• 대한수학회지
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• 제34권1호
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• pp.87-118
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• 1997

This paper is concerned with a mixed Lagrangian formulation of the wiscous, stationary, incompressible Navier-Stokes equations $$ (1.1) -\nu\Delta u + (u \cdot \nabla)u + \nabla_p = f in \Omega $$ and $$ (1.2) \nubla \cdot u = 0 in \Omega $$ along with inhomogeneous Dirichlet boundary conditions on a portion of the boundary $$ (1.3) u = ^{0 on \Gamma_0 _{g on \Gamma_g, $$ where $\Omega$ is a bounded open domain in $R^d, d = 2 or 3$, or with a boundary $\Gamma = \partial\Omega$, which is composed of two disjoint parts $\Gamma_0$ and $\Gamma_g$.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.1539-1544
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• 1991

In this paper we formulate and solve a generalized $H^{\infty}$ control problem. The conventional formulation of $H^{\infty}$ problem has some constraints in application, e.g. it can not deal with the servo problem. This is due to the superfluous requirement of internal stability of the augmented system. In this paper, we alleviate the stability of the augmented system to admit pole-zero cancellation on the imaginary aids outside the feedback loop of G22 and K. After such generalization, the servo problem is naturally incorporated into the $H^{\infty}$ synthesis.is.

• International Journal of Aeronautical and Space Sciences
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• 제16권2호
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• pp.177-189
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• 2015

This paper presents an all-direct domain decomposition approach for large-scale structural analysis. The proposed approach achieves computational robustness and efficiency by enforcing the compatibility of the displacement field across the sub-domain boundaries via local Lagrange multipliers and augmented Lagrangian formulation (ALF). The proposed domain decomposition approach was compared to the existing FETI approach in terms of the computational time and memory usage. The parallel implementation of the proposed algorithm was described in detail. Finally, a preliminary validation was attempted for the proposed approach, and the numerical results of two- and three-dimensional problems were compared to those obtained through a dual-primal FETI approach. The results indicate an improvement in the performance as a result of the implementing the proposed approach.

• Journal of Magnetics
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• 제16권1호
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• pp.77-82
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• 2011

This paper presents a new self-adjoint material sensitivity formulation for optimal designs and inverse problems in the high frequency domain. The proposed method is based on the continuum approach using the augmented Lagrangian method. Using the self-adjoint formulation, there is no need to solve the adjoint system additionally when the goal function is a function of the S-parameter. In addition, the algorithm is more general than most previous approaches because it is independent of specific analysis methods or gridding techniques, thereby enabling the use of commercial EM simulators and various custom solvers. For verification, the method was applied to the several numerical examples of dielectric material reconstruction problems in the high frequency domain, and the results were compared with those calculated using the conventional method.

• 한국전산구조공학회논문집
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• 제25권6호
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• pp.469-476
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• 2012

본 논문에서는 대규모 구조해석을 위하여 국부(local) 및 전역-국부 혼합(mixed) Lagrange 승수(Lagrange multiplier)를 이용한 새로운 유한요소 영역분할 기법을 제시한다. 제시되는 FETI 알고리즘은 계산 효율성을 향상시키기 위하여 기존의 FETI 기법들에서 사용되어 온 전통적인 Lagrange 승수법과는 달리, 국부 및 전역-국부 혼합 Lagrange 승수를 도입하고 ALF(Augmented Lagrangian Formulation)과의 결합을 유도하여 공유면 문제(interface problem)의 해의 수렴성을 향상 시켰다. 추가적으로, 몇 가지 수치예제 계산을 통해 기존의 FETI-DP 기법과 비교하여 유연도 행렬의 조건수, 계산 시간 그리고 메모리 사용량에 대한 계산결과를 제시하였다.

• Smart Structures and Systems
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• 제30권3호
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• pp.221-237
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• 2022

