Delamination of non-linear viscoelastic beams under bending in the plane of layers

Victor I. Rizov Techno-Press 2023 Coupled systems mechanics Vol.12 No.4

This paper deals with delamination analysis of non-linear viscoelastic multilayered beam subjected to bending in the plane of the layers. For this purpose, first, a non-linear viscoelastic model is presented. In order to take into account the non-linear viscoelastic behaviour, a non-linear spring and a non-linear dashpot are assembled in series with a linear spring connected in parallel to a linear dashpot. The behaviours of the non-linear spring and dashpot are described by applying non-linear stress-strain and stress-rate of strain relationships, respectively. The constitutive law of the model is derived. Due to the non-linear spring and dashpot, the constitutive law is non-linear. This law is used for describing the time-dependent mechanical behaviour of the beam under consideration. The material properties involved in the constitutive law vary along the beam length due to the continuous material inhomogeneity of the layers. Solution of the strain energy release rate for the delamination is obtained by analyzing the balance of the energy with considering of the non-linear viscoelastic behaviour. The strain energy release rate is found also by using the complementary strain energy for verification. A parametric study is carried-out by using the solution obtained. The solutions derived and the results obtained help to understand the time-dependent delamination of non-linear viscoelastic beams under loading in the plane of layers.

Study of V/Q Non-Linearity in Scientific CMOS Sensor

Jun-Lin Li,Yong-Fei Guo,Tai-Ji Lan 보안공학연구지원센터 2016 International Journal of Grid and Distributed Comp Vol.9 No.6

Scientific CMOS sensor usually manifests V/Q non-linearity in charge-to-voltage conversion. Starting from the mechanism underlying this non-linearity, we build the V/Q non-linearity model to study the influence of modulation transfer function (MTF) and signal-to-noise ratio (SNR). Meanwhile, simulation verification is carried out. The results show that V/Q non-linearity improves SNR but causes the decrease of MTF of the electronic device. We propose the combination of video response curve with photo response non-uniformity (PRNU) noise curve to locate V/Q non-linearity. The validity of this method is proved by simulation verification and physical experiment. The present study provides reference for design optimization and compensation for non-linearity in scientific CMOS sensor.

