (2) ◽  
pp. 307-323 ◽  
Author(s):  
Janak Raj Sharma ◽  
Rangan Kumar Guha ◽  
Rajni Sharma
Keyword(s):  
Nonlinear Equations ◽  
Newton Method ◽  
Fourth Order ◽  
Systems Of Nonlinear Equations

Member distortional buckling behaviour of hybrid double-I-box beams

2018 ◽  
Vol 45 (8) ◽  
pp. 605-622 ◽  
Author(s):  
M.S. Deepak ◽  
V.M. Shanthi
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Parametric Study ◽  
Flexural Rigidity ◽  
Numerical Study ◽  
Plate Thickness ◽  
Distortional Buckling ◽  
Study Results ◽  
Box Beams ◽  
The Moment

This paper compiles the experimental and finite-element parametric study on member distortional buckling behaviour of new built-up metal hybrid double-I-box beams (HDIBBs). The cross-section of this built-up beam is unique and looks similar to the shape of a double-I-box fabricated using four channel sections. The flange plates were provided with an intermediate stiffener. In these built-up beams there is more material in the flange portions far away from the horizontal centroidal axis of their cross-section. Hence, there is an increase in the flexural rigidity that enhances the moment capacity of the beam, under major axis bending. The geometry consists of torsionally rigid closed-box web portion that provides high resistance to minor axis lateral-buckling. The varying parameters considered were the ratio of yield stresses of the flange to the web steel plates, the ratio of breadth to the depth of the section, and the flange plate thickness. In the experimental programme, all the HDIBB members failed due to kinds of distortional buckling which was identified by web buckling and flange twist along edges. The results revealed that when flange plate slenderness increases there is a drop in the moment resistance capacity of the beams. The numerical study was performed using ABAQUS software. In comparison, there was good agreement between experimental and numerical results. The validated finite element models were further extended to perform parametric studies on ideal HDIBB models. Both the experimental and parametric study results were compared with the predicted strengths using effective width method equations specified in the Euro code standards EN 3-1-3. It was found that the current Euro code design rules slightly over-estimate the distortional buckling resistance capacity of closed form built-up cold-formed steel members. A new design equation was formulated and recommended for estimating the reduction in distortional buckling moment resistance capacity for HDIBBs.

On the Convergence Rate of the Continuous Newton Method

2019 ◽  
Vol 239 (6) ◽  
pp. 867-879
Author(s):  
A. Gibali ◽  
D. Shoikhet ◽  
N. Tarkhanov
Keyword(s):  
Convergence Rate ◽  
Newton Method ◽  
Continuous Newton Method

A perfect memory makes the continuous Newton method look ahead

2017 ◽  
Vol 92 (8) ◽  
pp. 085201
Author(s):  
M B Kim ◽  
J W Neuberger ◽  
W P Schleich
Keyword(s):  
Newton Method ◽  
Look Ahead ◽  
Continuous Newton Method ◽  
Perfect Memory
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