Optimization of a structure with contact conditions using equivalent loads

Sang-Il Yi,이현아,박경진 대한기계학회 2011 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.25 No.3

Engineering structures consist of various components, and the components interact with each other through contact. Engineers tend to consider the interaction in analysis and design. Interactions of the components have nonlinearity because of the friction force and boundary conditions. Nonlinear analysis has been developed to accommodate the contact condition. However, structural optimization using nonlinear analysis is fairly expensive, and sensitivity information is difficult to calculate. Therefore, an efficient optimization method using nonlinear analysis is needed to consider the contact condition in design. Nonlinear Response Optimization using Equivalent Loads (NROEL) has been proposed for nonlinear response structural optimization. The method was originally developed for optimization problems considering geometric/material nonlinearities. The method is modified to consider the contact nonlinearity in this research. Equivalent loads are defined as the loads for linear analysis, which generate the same response field as that of nonlinear analysis. A nonlinear response optimization problem is converted to linear response optimization with equivalent loads. The modified NROEL is verified through three examples with contact conditions. Three structural examples using the finite element method are demonstrated. They are shape optimization with stress constraints, size optimization with stress/displacement constraints and topology optimization. Reasonable results are obtained in the optimization process.

Accurate modeling and nonlinearity compensation in the speed mode of a twisted string actuator

Lee, Hyoryong,Choi, Hyunchul,Park, Sukho Elsevier 2019 Mechanism and machine theory Vol.137 No.-

<P><B>Abstract</B></P> <P>A twisted string actuator (TSA) is an effective method that can change the rotational motion of a motor into a linear motion, as well as control the speed and stiffness of the actuator. In particular, because the speed mode of the TSA (SM-TSA) can adjust the rotation–linear motion ratio by changing the diameter and length of the twisting shaft, it is a good to increase the usability of the TSA. However, the SM-TSA has a significant limitation in that it demonstrates a nonlinear translatory motion with respect to the constant rotational motion of the motor in terms of its operating principle. To solve this problem, a more accurate modeling method of the SM-TSA should be applied to predict the nonlinearity and compensate for the nonlinearity. Herein, we analyze the tendency of the twisted strings of the SM-TSA and propose a more precise modeling method of the nonlinear SM-TSA. In addition, a nonlinearity compensation algorithm using the proposed modeling of the SM-TSA is developed to linearize the nonlinear translatory motion. Through various experiments of the SM-TSA, we validated that the proposed model exhibits the nonlinearity of the SM-TSA more precisely when compared to the previous model. Additionally, we confirmed that the nonlinearity compensation algorithm using the proposed model can perform more accurate linearization of the translatory motion of the SM-TSA.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Analysis of twisting tendency in speed mode of twisted string actuator (SM-TSA). </LI> <LI> A new simple nonlinear analytical model of SM-TSA. </LI> <LI> A nonlinearity compensation algorithm using nonlinear models of SM-TSA. </LI> <LI> Proposed analytical model could follow more accurately twisting tendency in SM-TSA. </LI> <LI> Compensated linear translatory motion of SM-TSA using proposed analytical model. </LI> </UL> </P>

Experimental characterization of ultrasonic nonlinearity in concrete under cyclic change of prestressing force using Nonlinear Resonant Ultrasonic Spectroscopy

Kim, Gyu-Jin,Park, Sun-Jong,Kwak, Hyo-Gyoung Elsevier BV 2017 Construction and Building Materials Vol.157 No.-