비선형 패러다임 시대의 동양예술 창의성 고찰 -지(知)·호(好)·악(樂)·광(狂)과 능(能)·묘(妙)·신(神)·일(逸)을 중심으로-

김규철 ( Kim Kyu Cheul ) 한국동양예술학회 2020 동양예술 Vol.46 No.-

오늘날 우리는 원인으로 결과를 예측할 수 있는 선형시대를 넘어, 원인으로부터 결과를 예측할 수 없는 비선형의 패러다임 앞에 놓여있다. 비선형이 일상화된 것이다. 동양예술의 창의성도 이 패러다임의 측면에서 고찰할 필요가 대두되었다. 본 연구의 목적은 비선형 시대에서의 동양예술의 창의성 고찰이다. 연구순서는 ①선형과 비선형에 대한 기본적인 이해를 구한다. ②선형적 창작 태도로서의 ‘知·好·樂’, 창작 결과로서의 ‘能·妙·神’에 대해 파악한다. ③비선형적 창작 태도로서의 ‘狂’과 창작 결과로서 ‘逸’을 고찰한다. ④둘을 종합하여 비선형시대의 창작 태도로서의 狂과 逸의 중요성과 그 역할에 대해 파악하였다. 선형적 창작태도는 논어 옹야 20장 ‘아는 것은 좋아하는 것만 못하고, 좋아하는 것은 즐기는 것만 못하다’에서의 ‘知·好·樂’에서 그 의미를 파악하였다. 연구결과, 知의 단계는 기법을 충실하게 습득한 후 창작을 하는 단계, 好의 단계는 기법을 아는 것을 넘어 창작하는 자체를 좋아하는 단계, 樂(락)의 단계는 기법을 알고 좋아하는 단계를 넘어 즐기면서 창작을 하는 단계라고 파악하였다. 비선형적 창작태도로서의 광(狂)은 다른 생각과 다른 행동 그리고 몰입을 통해 순수했던 자신의 본성으로 돌아가거나, 본성을 되찾기 위한 다리로 파악하였다. 선형적 창작결과는 북송(北宋)의 황휴복(黃休復)이 『익주명화록 益州名畵錄』에서 우열을 나눈 能·妙·神·逸4격 중 能·妙·神으로 파악하였다. 연구결과, 能品은 그리고자 하는 대상의 모습이 그림에 온전히 표현되어 있는 것이고, 妙品은 온전한 형상과 더불어 작가의 성품·마음·표현의도가 전해지는 것을 의미한다. 神品은 대상의 형상과 작가의 정신을 모두 갖추었으되 그 경지가 높은 작품이라고 파악하였다. 비선형적 창작결과로서의 일(逸)은 필이 간략해도 형태는 갖추어지며, 자연에서 얻고, 본뜰 수 없으며, 유법을 넘어 예상 밖에서 나오는 걸작(逸品)이다. 결국 知·好·樂의 창작 태도로 유법을 완성하고, 몰입을 통한 狂이라는 다리를 통해 逸이라는 창작결과에 도달하게 된다. 즉 逸의 창작결과는 원인으로 결과를 예측할 수 없는 비선형적인 과정을 거친다. 즉, 狂은 逸로 가기 위한 다리이고, 逸은 狂의 태도가 만든 결과라고 말할 수 있다. 비선형적인 상황이 일상화된 오늘날, 예술가들이 복원할 수 있는 狂의 진취성은 창작예술의 중요한 요소이다. Today, the age of linear thinking, when we could predict outcomes from causes, has ended, and we are facing an age of non-linear thinking in which causes are not the basis for predicting the outcomes. Non-linearity has become the norm. Understanding the creative aspects of Eastern art must also be approached from this paradigm shift. The main purpose of this study is to review the creative nature of Eastern art in the age of non-linearity. Its order is as follows: (1) gain a basic understanding of linearity and non-linearity; (2) identify the Ji(知, know-how), Ho(好, liking), and Lac(樂, enjoying) of the linear creative attitude, and the Neong(能, skillful), Meo(妙, beguiling), and Shin(神, divine) of the creative result; (3) study the Gwang(狂, crazy) of non-linear creative attitude and the Il(逸, masterpiece) of the creative result; and (4) combine the two in (3) to understand the importance and role of Gwang(狂) and Il(逸) as the creative attitude in the age of non-linearity. The meaning of linear creative attitude was identified in the Ji(知), Ho (好), and Lac(樂) in The Analects of Confucius Yongye Chapter 20, which states, “To know is not as good as liking, and liking is not as good as enjoying.” There search results identified the Ji(知) stage to be the point in time techniques are faithfully acquired and then creation occurs, the Ho(好) stage as where one surpasses simply knowing techniques and likes the act itself of creating, and the Lac(樂) stage as where one, surpassing knowing and liking techniques, enjoys creating. Gwang(狂) as a non-linear creative attitude was identified as a return to one’s own innocent nature through different thoughts, actions, and immersion―or the bridge to reclaim one’s nature. Linear creative results were identified as the Neong(能), Meo(妙), and Shin(神) from the four classes of Neong(能), Meo(妙), Shin(神), and Il(逸) described in 『Yi zhou Minghuala』 by Huang Xiufu(黃休復) of the Northern Song Dynasty (北宋). The research results identified skilled pieces(能品) as those that wholly express the image of the subject that is painted, and beguiling pieces(妙 品) as those where the character, spirit, and intent of the artist is conveyed in addition to the whole image. Divine pieces(神品), on the other hand, were found to be those that not only had the form of the subject and the spirit of the artist but also were of an exceptionally high level. Il(逸) as a non-linear creative result was a masterpiece(逸品) that had form even though the strokes were simple, was gained from nature, could not be imitated, and had surpassed laws to come from the unexpected. Ultimately, the creative attitudes of Ji(知), Ho(好), and Lac(樂) complete the laws, and the creative result of Il(逸) is achieved through the bridge of Gwang(狂)―that is, the creative result of Il(逸) goes through a non-linear process where the cause cannot predict the outcome. Therefore, Gwang(狂) is a bridge to arrive at Il(逸), and Il(逸) can be said to be the result of the attitude of Gwang(狂). Today, when non-linear situations have become the norm, the progressiveness of Gwang(狂) that artists can reproduce is an important element of creative arts.

