scholarly journals THE PSEUDO-SHOCK: A NON-LINEAR PROBLEM OF TRANSLATIONAL RELAXATION

1965 ◽  
Author(s):  
B. L. HICKS
Keyword(s):  
Linear Problem ◽  
Non Linear

Deformation of Rectangular Slender Webplates with Boundary Members Flexible in the Webplate Plane

1966 ◽  
Vol 17 (4) ◽  
pp. 371-394 ◽  
Author(s):  
J. Djubek
Keyword(s):  
Linear Problem ◽  
Numerical Results ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Non Linear

SummaryThe paper presents a solution of the non-linear problem of the deformation of slender rectangular plates which are stiffened along their edges by elastically compressible stiffeners flexible in the plane of the plate. The webplate is assumed to be simply-supported along its contour. Numerical results showing the effect of flexural and normal rigidity of stiffeners are given for a square webplate loaded by shear and compression.

scholarly journals Huber approximation for the non-linear problem

2006 ◽  
Vol 169 (3) ◽  
pp. 1096-1107 ◽  
Author(s):  
Mustafa Ç. Pınar ◽  
Wolfgang M. Hartmann
Keyword(s):  
Linear Problem ◽  
Non Linear

Non-linear solution to the maximum height orbit transfer guidance problem

2012 ◽  
Vol 226 (6) ◽  
pp. 620-630 ◽  
Author(s):  
H H Afshari ◽  
E Taheri
Keyword(s):  
Linear Problem ◽  
Perturbation Technique ◽  
Variable Mass ◽  
Pseudospectral Method ◽  
Performance Measure ◽  
Maximum Height ◽  
Orbit Transfer ◽  
Linear Solution ◽  
Two Body Problem ◽  
Non Linear

An optimal control solution to the highly non-linear problem of orbit transfer mission is achieved by using a newly proposed analytical perturbation technique. The problem is classified as a two-point boundary value problem in order to optimize a performance measure in a given time. Assuming a constant thrust operating in a given length of time, it is sought to find the thrust direction history of a transfer from a given initial orbit to the largest possible orbit. The system dynamical model is stated by regarding a variable mass spacecraft moving in the variable gravitational field of the Earth, based on the two-body problem. To assess the perturbation solution fidelity, a numerical solution based on the Gauss pseudospectral method has been employed. The main novelty of this work is in applying a new analytical solution strategy that is a combination of perturbation technique and backward integration to a highly non-linear problem in the calculus of variations approach.

scholarly journals Implementation of Newton’s Algorithm Using FORTRAN

2020 ◽  
Vol 1 (6) ◽  
Author(s):  
Shahida Anusha Siddiqui ◽  
Ali Ahmad
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Linear Problem ◽  
State Of The Art ◽  
Life Sciences ◽  
Legacy Code ◽  
Non Linear ◽  
Linear Problems

AbstractA lot of software today dealing with various domains of engineering and life sciences have to deal with non-linear problems. In order to reduce the problem to a linear problem, a lot of state of the art solutions already exist. This work focus on the implementation of Newton’s Algorithm (also known as Newton’s method), to determine the roots of a given function within a specific user defined interval. The software for this implementation is FORTRAN. Even though FORTRAN is considered to be outdated, it still has a lot of application due to its long history and the existing legacy code. The code is written in such a manner that a user can provide a function and a specific interval and the code should in turn run iterations over the interval and should display all the possible roots within that interval. The results are compared at the end for their accuracy. The program is successful in finding out all the roots within an interval.

scholarly journals Non-linear unsteady inverse boundary problem for heat conduction equation

2017 ◽  
Vol 38 (2) ◽  
pp. 81-100 ◽  
Author(s):  
Magda Joachimiak ◽  
Michał Ciałkowski
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Linear Problem ◽  
Conduction Equation ◽  
Direct And Inverse Problems ◽  
Heat Conduction Coefficient ◽  
Nitrification Process ◽  
Non Linear ◽  
Unsteady Heat Conduction ◽  
Inverse Boundary Problem

AbstractDirect and inverse problems for unsteady heat conduction equation for a cylinder were solved in this paper. Changes of heat conduction coefficient and specific heat depending on the temperature were taken into consideration. To solve the non-linear problem, the Kirchhoff’s substitution was applied. Solution was written as a linear combination of Chebyshev polynomials. Sensitivity of the solution to the inverse problem with respect to the error in temperature measurement and thermocouple installation error was analysed. Temperature distribution on the boundary of the cylinder, being the numerical example presented in the paper, is similar to that obtained during heating in the nitrification process.

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