This paper is concerned with nonlinear modeling and efficient numerical simulation of electrostrictive materials and structures. Two types of such materials are considered: relaxor ferroelectric ceramics and electrostrictive polymers. For ceramics, a geometrically linear formulation is developed, whereas polymers are studied in a geometrically nonlinear regime. In the paper, we focus on constitutive modeling first. For the reversible constitutive response under consideration, we introduce the augmented Helmholtz free energy, which is composed of a purely elastic part, a dielectric part and an augmentation term. For the elastic part, we involve an additive decomposition of the strain tensor into an elastic strain and an electrostrictive eigenstrain, which depends on the polarization of the material. In the geometrically nonlinear case, a corresponding multiplicative decomposition of the deformation gradient tensor replaces the additive strain decomposition used in the geometrically linear formulation. For the dielectric part, we first introduce the internal energy, to which a Legendre transformation is applied to compute the free energy. The augmentation term accounts for the contribution from vacuum to the energy. In our formulation, the augmented free energy depends not only on the strain and the electric field, but also on the polarization and an internal polarization; the latter two are internal variables. With the constitutive framework established, a Finite Element implementation is briefly discussed. We use high-order elements for the discretization of the independent variables, which include also the internal variables and, in case the material is assumed incompressible, the hydrostatic pressure, which is introduced as a Lagrange multiplier. The elements are implemented in the open source code Netgen/NGSolve. Finally, example problems are solved for both, relaxor ferroelectric ceramics and electrostrictive polymers. We focus on thin plate-type structures to show the efficiency of the numerical scheme and its applicability to thin electrostrictive structures.

• Coupled systems mechanics
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• 제7권5호
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• pp.583-610
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• 2018

This paper discusses the issues associated with modeling frictional contact between solid bodies undergoing large deformations. The most common model for friction on contact interfaces in solid mechanics is the Coulomb friction model, in which two distinct responses are possible: stick and slip. Handling the transition between these two phases computationally has been a source of algorithmic instability, lack of convergence and non-unique solutions, particularly in the presence of large deformations. Most computational models for frictional contact have used penalty or updated Lagrangian approaches to enforce frictional contact conditions. These two approaches, however, present some computational challenges due to conditioning issues in penalty-type implementations and the iterative nature of the updated Lagrangian formulation, which, particularly in large simulations, may lead to relatively slow convergence. Alternatively, a plasticity-inspired implementation of frictional contact has been shown to handle the stick-slip conditions in a local, algorithmically efficient manner that substantially reduces computational cost and successfully avoids the issues of instability and lack of convergence often reported with other methods (Laursen and Simo 1993). The formulation of this approach, however, has been limited to the small deformations realm, a fact that severely limited its application to contact problems where large deformations are expected. In this paper, we present an algorithmically consistent formulation of this method that preserves its key advantages, while extending its application to the realm of large-deformation contact problems. We show that the method produces results similar to the augmented Lagrangian formulation at a reduced computational cost.

• 제어로봇시스템학회논문지
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• 제14권8호
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• pp.792-799
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• 2008

Motion estimation is crucial in a remote control for its convenience or accuracy. Time delays, however, can occur in the problem because data communication is required through a network. In this paper, state estimation problem with uncertain time delayed measurements is addressed. In dynamic system with noise, after taking measurements, it often requires some time until that is available in the filter algorithm. Standard filters not considering this time delays cannot be used since the current measurement is related with a past state. These delayed measurements are solved with augmented extended Kalman filter, and the uncertainty of delayed time is also resolved based on an explicit formulation. The proposed method is analyzed and verified by simulations.

• 한국군사과학기술학회지
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• 제12권3호
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• pp.272-281
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• 2009

In this paper, three-dimensional optimal evasive maneuver patterns for air-to-surface attack missiles against proportionally navigated anti-air defense missiles were investigated. An interception error of the defense missile is produced by an evasive maneuver of the attack missile. It is assumed that the defense missiles are continuously launched during the flight of attack missile. The performance index to be minimized is then defined as the negative square integral of the interception errors. The direct parameter optimization technique based on SQP and a co-evolution method based on the augmented Lagrangian formulation are adopted to get the attack missile's optimal evasive maneuver patterns. The overall shape of the resultant optimal evasive maneuver is represented as a deformed barrel-roll.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.45.3-45
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• 2001

This paper deal with a fault detection algorithm for front wheel passenger car systems by using robust $H{\infty}$ control theory. Firstly, we present a unified formulation of vehicle dynamics for front wheel car systems and transform this formulation into state space form. Also, by considering the cornering stiffness which depends on the tyre-road contact conditions, a multiplicative uncertainty for vehicle model is described. Next, the failures of sensor and actuator for vehicle system are defined in which the fault .lter is considered. From the nominal vehicle model, an augmented system includes the multiplicative uncertainty and the model of fault filter is proposed. Lastly by using $H{\infty}$ norm property the fault detect conditions are deefi.ned, and the actuator and sensor failures are detected and isolated by designing the robust $H{\infty}$ controller, respectively.