ON ANALYTICAL SOLUTION OF NON LINEAR ROLL EQUATION OF SHlPS

S. Rao TATA,Kuniaki SHOJI,Shigeo MITA,Kiyokazu MINAMI 한국항해항만학회 2006 한국항해항만학회 학술대회논문집 Vol.2006 No.-

Out of all types of motions the critical motions leading to capsize is roll. The dynamic amplification in case of roll motion may be large for ships as roll natural frequency generally falls within the frequency range of wave energy spectrum typical used for estimation of motion spectrum. Roll motion is highly non-linear in nature. There are various representations of non-linear damping and restoring available in literature. In this paper an uncoupled non-linear roll equations with three representation of damping and cubic restoring term is solved using a perturbation technique. Damping moment representations are linear plus quadratic velocity damping, angle dependant damping and linear plus cubic velocity dependant damping. Numerical value of linear damping coefficient is almost same for all types but non-linear damping is different. Linear and non-linear damping coefficients are obtained form free roll decay tests. External rolling moment is assumed as deterministic with sinusoidal form. Maximum roll amplitude of non-linear roll equation with various representations of damping is calculated using analytical procedure and compared with experimental results, which are obtained from forced tests in regular waves by varying frequency with three wave heights. Experiments indicate influence of non-linearity at resonance frequency. Both experiment and analytical results indicates increase in maximum roll amplitude with wave slope at resonance. Analytical results are composed with experiment results which indicate maximum roll amplitude analytically obtained with angle dependent and cubic velocity damping are equal and difference from experiments with these damping are less compared to non-linear equation with quadratic velocity damping.

비선형 인과의 불교철학적 이해

김종욱(Kim, Jong-Wook) 동국대학교 불교문화연구원 2016 佛敎學報 Vol.0 No.77

실체론에서 관계론으로의 전환을 지향하는 현대 과학의 대표인 시스템 이론과 복잡계 과학에서 관계론은 인과 관계의 비선형성으로 특징지어진다. 비선형 인과란 원인이 결과를 향해 일방향적으로 영향을 미친다는 선형 인과에 대한 거부로서, 결과가 다시 자신의 원인에게 영향을 주어 그 원인을 재구조화한다는 인과의 양방향성을 가리킨다. 그런데 기존의 대다수 학문에서 인과율은 원인에서 결과로 일방적으로 영향을 미친다는 선형 인과로 인식되어왔다. 고대의 이데아론과 중세의 창조론과 근대의 기계론은 모두 인과가 선형적으로 원인에서 결과로 일방향으로만 간다고 본다는 점에서 공통되는데, 이런 선형 인과는 그 일방향성으로 인해 사물과 인간을 위계화하고 도구화하는 데 훌륭한 수단이 될 수 있었다. 그러나 현대의 복잡계 과학에선 이런 인과의 일방향성을 거부하고, 결과도 원인에 영향을 미칠 수 있다는 양방향성의 비선형 인과를 주장한다. 복잡계 과학에서 나타나는 비선형 인과의 방식은 불교 교학의 핵심 개념인 연기와 공에서도 발견된다. 무명과 행, 행과 식, 식과 명색 등 십이연기의 각 관계 항목들에서 결과가 거꾸로 원인에게 그 영향을 피드백하는 비선형적 현상이 나타난다. 그리고 원인과 결과 사이의 비선형적 상호의존성은 인과의 성격이 비실체적 공성임을 함축하고, 이런 인과의 공성은 인선과후(因先果後)의 선형성뿐만 아니라 과선인후(果先因後)의 비선형성도 가능함을 보여준다. 더욱이 인선과후의 선형성과 과선인후의 비선형성 간의 중도적 균형은 정신과 물질, 몸과 마음 혹은 뇌와 마음의 관계에서 균형 잡힌 시각을 제공해준다. 이런 시각은 뇌가 마음을 일으키고 형성하지만, 마음이 변화하면 뇌 역시도 변화한다는 뇌 가소성에서 분명하게 드러난다. 마음의 변화로 뇌의 변화가 일어난다는 비선형적 가소성을 가장 잘 보여주는 것이 불교의 명상 수행인데, 명상을 통한 마음의 변화는 뇌파의 변화와 아울러 뇌구조에 상당한 변화를 가져온다. Representative of contemporary science, systems theory and complexity science aim at the transition from substance theory to relational theory. In complexity science, relational theory is characterized by the non-linearity of causation. Linear causality holds that a cause influences an effect unilaterally, while non-linear causality posits that an effect influences its cause in reverse, and thus restructures the cause. The bilateralness of cause and effect characterizes non-linear causality. The majority of the existing sciences have historically supported linear causality. The idea of theory in ancient philosophy, the doctrine of creation in the Middle Ages, and mechanical philosophy in the modern era all have the unilateralness of linear causality as a common denominator. Their unilateralization brought about the hierarchy between the human and nature, and hence the instrumentalization of nature. However, contemporary complexity science rejects the unilateralness of linear causality in favor of the bilateralness of -non-linear causality. The non-linear causality style of complexity science can be found in pratītyasamutpāda and śūnyatā, core constructs of Buddhist doctrine. Avidyā and saṃskāra, saṃskāra and vijñāna, vijñāna and namarūpa, and so on, in twelve links of dependent origination represent the feedback phenomenon of non-linear causality. The non-linear interdependence between cause and effect implies the non-substantial śūnyatā in causality. This śūnya causation admits not only the linearity of cause first and effect last, but also the non-linearity of effect first and cause last. The middle way between the linearity of cause coming first and effect last, and the non-linearity of effect first and cause last provides a well-balanced perspective of the relation of mind - matter, mind - body, and mind - brain. - This vision comes out in the plasticity of the brain, which can make alterations in its structure and function through experience and practice, or through thinking and acting by itself. The continuous practice of meditation activates theta and gamma brain waves; strengthens the left prefrontal lobe, related to positive feeling; enlarges the hippocampus and orbitofrontal cortex related to memory and emotion control; activates the parasympathetic nervous system, related to inhibitory and relaxant actions.

