• 한국전산구조공학회논문집
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• 제27권3호
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• pp.137-145
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• 2014

본 논문에서는 브리징 스케일 분해를 기반으로 멀티스케일 문제에 대한 설계민감도 해석법을 개발하였다. 나노 기술의 급속한 발전으로 인해 나노 수준의 해석의 필요성이 지속적으로 증가하고 있다. 최근 분자동역학과 연속체역학의 연성문제에서 많은 해석 방법들이 개발되었다. 본 논문에서는 연성시스템 해석을 위해 브리징 스케일 기법을 사용한다. 전체 영역의 분자동역학 시스템의 해석은 많은 양의 계산 비용이 들기때문에 분자동역학과 연속체 시뮬레이션의 연성시스템을 선호한다. 분자동역학과 연속체 수준 사이의 정보 교환은 분자동역학과 연속체의 경계에서 일어난다. 브리징 스케일 법에서 일반화된 랑지벵 방정식은 축소된 영역의 분자동역학 시스템 해석을 위하여 요구되고, 시간이력 커널을 사용하여 구한 GLE 힘은 분자동역학 시스템에서 경계에 있는 원자들에 작용한다. 그러므로 분자동역학과 연속체 수준의 시뮬레이션을 분리해서 해석할 수 있으며 계산 과정을 가속시킬 수 있다. 연성문제의 시뮬레이션 이후에는 설계의 최적화를 위해 설계민감도 해석의 필요성이 자연스럽게 나타나며 전체 시스템의 성능은 나노 스케일의 효과를 고려해서 최적화된다. 설계구배 기반 최적화에서 설계민감도가 요구되지만 유한차분법으로 구한 민감도는 문제가 대형화될 때 계산비용의 제한때문에 비실용적이나 해석적 설계민감도는 효율적인 강점을 갖는다. 본 연구에서는 연성된 분자동역학-연속체 멀티스케일 문제에서 해석적 설계민감도를 유도하여 정확성과 향후 최적설계로의 활용 가능성을 확인하였다.

• Steel and Composite Structures
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• 제37권6호
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• pp.663-678
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• 2020

This paper proposes a novel topology optimization method generating multiple materials for external linear plane crack structures based on the combination of IsoGeometric Analysis (IGA) and eXtended Finite Element Method (X-FEM). A so-called eXtended IsoGeometric Analysis (X-IGA) is derived for a mechanical description of a strong discontinuity state's continuous boundaries through the inherited special properties of X-FEM. In X-IGA, control points and patches play the same role with nodes and sub-domains in the finite element method. While being similar to X-FEM, enrichment functions are added to finite element approximation without any mesh generation. The geometry of structures based on basic functions of Non-Uniform Rational B-Splines (NURBS) provides accurate and reliable results. Moreover, the basis function to define the geometry becomes a systematic p-refinement to control the field approximation order without altering the geometry or its parameterization. The accuracy of analytical solutions of X-IGA for the crack problem, which is superior to a conventional X-FEM, guarantees the reliability of the optimal multi-material retrofitting against external cracks through using topology optimization. Topology optimization is applied to the minimal compliance design of two-dimensional plane linear cracked structures retrofitted by multiple distinct materials to prevent the propagation of the present crack pattern. The alternating active-phase algorithm with optimality criteria-based algorithms is employed to update design variables of element densities. Numerical results under different lengths, positions, and angles of given cracks verify the proposed method's efficiency and feasibility in using X-IGA compared to a conventional X-FEM.

• Smart Structures and Systems
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• 제13권4호
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• pp.587-614
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• 2014

In recent years the interest in online monitoring of lightweight structures with ultrasonic guided waves is steadily growing. Especially the aircraft industry is a driving force in the development of structural health monitoring (SHM) systems. In order to optimally design SHM systems powerful and efficient numerical simulation tools to predict the behaviour of ultrasonic elastic waves in thin-walled structures are required. It has been shown that in real industrial applications, such as airplane wings or fuselages, conventional linear and quadratic pure displacement finite elements commonly used to model ultrasonic elastic waves quickly reach their limits. The required mesh density, to obtain good quality solutions, results in enormous computational costs when solving the wave propagation problem in the time domain. To resolve this problem different possibilities are available. Analytical methods and higher order finite element method approaches (HO-FEM), like p-FEM, spectral elements, spectral analysis and isogeometric analysis, are among them. Although analytical approaches offer fast and accurate results, they are limited to rather simple geometries. On the other hand, the application of higher order finite element schemes is a computationally demanding task. The drawbacks of both methods can be circumvented if regions of complex geometry are modelled using a HO-FEM approach while the response of the remaining structure is computed utilizing an analytical approach. The objective of the paper is to present an efficient method to couple different HO-FEM schemes with an analytical description of an undisturbed region. Using this hybrid formulation the numerical effort can be drastically reduced. The functionality of the proposed scheme is demonstrated by studying the propagation of ultrasonic guided waves in plates, excited by a piezoelectric patch actuator. The actuator is modelled utilizing higher order coupled field finite elements, whereas the homogenous, isotropic plate is described analytically. The results of this "semi-analytical" approach highlight the opportunities to reduce the numerical effort if closed-form solutions are partially available.