<P><B>Abstract</B></P> <P>In this paper, an experimental study was conducted to investigate the effect of varying prestressing force on the nonlinearity of concrete. Prestressed concrete beams, which have been rarely studied in terms of ultrasonic nonlinearity, were prepared. When the prestressing force changes, the stress condition of the concrete inside the beam is affected. This leads to the generation of micro-cracks and a change of the mechanical properties, and as such it is necessary to introduce a nonlinear ultrasonic technique that sensitively reflects microstructural change. In the experiment, a repetitive prestressing load history, which includes maximum levels of 45%, 60%, and 75% based on the compressive strength, was designed to evaluate the effects of repetitive loading and different levels of loading on the nonlinearity. A comparison with the measured results of the linear ultrasonic method was also carried out to verify the stress-dependent change of nonlinearity induced by external loads. With the experimental results, the adopted technique is found to be more sensitive to damage then conventionally used ultrasonic method. As the investigation of the methodology is effective in prestressed concrete structures, the possibility of ultrasonic nonlinearity as an indicator of prestressing force is evaluated.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Prestressing force effects on decreasing the ultrasonic nonlinearity. </LI> <LI> Cyclic loading effects on increasing the ultrasonic nonlinearity. </LI> <LI> Sensitivity comparison of NRUS with UPV on measuring the ultrasonic nonlinearity. </LI> </UL> </P>

체적파 혼합기법을 이용한 재료 손상 진단 적용 가능성 연구

최정석(Jeongseok Choi),조윤호(Younho Cho) 한국비파괴검사학회 2016 한국비파괴검사학회지 Vol.36 No.1

초음파 비선형 진단을 이용한 기법의 경우 재료의 단순 결함 검출뿐만 아니라 부식, 소성변형과 같은 미세손상을 평가할 때 주로 이용된다. 1차 조화파(primary wave)와 2차 조화파(second harmonic wave)의 진폭의 비를 이용하여 비선형성을 나타내며, 이러한 비선형성의 비교 결과를 진단에 사용한다. 실험 특성상 비선형성은 재료의 비선형성뿐만 아니라 장비의 비선형성 또한 포함하게 된다. 장비 비선형성은 사용자가 측정하고자 하는 값이 아니므로 오차로 작용하여 분석을 방해한다. 본 연구에서는 오차로 작용하는 장비의 비선형성을 감소시켜 보다 정확한 진단을 위해 체적파 혼합기법을 사용하였다. 체적파 혼합기법의 가장 큰 특징은 기존의 초음파 비선형 진단보다 장비의 비선형성을 줄일 수 있다는 점이다. 본 연구에서는 체적파 혼합기법을 이론 및 실험적으로 검증하였으며, 기존의 초음파 비선형 진단기법의 결과와 체적파 혼합기법의 결과를 비교하여 장단점 및 적용 가능성 분석에 초점을 두었다. Ultrasonic nonlinear evaluation is generally utilized for detection of not only defects but also microdamage such as corrosion and plastic deformation. Nonlinearity is determined by the amplitude ratio of primary wave second harmonic wave, and the results of its comparison are used for evaluation. Owing to the experimental features, the experimental nonlinearity result contains system nonlinearity and material nonlinearity. System nonlinearity is that which is unwanted by the user; hence, it acts as an error and interrupts analysis. In this study, a bulk wave mixing technique is implemented in order to minimize the system nonlinearity and obtain the reliable analysis results. The biggest advantage of this technique is that experimental nonlinearity contains less system nonlinearity than that for the conventional nonlinear ultrasonic technique. Theoretical and experimental verifications are performed in this study. By comparing the results of the bulk wave mixing technique with those of the conventional technique, the strengths, weaknesses, and application validity of the bulk wave mixing technique are determined.

등가하중을 이용한 비선형 정적 응답 위상최적설계의 기초연구

이현아(Hyun-Ah Lee),Ahmad Zeshan,박경진(Gyung-Jin Park) 대한기계학회 2010 大韓機械學會論文集A Vol.34 No.12

