Application of Topology Optimization for Shell Structure

첸레이(Lei Chen),장강원(Gang-Won Jang),백태현(Tae Hyun Baek) 대한기계학회 2011 대한기계학회 춘추학술대회 Vol.2011 No.5

Topology optimization could help engineers solve structures problem by providing the optimal distribution of a limited amount of material in a design space. Here, the shell structures are studied and are extended to topology optimization. Shell elements are widely applied on curved thin structure. But, locking problems will take place when the structure is very thin, such as shear locking and membrane locking problems Furthermore, volumetric locking will occur when incompressible material problems are involved. To solve locking problems, selective reduced integration method is employed. By calculating sensitivity analysis of constraint function, the minimum compliance of the shell with given mass is obtained by method of moving asymptotes (MMA). The optimized shapes calculated in this study are compared with the shapes of other papers or natural models. Good agreement shows the method presented in this study is reasonable and available.

하이브리드 기법에 의한 경사균열 팁 주위의 광탄성 응력장 해석

첸레이(Lei Chen),서진(Jin Seo),이병희(Byung Hee Lee),김명수(Myung Soo Kim),백태현(Tae Hyun Baek) 대한기계학회 2010 대한기계학회 춘추학술대회 Vol.2010 No.5

본 연구에서는 균열선단 주위의 응력장을 균열선단으로부터 떨어진 일직선상에서 유한요소법에 의해 계산된 광탄성 등색프린지 차수와 급수형 등각사상 맵핑함수를 이용하여 해석하였다. 해석된 광탄성 응력장을 실제의 광탄성프린지와 비교하였다. 정성적인 비교가 용이하도록 디지털 영상처리에 의해 등색프린지 패턴을 2 배로 증식시키고, 증식된 프린지를 다시 세선처리하여 서로 비교하였다. 유한요소법으로 계산된 프린지 차수를 이용한 하이브리드 응력장 해석에 의해 계산된 프린지와 광탄성 실험에 의한 실제의 프린지를 정성적이고 정량적인 비교를 하였다. 입력된 변위와 계산된 변위의 퍼센트 오차는 18개의 데이터 모두 6.0% 이하로 서로 일치하였다. 또한 응력함수의 항의 수를 m = 1 일 경우에도 하이브리드 기법에 의한 정규화시킨 응력확대계수 K<SUB>l</SUB> 및 K<SUB>ll</SUB>는 유한요소법과 경험식으로 계산된 값과 서로 잘 일치하였다. Various structural and mechanical parts with cracks fractured at the stress which is much lower than the ultimate strength because the stresses in the vicinity of the crack tip are always much higher than those far away from it. Due to the complexity of the engineering problems, it is difficult to obtain the stress field around the crack tip directly by theoretical derivation. In this paper, the hybrid technique is employed. At first, the isochromatic fringe data of given points are calculated by finite element method and are used as input data of complex variable formulations. Then the numerical model of specimen is transformed from the physical plane to the complex plane by conformal mappings. The stress field is analyzed and mixed-mode stress intensity factors are calculated on this complex plane. The results are also calculated by finite element method and theoretical method and compared with each other. In order to conveniently compare those values with each, both actual and regenerated photoelastic fringe patterns are two times multiplied and sharpened by digital image processing.

하이브리드 기법에 의한 경사균열 팁 주위의 광탄성 응력장 해석

첸레이(Lei Chen),서진(Jin Seo),이병희(Byung Hee Lee),김명수(Myung Soo Kim),백태현(Tae Hyun Baek) 대한기계학회 2010 大韓機械學會論文集A Vol.34 No.9

본 연구에서는 균열선단 주위의 응력장을 균열선단으로부터 떨어진 일직선상에서 유한요소법에 의해 계산된 광탄성 등색프린지 차수와 급수형 등각사상 맵핑함수를 이용하여 해석하였다. 해석된 광탄성 응력장을 실제의 광탄성프린지와 비교하였다. 정성적인 비교가 용이하도록 디지털 영상처리에 의해 등색프린지 패턴을 2 배로 증식시키고, 증식된 프린지를 다시 세선처리하여 서로 비교하였다. 유한요소법으로 계산된 프린지 차수를 이용한 하이브리드 응력장 해석에 의해 계산된 프린지와 광탄성 실험에 의한 실제의 프린지를 정성적이고 정량적인 비교를 하였다. 입력된 변위와 계산된 변위의 퍼센트 오차는 18 개의 데이터 모두 6.0% 이하로 서로 일치하였다. 또한 하이브리드 기법에 의한 정규화시킨 응력확대계수 KⅠ 및 KⅡ 는 유한요소법과 경험식으로 계산된 값에 근접하였다. In this paper, a hybrid technique is presented. First, the isochromatic fringe data of a given set of points are calculated by the finite element method and are used as input data in complex variable formulations. Then the numerical model of the specimen with a central inclined crack is transformed from the physical plane to the complex plane by conformal mapping. The stress field is analyzed and the mixed-mode stress intensity factors are calculated for this complex plane. The stress intensity factors are calculated by the finite element method as well as by a theoretical method and compared with each other. In order to conveniently compare these values with each other, both actual and regenerated photoelastic fringe patterns are multiplied by a factor of two and sharpened by digital image processing.