• 한국전산구조공학회논문집
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• 제27권2호
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• pp.63-70
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• 2014

본 논문에서는 압전 수정진동자의 설계민감도 해석 및 위상 최적설계 기법을 개발하였다. 압전 수정진동자는 가해지는 전하에 의해 두께방향 전단 변형하게 되거나, 혹은 그 반대방향으로 기계 변형에 의해 전기적 신호를 검출하게 된다. 엄밀한 두께방향 전단해석을 위해 두께방향으로 고차 보간을 하는 고차 민들린(Mindlin) 판 이론을 도입하였다. 압전 수정진동자에서 수정판은 부도체이기 때문에 전기적 신호를 검출하거나 전기적 신호에 의해 수정판을 기계적으로 진동시키기 위해 수정판의 상/하 표면에 얇은 전극경을 도포한다. 비록 전극경이 매우 얇기는 하지만 그 무게와 형상에 따라 진동자의 거동이 달라지기 때문에, 설계민감도 해석 및 위상 최적설계를 위한 설계변수는 전극경의 질량 밀도와 관계된다. 따라서 위상 최적설계 문제는 두께방향 전단 변형에너지를 최대화하는 최적의 전극경 분포를 구하도록 구성한다. 또한 보다 의미있는 설계안을 얻기 위해 전극경의 재료량과 면적에 제약조건을 부여한다. 두께방향 전단 주파수(고유치)와 상응하는 모드형상(고유벡터)에 대한 설계구배는 고유벡터 확장법을 이용한 해석적 설계민감도 해석법을 통해 매우 효율적이고 정확하게 계산될 수 있다. 수치예제를 통해 제안된 해석적 설계민감도가 유한차분 설계민감도와 비교하여 매우 효율적이고 정확하게 계산됨을 확인하였다. 또한 위상 최적설계를 통해 도출된 최적 전극경 설계가 모드형상과 두께방향 전단 변형에너지를 개선시킴을 확인하였다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2013년도 춘계학술대회 논문집
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• pp.835-841
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• 2013

Modern solid-state gyroscopes (HRG) with hemispherical resonators from high-purity quartz glass and special surface superfinishing and ultrathin gold coating become the best instruments for precise-grade inertial reference units (IRU) targeting long-term space missions. Designing of these sensors could be a notable contribution into development of Korea as a space nation. In participial, 40mm diameter thin-shell resonator from high-purity fused quartz, fabricated as a single-piece with its supporting stem has been designed, machined, etched, tuned, tested, and delivered by STM Co. (ATS of Ukraine) several years ago; an extremely-high Q-factor (upto 10~20 millions) has been shown. Understanding of the best way how to match such a unique sensor with inner glass assembly of the gyro means how to use the high potential in a maximal extent; and this has become the urgent task. Inner quartz glass assembly has a very thin indium (In) layer soldered the resonator and its silica base (case), but effects of internal resonances between operational modal pair of the shell-cup and its side (parasitic) modes can notable degrade the potential of the sensor as a whole, instead of so low level of resonator's intrinsic losses. Unfortunately, there are special combinations of dimensions of the parts (so-called, "resonant sizes"), when intensive losses of energy occurs. The authors proposed to use the length of stem's fixture as an additional design parameter to avoid such cases. So-called, a cyclic scheme of finite element method (FEM) and ANSYS software were employed to estimate different combinations of gyro assembly parameters. This variant has no mismatches of numerical origin due to FEM's discrete mesh. The optimum length and dangerous "resonant lengths" have been found. The special attention has been paid to analyses of 3D effects in a cup-stem transient zone, including determination of a difference between the positions of geometrical Pole of the resonant hemisphere and of its "dynamical Pole", i.e., its real zone of oscillation node. Boundary effects between the shell (cup) and 3D short "beams" (inner and outer stems) have been ranged. The results of the numerical experiments have been compared with the classic model of a quasi-hemispherical shell band with inextensional midsurface, and the solution using Rayleigh's functions of the $1^{st}$ and $2^{nd}$ kinds. To guarantee the truth of the recommended sizes to a designer of the real device, the analytical and FEM results have been compared with experimental data for a party of real resonators. The consistency of the results obtained by different means has been shown with errors less than 5%. The results notably differ from the data published earlier by different researchers.