The Compliance Method for Measurement of Near Surface Residual Stresses—Analytical Background

1994 ◽  
Vol 116 (4) ◽  
pp. 550-555 ◽  
Author(s):  
M. Gremaud ◽  
W. Cheng ◽  
I. Finnie ◽  
M. B. Prime
Keyword(s):  
Numerical Simulation ◽  
Residual Stresses ◽  
Random Errors ◽  
Residual Stress Field ◽  
Near Surface ◽  
Surface Residual Stresses ◽  
Zero Shift ◽  
Stress States ◽  
The Stability ◽  
Piecewise Functions

Introducing a thin cut from the surface of a part containing residual stresses produces a change in strain on the surface. When the strains are measured as a function of the depth of the cut, residual stresses near the surface can be estimated using the compliance method. In previous work, the unknown residual stress field was represented by a series of continuous polynomials. The present paper shows that for stress states with steep gradients, superior predictions are obtained by using “overlapping piecewise functions” to represent the stresses. The stability of the method under the influence of random errors and a zero shift is demonstrated by numerical simulation.

scholarly journals Two types of permutation polynomials with special forms

2019 ◽  
Vol 56 ◽  
pp. 1-16 ◽  
Author(s):  
Dabin Zheng ◽  
Mu Yuan ◽  
Long Yu
Keyword(s):  
Permutation Polynomials

Several classes of permutation trinomials from Niho exponents over finite fields of characteristic 3

2019 ◽  
Vol 18 (04) ◽  
pp. 1950069
Author(s):  
Qian Liu ◽  
Yujuan Sun
Keyword(s):  
Positive Integer ◽  
Finite Field ◽  
Coding Theory ◽  
Permutation Polynomials ◽  
Combinatorial Designs ◽  
Dickson Polynomial ◽  
Niho Exponents ◽  
Characteristic 3 ◽  
Permutation Trinomials ◽  
Algebraic Forms

Permutation polynomials have important applications in cryptography, coding theory, combinatorial designs, and other areas of mathematics and engineering. Finding new classes of permutation polynomials is therefore an interesting subject of study. Permutation trinomials attract people’s interest due to their simple algebraic forms and additional extraordinary properties. In this paper, based on a seventh-degree and a fifth-degree Dickson polynomial over the finite field [Formula: see text], two conjectures on permutation trinomials over [Formula: see text] presented recently by Li–Qu–Li–Fu are partially settled, where [Formula: see text] is a positive integer.

scholarly journals Permutation polynomials over Galois fields of characteristic

2021 ◽  
Vol 13 (2) ◽  
pp. 84-86
Author(s):  
Z.L. Dahiru ◽  
A.M. Lawan
Keyword(s):  
Permutation Polynomial ◽  
Permutation Polynomials ◽  
Galois Fields ◽  
Characteristic 2

In this paper, a class of permutation polynomial known as o-polynomial over Galois fields of characteristic 2 was studied. A necessary and sufficients condition for a monomial 𝑥2k to be an o-polynomial over F2t  is given and two results obtained by Gupta and Sharma (2016) were deduced.

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