실제 대부분의 공학 문제들은 크고 작은 비선형성을 내포한다. 구조물의 최적설계 과정에서는 다수의 구조물 사이에 발생하는 접촉이나 비선형 물성치를 가지는 재료, 또는 대변형을 고려해야만 한다. 그러나 민감도 계산이 고가이기 때문에 비선형성을 최적화에 고려하는 것은 매우 어렵다. 따라서 비선형 정적 반응 위상최적설계를 위하여 등가하중법을 사용한다. 등가하중이란 비선형 해석에서 유발되는 반응장과 동일한 반응장을 유발하는 선형 정적하중이다. 등가하중법은 치수/형상최적설계를 위하여 연구되어 왔다. 위상최적설계는 치수/형상최적설계에 비하여 설계변수가 많기 때문에 기존의 등가하중법을 그대로 적용할 수 없기 때문에 위상최적설계를 위하여 등가하중법을 확장하고 수정한다. 간단한 예제를 통하여 등가하중법을 이용한 위상최적설계 결과가 수치적으로 도출한 결과와 유사함을 보이고 실제 공학 예제의 위상최적설계를 통하여 기존의 선형 정적 위상최적설계와 결과를 비교한다. Most components in the real world show nonlinear response. The nonlinearity may arise because of contact between the parts, nonlinear material, or large deformation of the components. Structural optimization considering nonlinearities is fairly expensive because sensitivity information is difficult to calculate. To overcome this difficulty, the equivalent load method was proposed for nonlinear response optimization. This method was originally developed for size and shape optimization. In this study, the equivalent load method is modified to perform topology optimization considering all kinds of nonlinearities. Equivalent load is defined as the load for linear analysis that generates the same response field as that for nonlinear analysis. A simple example demonstrates that results of the topology optimization using equivalent load are very similar to the numerical results. Nonlinear response topology optimization is performed with a practical example and the results are compared with those of conventional linear response topology optimization.

비선형적 공간그래픽 특성 연구

진민선,이찬 한국문화공간건축학회 2016 한국문화공간건축학회논문집 Vol.- No.55

Society is diversifying in all fields, including economy, science, culture, and art. The urban environment has welcomed organic system changes, facing a turning point in most fields, including various genres’ emergence and domains’ expansion and convergence. Like post-structuralism, which embraces cultural complexity and diverse social discourses to create new domains and mutual influence by creating new elements, graphics and spaces are organically bonded and mutually grafted, resulting in spatialization of graphics and vice versa. This study aims to identify and analyze spatial graphics’ nonlinear nature by examining their theoretical backgrounds and concepts and analyzing cases in modern spaces. First, a literature review was used to define nonlinear space’s concepts and characteristics. Second, we defined the concept of nonlinear spatial graphics by considering the concept, formation, and background of spatial graphics through a variety of art trends. Lastly, we observed the characteristics of nonlinear spatial graphics in modern spaces by conducting various case analyses while interpreting the concept of spatial graphics in modern spaces in an extended concept. Through case analysis of different nonlinear spatial graphics, we discovered a common, distinctive repetition and expandability. There is a continuous appearance of complex irregular patterns, animated organic expression from dynamic images and sense of fluidity, and, sometimes, an atypical structure from the combination of non-geometric forms that are modified from the disassembling of Euclidean geometric forms. Nonlinear spatial graphics’ characteristics in specific spaces showed they were derived nonlinearly. When we observed the concept of nonlinearity as a concept of expansion, it was not divided into architecture, space, and graphics. The shift of the paradigm is influencing space and spatial graphics. It is possible that with spatial graphics, nonlinearity is an endless new paradigm that can evolve into a creative world.

Nonlinear Aeroelastic Instability of a Supersonic Missile Wing. with Pitch Axis Freeplay

Kim, Dong-Hyun,Lee, In,Paek, Seung-Kil The Korean Society for Aeronautical and Space Scie 2003 International Journal of Aeronautical and Space Sc Vol.4 No.1

In this study, nonlinear aeroelastic characteristics of an supersonic missile wing with strong shock interferences are investigated. The missile wing model has a freeplay structural nonlinearity at its pitch axis. To practically consider the effects of freeplay structural nonlinearity, the fictitious mass method is applied to structural vibration analysis based on finite element method. Nonlinear aerodynamic flows with unsteady shock waves are also considered in supersonic flow regions. To solve the nonlinear aeroelastic governing equations including the freeplay effect, a modal-based coupled time-marching technique based on the fictitious mass method is used in the time-domain. Various aeroelastic computations have been performed for the nonlinear wing structure model. Linear and nonlinear aeroelastic analyses have been conducted and compared with each other in supersonic flow regions. Typical nonlinear limit cycle oscillations and phase plots are presented to show the complex vibration phenomena with simultaneous fluid-structure nonlinearities.