Identification of Anisotropic Bearing Non-linearity

Dong-Ju Han 한국항공우주학회 2004 International Journal of Aeronautical and Space Sc Vol.5 No.2

Among other critical conditions in rotor systems the large non-linear vibration excited by bearing non-linearity causes the rotor failure. For reducing this catastrophic failure and predictive analysis of this phenomena the identification analysis of bearing non-linearity in an anisotropic rotor system using the higher order dFRFs are developed and are shown to be theoretically feasible as in non-rotating structures. For the identification of the anisotropic rotor with anisotropic bearing non-linearity expressed by the displacement in polynomial form, the higher order dFRFs based upon the Volterra series are investigated and depict their features by using the simple forms of the normal and reverse dFRFs. They produce additional sub-harmonic resonant peaks, which indicate the existence of higher order non-linearties, and show the energy transfer such that the modes for normal and reverse dFRFs are exchanged, which are the fundamental differences from what we can expect in linear ones.

Non-linear analysis of dealamination fracture in functionally graded beams

Rizov, Victor I. Techno-Press 2017 Coupled systems mechanics Vol.6 No.1

The present paper reports an analytical study of delamination fracture in the Mixed Mode Flexure (MMF) functionally graded beam with considering the material non-linearity. The mechanical behavior of MMF beam is modeled by using a non-linear stress-strain relation. It is assumed that the material is functionally graded along the beam height. Fracture behavior is analyzed by the J-integral approach. Non-linear analytical solution is derived of the J-integral for a delamination located arbitrary along the beam height. The J-integral solution derived is verified by analyzing the strain energy release rate with considering the non-linear material behavior. The effects of material gradient, crack location along the beam height and material non-linearity on the fracture are evaluated. It is found that the J-integral value decreases with increasing the upper crack arm thickness. Concerning the influence of material gradient on the non-linear fracture, the analysis reveals that the J-integral value decreases with increasing the ratio of modulus of elasticity in the lower and upper edge of the beam. It is found also that non-linear material behavior leads to increase of the J-integral value. The present study contributes for the understanding of fracture in functionally graded beams that exhibit material non-linearity.

Non-linear analysis of dealamination fracture in functionally graded beams

Rizov, Victor I. 테크노프레스 2016 Multiscale and multiphysics mechanics Vol.1 No.4

The present paper reports an analytical study of delamination fracture in the Mixed Mode Flexure (MMF) functionally graded beam with considering the material non-linearity. The mechanical behavior of MMF beam is modeled by using a non-linear stress-strain relation. It is assumed that the material is functionally graded along the beam height. Fracture behavior is analyzed by the J-integral approach. Non-linear analytical solution is derived of the J-integral for a delamination located arbitrary along the beam height. The J-integral solution derived is verified by analyzing the strain energy release rate with considering the non-linear material behavior. The effects of material gradient, crack location along the beam height and material non-linearity on the fracture are evaluated. It is found that the J-integral value decreases with increasing the upper crack arm thickness. Concerning the influence of material gradient on the non-linear fracture, the analysis reveals that the J-integral value decreases with increasing the ratio of modulus of elasticity in the lower and upper edge of the beam. It is found also that non-linear material behavior leads to increase of the J-integral value. The present study contributes for the understanding of fracture in functionally graded beams that exhibit material non-linearity.

