scholarly journals A New Approach of Constrained Interpolation Based on Cubic Hermite Splines

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
J. Saeidian ◽  
M. Sarfraz ◽  
A. Azizi ◽  
S. Jalilian
Keyword(s):  
Linear Programming ◽  
Constrained Interpolation ◽  
New Approach ◽  
Theoretical Support ◽  
Suitable Function ◽  
Hermite Splines

Suppose we have a constrained set of data and wish to approximate it using a suitable function. It is natural to require the approximant to preserve the constraints. In this work, we state the problem in an interpolating setting and propose a parameter-based method and use the well-known cubic Hermite splines to interpolate the data with a constrained spline to provide with a C 1 interpolant. Then, more smoothing constraints are added to obtain C 2 continuity. Additionally, a minimization criterion is presented as a theoretical support to the proposed study; this is performed using linear programming. The proposed methods are demonstrated with illustrious examples.

Plastic flow and fracture of glass

1964 ◽  
Vol 282 (1388) ◽  
pp. 33-43 ◽  
Keyword(s):  
Plastic Flow ◽  
Energy Balance Equation ◽  
Static Fatigue ◽  
Secondary Effects ◽  
New Approach ◽  
Theoretical Support ◽  
A Value ◽  
Fracture Theory ◽  
As Stress ◽  
Almost All

It is usual to regard glass as a purely brittle solid and this has been taken for granted in almost all past papers on the mechanical strength, static fatigue, and ageing properties of glasses. However, in the present note this approach is rejected as being incompatible with experimental evidence of plastic flow in glass, and incapable of explaining the strengths observed. Instead a completely new approach is attempted in which glass is treated as an elastic-plastic solid and a complete theory of glass flow and strength is developed. The note summarizes the contents of three papers soon to be published which develop these ideas in more detail, and readers are referred to these three papers (Marsh 1964 a , b , c ) for full experimental and theoretical support of the ideas presented here. In brittle fracture theory glass is expected to exhibit its theoretical cohesive strength if it is flaw-free (e. g. untouched glass fibre), but if handled surface cracks are introduced and the strength should fall to a value predicted either by the Griffith (1920) energy balance equation or by the known stress concentration factor at the crack tip. Secondary effects such as static fatigue and ageing can then be explained as stress corrosion phenomena.

scholarly journals A New Approach to Find an Optimal Solution of a Fuzzy Linear Programming Problem by Fuzzy Dynamic Programming

2018 ◽  
Vol 7 (4.10) ◽  
pp. 360
Author(s):  
T. Nagalakshmi ◽  
G. Uthra
Keyword(s):  
Dynamic Programming ◽  
Linear Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
New Approach ◽  
The Cost ◽  
Recursive Equations

This paper mainly focuses on a new approach to find an optimal solution of a fuzzy linear programming problem with the help of Fuzzy Dynamic Programming. Linear programming deals with the optimization of a function of variables called an objective function, subject to a set of linear inequalities called constraints. The objective function may be maximizing the profit or minimizing the cost or any other measure of effectiveness subject to constraints imposed by supply, demand, storage capacity, etc., Moreover, it is known that fuzziness prevails in all fields. Hence, a general linear programming problem with fuzzy parameters is considered where the variables are taken as Triangular Fuzzy Numbers. The solution is obtained by the method of FDP by framing fuzzy forward and fuzzy backward recursive equations. It is observed that the solutions obtained by both the equations are the same. This approach is illustrated with a numerical example. This feature of the proposed approach eliminates the imprecision and fuzziness in LPP models. The application of Fuzzy set theory in the field of dynamic Programming is called Fuzzy Dynamic Programming. 

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