Preliminary Study on Nonlinear Response Topology Optimization Using Equivalent Loads

Z. Ahmad,H.A. Lee(이현아),G.J. Park(박경진) 대한기계학회 2009 대한기계학회 춘추학술대회 Vol.2009 No.11

Most of the components in the real world show nonlinear response. The nonlinearity may be due to some reasons, like contact between the parts, or large deformation of the components, etc. Nonlinear analysis has been developed very well. However, structural optimization is fairly expensive and sensitivity analysis is difficult to calculate. In order to overcome this difficulty, nonlinear response optimization using equivalent loads (NROEL) was proposed for nonlinear structural optimization. This method was originally developed for size and shape optimization. In this research, this method is modified to perform topology optimization considering nonlinearity. Equivalent loads are defined as the loads for linear analysis, which generate the same response field as that of nonlinear analysis. A simple example verifies that the topology optimization results using equivalent loads are very close to the numerical results. Nonlinear response topology optimization is performed with a practical example. The results are compared with conventional linear response topology optimization.

비선형 차수에 따른 Boussinesq 모형의 천수변형 특성

박승민(Park, Seung-Min),윤종태(Yoon, Jong-Tae) 한국해안해양공학회 2008 한국해안해양공학회 논문집 Vol.20 No.1

비선형의 정도에 따른 Boussinesq 모형의 특성을 비교하기 위해 약비선형 모형인 MIKE21 BW 모듈과 완전비선형 모형인 FUNWAVE 모형을 이용하여 수치실험을 수행하였다. 진폭별 조파실험, 심해 파형경사별 천수실험 그리고 사주 지형상의 파랑 전파실험을 수행하였고, 이상의 실험을 통해 비선형성이 부각되는 천해역에서 비선형 모형의 중요성을 확인하였다. 특히 완전 비선형 모형이 약비선형 모형에 비해 비대칭 파형의 재현성이 우수하고, 천수현상에 따른 파고의 증가가 상대적으로 크게 나타나는 모형 간 특성을 확인하였다. Numerical experiments with weakly nonlinear MIKE21 BW module and fully nonlinear FUNWAVE model are performed to identify the nonlinear characteristics of Boussinesq models with varying nonlinearity. Generation of waves with varying amplitudes, nonlinear shoaling and wave propagation over submerged bar experiments showed the importance of nonlinear model in shallow water where nonlinearity becomes prominent. Fully nonlinear model showed the nonsymmetrical wave form more clearly and gave larger shoaling coefficients than those of weakly nonlinear model.

The Study of Ultrasonic Nonlinearity in Heat Treatment Material

Weibin Li(이위빈),Jaesun Lee(이재선),Younho Cho(조윤호) 대한기계학회 2009 대한기계학회 춘추학술대회 Vol.2009 No.11

Nonlinear ultarsonic is very senstive to material property change. This paper attempts to study the correlation between heat treatment and ultrasonic nonlinearity by taking the nonlinearity factors into account. The modified ultrasonic velocity formula was deriven. It turns out that nonlinearity varies with ultrasonic velocity change in the material heat treatment, the experimental results show that relative nonlinearity parameters obtained from the modified ultrasonic velocity and the rai\tio of amplitudes(second harmonic and fundamental wave)have a good agreement. Both of them prove that the heat treatment can change the material nonlinearity. Furthermore, then relative nonlinearity calculated from the modified velocity is much more sensitive, representing the relative nonlinearity change based on the modified ultrasonic velocity in this case.