Non-linear rheology of tension structural element under single and variable loading history Part I: Theoretical derivations

Kmet, S. Techno-Press 2004 Structural Engineering and Mechanics, An Int'l Jou Vol.18 No.5

The present paper concerns the macroscopic overall description of rheologic properties for steel wire and synthetic fibre cables under variable loading actions according to non-linear creep and/or relaxation theory. The general constitutive equations of non-linear creep and/or relaxation of tension elements - cables under one-step and the variable stress or strain inputs using the product and two types of additive approximations of the kernel functions are presented in the paper. The derived non-linear constitutive equations describe a non-linear rheologic behaviour of the cables for a variable stress or strain history using the kernel functions determined only by one-step - constant creep or relaxation tests. The developed constitutive equations enable to simulate and to predict in a general way non-linear rheologic behaviour of the cables under an arbitrary loading or straining history. The derived constitutive equations can be used for the various tension structural elements with the non-linear rheologic properties under uniaxial variable stressing or straining.

승품 응시자 변화예측을 위한 선형, 비선형, 시계열 모형 검증 - 경기지역을 중심으로 -

김우진 ( Kim Woo-jin ),김기상 ( Kim Ki-sang ),이정일 ( Lee Jung-il ),이현희 ( Lee Hyun-hee ) 국기원 2017 국기원태권도연구 Vol.8 No.1

본 연구는 국기원에서 제공하고 있는 통계 및 정책 자료를 활용하여 경기도 지역 “1품 응시자” 변화를 예측하는데 주요 목적이 있다. 이를 위해 공개된 자료 중 2012년 05월부터 2016년 11월까지 총 55개월의 시계열 자료를 활용하였으며, 선형모형, 비선형모형, 시계열 모형 등을 설정한 뒤 모형 비교를 실시하였다. 이상의 내용을 분석하기 위하여 SPSS 18.0과 StataMP 14.0 프로그램을 사용하였으며, 선형회귀분석, 비선형회귀분석, 시계열분석, 모형적합지수 분석, Ramsey`s RESET검증, 자기상관 및 편자상관, Ljung-Box Q 검정 등을 실시하였다. 분석을 토대로 나타난 결과를 요약하면 다음과 같다. 첫째, 선형회귀모형을 검증한 결과 시간이 한 단위 증가할 때 승품 응시자는 38.406씩 증가하는 것으로 나타났으며, 통계적으로 유의한 것으로 나타났다. 또한 자기 상관이 없는 것으로 나타나 선형회귀모형이 가능한 것으로 분석되었다. 둘째, 비선형 회귀모형 검증 결과 승품응시자는 시간이 흐를수록 2차 함수 모양, 즉 지수적으로 감소하는 것으로 나타났다. 그러나 Ramsey`s RESET검증 결과 1품 응사자는 비선형적으로 증가하거나 감소하지 않고 선형적으로만 증가하는 것으로 나타났다. 셋째, 시계열 모형 즉 단순지수 평활법, Holt 선형추세, Brown 선형추세, Winters` Additive, Winters` Multiplicative 등을 비교해본 결과 Winters` Additive 모형이 가장 적절한 것으로 나타났으며, 이 모형을 통해 예측해 본 결과 2016년 12월에는 4900.6명, 2017년 1월에는 5873.1명, 2017년 2월에는 3610.9명, 2017년 3월에는 5360.6명, 2017년 4월에는 7629.1명, 2017년 5월에는 5812.5명, 2017년 6월에는 5565.8명으로 예측되었다. This main purpose of this study is to forecast the change of “1<sup>st</sup> poom promotion test applicants” at Gyeonggi-do region by using statistic and policy data that is provided by Kukkiwon. For that, total 55 months of time series data ranging from May 2012 to November 2016 was used and model comparison was carried out after setting liner model, non-linear model and time series model. SPSS 18.0 and StataMP 14.0 program were used to analyze the contents and linear regression analysis, non-linear regression analysis, time series analysis, model fit index analysis, Ramsey`s RESET verification, auto-correlation, partial auto-correlation and Ljung-Box Q verification were carried out. A summary of the results that came from the analysis is as following. First, as the results of verifying linear regression model, it appeared that promotion test applicants increased by 38.406 when time increased by one unit and it also appeared to be meaningful statistically. And it was analyzed that linear regression model was possible as it appeared that there was no auto-correlation. Second, it appeared that promotion test applicants increased in the shape of quadratic function that is exponentially as the result of verifying non-linear regression model. But, as the result of Ramsey`s RESET verification, it appeared that the promotion test applicants did not increase or decrease in non-linear way but increased in linear way. Third, as a results of comparing to time series model that is simple exponential smoothing, Holt linear trend, Brown linear trend and Winters` Additive, Winters` Multiplicative, it appeared that Winters` Additive model was most suitable and as the results of forecasting this mode, it was forecasted that 4900.6 in December 2016, 5873.1 in January 2017, 3610.9 in February 2017, 5360.6 in March 2017, 7629.1 in April, 5812.5 in May 2017 and 5565.8 in June 2017.