최적화기법에 의한 나뭇잎 그물맥 시뮬레이션

첸레이(Lei Chen),리웨이정(Weizheng Li),장강원(Gang Won Jang),백태현(Tae Hyun Baek) 대한기계학회 2013 大韓機械學會論文集B Vol.37 No.4

본 연구에서는 나뭇잎 그물맥 구조를 시뮬레이션하기 위해 잎 그물맥을 상 하 보강 박막판과 비압축성 유체가 흐르는 중간층 구조로 모델링하여 다중물리 현상으로 간주하고, 위상 최적화법을 다중물리 설계영역에 적용하였다. Mindlin-Reissner 판 모델에 기인한 횡방향 전단잠금 문제를 해결하기 위해 P1 비적합 요소와 선택 감소 적분법을 이용하였다. 다시-스토크스 유체 유동 채널에 대해 최적설계법을 적용하여 유동 시스템의 다중물리 모델을 해석하였으며, 잎의 그물맥 시뮬레이션을 수행하였다. 계산된 최적형상을 잎의 자연 그물 맥 패턴과 비교하였으며 비슷한 형상을 얻었다. 이와 같은 학제간 연구를 통해 나무 잎 그물맥 시스템을 이해할 수 있는 계기가 될 것으로 사료된다. This study attempts to simulate the structure of a woody leaf netted venation system by using topology optimization techniques. Based on finite element method (FEM) analysis of an incompressible fluid, a topology optimal design is applied to those woody leaf netted venation models. To solve the transverse shear locking problem of a thin plate caused by the Mindlin-Reissner plate model where a leaf netted venation is assumed to be a thin plate, a P1-nonconforming element and selective reduced integration are employed. Topology optimal design is applied to multiple physical domains. Combined with the Darcy-Stokes flow problems and extended to the optimal design of fluid channels, the multiple physical models of the flow system are analyzed and venation patterns of leafs are simulated. The calculated optimal shapes are compared with the natural shapes of woody leaf venation patterns. This interdisciplinary approach may improve our understanding of the leaf venation system.

광탄성 위상이동법을 이용한 경사균열 선단주위의 응력분포 결정법

첸레이(Lei Chen),리웨이정(Weizheng Li),백태현(Tae Hyun Baek) 대한기계학회 2011 대한기계학회 춘추학술대회 Vol.2011 No.5

Photoelasticity method is one kind of experimental method and has been widely used in many domains of engineering to determine the stress distribution of structures. Without complicated mathematical formulation, this technique can conveniently provide a fairly accurate whole-field stress analysis for a mechanical structure. Here, an inclined crack tips of finite-width plate made of PSM-1 is studied by 8-step phase-shifting method. This method is one kind of photoelastic phase-shifting technique and can be used for the determination of the phase values of isochromatics and isoclinics. According to stress-optic law, the stress distribution could be obtained from fringe patterns. The results obtained by polariscope arrangement combined with 8-step method and ABAQUS FEM simulations are compared with each other. Good agreement shows that 8-step phase-shifting method is reliable and reasonable.

Topology Optimization of the Plate under Bending Moment by Using P1-nonconforming Element

Lei Chen(첸레이),Gang-Won Jang(장강원),Tae Hyun Baek(백태현) 대한기계학회 2010 대한기계학회 춘추학술대회 Vol.2010 No.5

When the Mindlin model is applied to analyze the thin plate under bending moment, the displacement of plate is much lower than the exact value. This phenomenon is caused by shear locking of model. Here, a new nonconforming quadrilateral element P1, which is one kind of discontinuous element and owns the Poisson locking-free property, was applied to Mindlin plate. The results prove that reduced P1- nonconforming element can solve shear locking problem. Topology optimal design of plate under bending moment was based on P1 nonconforming element, whose purpose was to obtain the minimum compliance for a given mass of plate. Topology optimal shape of the plate is verified by some typical bending plate model. This paper presents a new method to solve shear locking problem of Mindlin plate and it can be used to solve other domains.

Topology Optimization of Multilayer Plate Structures by Using P1- Nonconforming Element

Lei Chen(첸레이),Gang-Won Jang(장강원),Tae Hyun Baek(백태현) 대한기계학회 2011 대한기계학회 춘추학술대회 Vol.2011 No.10

Based on finite element method, topology optimization is applied to design optimal shape of a given design space. In this study, the multilayer plate structures are analyzed and extended to topology optimization design. In order to solving shear locking problem of thin plate caused by Mindlin-Reissner plate model, P1-nonconforming element and selective reduced integration are employed. P1 quadrilateral element is one kind of discontinuous and Poisson’ locking-free element. Furthermore, P1-nonconforming element has linear shape functions that are defined at middle point of each edge. Here, Darcy-Stokes fluid model and reinforcement plate model are applied on different layers. By calculating sensitivity analysis of multiobjective function, the minimum compliance and dissipated power of the model with given mass is obtained by method of moving asymptotes (MMA). Some numerical examples of multilayer plate structure are studied and compared with the reference results.

등색프린지 데이터를 이용한 인장하중 판재 중앙 균열선단 주위의 하이브리드 광탄성 응력장 해석

백태현(Tae Hyun Baek),첸레이(Lei Chen) 대한기계학회 2007 大韓機械學會論文集A Vol.31 No.12

An experimental test is presented for photoelastic stress analysis around a crack tip in tensile loaded plate. The hybrid method coupling photoelastsic fringe inputs calculated by finite element method and complex variable formulations involving conformal mappings and analytical continuity is used to calculate full-field stress around the crack tip in uniaxially loaded, finite width tensile plate. In order to accurately compare calculated fringes with experimental ones, both actual and regenerated photoelastic fringe patterns are two times multiplied and sharpened by digital image processing. Regenerated fringes by hybrid method are quite comparable to actual fringes. The experimental results indicate that Mode I stress intensity factor analyzed by the hybrid method are accurate within three percent compared with ones obtained by empirical equation and finite element analysis.