scholarly journals Incompatible Deformations in Additively Fabricated Solids: Discrete and Continuous Approaches

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2331
Author(s):  
Sergey Lychev ◽  
Konstantin Koifman ◽  
Nikolay Djuzhev
Keyword(s):  
Linear Models ◽  
Deformable Body ◽  
Common Factor ◽  
Affine Connection ◽  
Geometric Approach ◽  
Full Description ◽  
Additive Process ◽  
Reference Shape ◽  
Non Linear ◽  
Local Deformations

The present paper is intended to show the close interrelationship between non-linear models of solids, produced with additive manufacturing, and models of solids with distributed defects. The common feature of these models is the incompatibility of local deformations. Meanwhile, in contrast with the conventional statement of the problems for solids with defects, the distribution for incompatible local deformations in additively created deformable body is not known a priori, and can be found from the solution of the specific evolutionary problem. The statement of the problem is related to the mechanical and physical peculiarities of the additive process. The specific character of incompatible deformations, evolved in additive manufactured solids, could be completely characterized within a differential-geometric approach by specific affine connection. This approach results in a global definition of the unstressed reference shape in non-Euclidean space. The paper is focused on such a formalism. One more common factor is the dataset which yields a full description of the response of a hyperelastic solid with distributed defects and a similar dataset for the additively manufactured one. In both cases, one can define a triple: elastic potential, gauged at stress-free state, and reference shape, and some specific field of incompatible relaxing distortion, related to the given stressed shape. Optionally, the last element of the triple may be replaced by some geometrical characteristics of the non-Euclidean reference shape, such as torsion, curvature, or, equivalently, as the density of defects. All the mentioned conformities are illustrated in the paper with a non-linear problem for a hyperelastic hollow ball.

An evaluation of bias in propensity score-adjusted non-linear regression models

2016 ◽  
Vol 27 (3) ◽  
pp. 846-862 ◽  
Author(s):  
Fei Wan ◽  
Nandita Mitra
Keyword(s):  
Propensity Score ◽  
Regression Model ◽  
Treatment Effect ◽  
Remainder Term ◽  
Linear Models ◽  
Geometric Approach ◽  
Linear Regression Models ◽  
Propensity Score Methods ◽  
Non Linear ◽  
Model Versus

Propensity score methods are commonly used to adjust for observed confounding when estimating the conditional treatment effect in observational studies. One popular method, covariate adjustment of the propensity score in a regression model, has been empirically shown to be biased in non-linear models. However, no compelling underlying theoretical reason has been presented. We propose a new framework to investigate bias and consistency of propensity score-adjusted treatment effects in non-linear models that uses a simple geometric approach to forge a link between the consistency of the propensity score estimator and the collapsibility of non-linear models. Under this framework, we demonstrate that adjustment of the propensity score in an outcome model results in the decomposition of observed covariates into the propensity score and a remainder term. Omission of this remainder term from a non-collapsible regression model leads to biased estimates of the conditional odds ratio and conditional hazard ratio, but not for the conditional rate ratio. We further show, via simulation studies, that the bias in these propensity score-adjusted estimators increases with larger treatment effect size, larger covariate effects, and increasing dissimilarity between the coefficients of the covariates in the treatment model versus the outcome model.

G Optimal Design in Non linear Models to Increase Silicon Oxide Purity Levels and Electrical Conductivity

2018 ◽  
pp. 150-155
Author(s):  
Muklas Rivai
Keyword(s):  
Electrical Conductivity ◽  
Optimal Design ◽  
Linear Models ◽  
Silicon Oxide ◽  
Information Matrix ◽  
Relevant Information ◽  
Non Linear

Optimal design is a design which required in determining the points of variable factors that would be attempted to optimize the relevant information so that fulfilled the desired criteria. The optimal fulfillment criteria based on the information matrix of the selected model.

Modelling development ofCallosobruchus maculatusandAnisopteromalus calandraeat various constant temperatures using linear and non-linear models

2014 ◽  
Vol 24 (11) ◽  
pp. 1308-1320 ◽  
Author(s):  
M. Mobarakian ◽  
A.A. Zamani ◽  
J. Karmizadeh ◽  
N. Moeeny Naghadeh ◽  
M.S. Emami
Keyword(s):  
Linear Models ◽  
Non Linear

scholarly journals Early Detection of Defects through the Identification of Distortion Characteristics in Ultrasonic Responses

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 850
Author(s):  
Pietro Burrascano ◽  
Matteo Ciuffetti
Keyword(s):  
Early Detection ◽  
Additive Noise ◽  
Linear Models ◽  
High Stress ◽  
Damage Index ◽  
Hammerstein Model ◽  
Linear Behavior ◽  
Non Linear ◽  
Ultrasonic Techniques ◽  
Detection Of Defects

Ultrasonic techniques are widely used for the detection of defects in solid structures. They are mainly based on estimating the impulse response of the system and most often refer to linear models. High-stress conditions of the structures may reveal non-linear aspects of their behavior caused by even small defects due to ageing or previous severe loading: consequently, models suitable to identify the existence of a non-linear input-output characteristic of the system allow to improve the sensitivity of the detection procedure, making it possible to observe the onset of fatigue-induced cracks and/or defects by highlighting the early stages of their formation. This paper starts from an analysis of the characteristics of a damage index that has proved effective for the early detection of defects based on their non-linear behavior: it is based on the Hammerstein model of the non-linear physical system. The availability of this mathematical model makes it possible to derive from it a number of different global parameters, all of which are suitable for highlighting the onset of defects in the structure under examination, but whose characteristics can be very different from each other. In this work, an original damage index based on the same Hammerstein model is proposed. We report the results of several experiments showing that our proposed damage index has a much higher sensitivity even for small defects. Moreover, extensive tests conducted in the presence of different levels of additive noise show that the new proposed estimator adds to this sensitivity feature a better estimation stability in the presence of additive noise.

Testing linear restrictions on non-linear models

1984 ◽  
Vol 15 (1-2) ◽  
pp. 91-96
Author(s):  
K.R. Sawyer ◽  
M.C. Rosalsky
Keyword(s):  
Linear Models ◽  
Non Linear ◽  
Linear Restrictions ◽  
Testing Linear
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