• Interaction and multiscale mechanics
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• 제1권3호
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• pp.339-355
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• 2008

A Galerkin meshfree method is presented for analyzing shear deformable cylindrical panels. Based upon the analogy between the cylindrical panel and the curved beam a pure bending mode for cylindrical panel is rationally constructed. The meshfree approximation employed herein is characterized by an enhanced moving least square or reproducing kernel basis function that can exactly represent the pure bending mode and thus meets the requirement of Kirchhoff mode reproducing condition. The variational form is discretized using the efficient stabilized conforming nodal integration with a smoothed nodal gradient based curvature. The resulting meshfree formulation satisfies the integration constraint for bending exactness. Moreover, it is shown here that the smoothed gradient preserves several desired properties which are valid for the standard gradient obtained by direct differentiation, such as partition of nullity and reproduction of a constant strain field. The efficacy of the proposed approach is demonstrated by two benchmark cylindrical panel examples.

• 전자공학회논문지B
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• 제29B권3호
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• pp.25-34
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• 1992

This paper proposes a Self-Tuning control algorithm for tracking the reference trajectory by measuring the end-point of robot manipulator whose links are light and flexible, and the performance of it is tested through the computer simulation. As an object of system, a flexible robot manipulator with two-links is considered and an assumed mode shape method including gravity force is adopted to analyze the vibration modes for each links and dynamics equation is derived. The controller is designed as a combined form which consists of dynamic feedforward compensator and self-tuning feedback controller. The one supplies nominal torque and the other supplies variational torque to manipulator. Apart from the, K-incremental predictor is also proposed in order to eliminate the offset error. and it shows that the result of simulation adapted well to load change and rapid velocity.

• Interaction and multiscale mechanics
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• 제3권2호
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• pp.123-143
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• 2010

The essential idea of the element-free Galerkin method (EFG) is that moving least-squares (MLS) approximation are used for the trial and test functions with the variational principle (weak form). By using the weighted orthogonal basis function to construct the MLS interpolants, we derive the formulae for an improved element-free Galerkin (IEFG) method for solving three-dimensional problems in linear elasticity. There are fewer coefficients in improved moving least-squares (IMLS) approximation than in MLS approximation. Also fewer nodes are selected in the entire domain with the IEFG method than is the case with the conventional EFG method. In this paper, we selected a few example problems to demonstrate the applicability of the method.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1996년도 춘계학술발표회논문집(1)
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• pp.157-162
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• 1996

A novel nodal method is developed for the two-dimensional multi-group diffusion equations based on the Spectral-Galerkin approach. In this study, the nodal diffusion equations with Robin boundary condition are reformulated in a weak (variational) form, which is then approximated spatially by choosing appropriate basis functions. For the nodal coupling relations between the neighbouring nodes, the continuity conditions of partial currents are utilized. The resulting discrete systems with sparse structured matrices are solved by the Preconditioned Conjugate Gradient Method (PCG) and sweeping technique. The method is validated on two test problems.

• 한국소음진동공학회논문집
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• 제13권3호
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• pp.172-179
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• 2003

Linear matrix Inequality based $H_\infty$ robust controller is designed to control the motion of a 4-axis unbalanced rigid asymmetric rotor supported and controlled by two active magnetic bearings in this paper. To this end, the equations of motion of the system are derived via Hamilton's variational principle and transformed to a state-space form for the standard $H_\infty$ control problem. LMI-based controller, which does not require additional assumptions beyond the usual stabilizability and detectability assumptions, is designed based upon the pole place weighting function and loopshaping technique. The obtained results are compared with those reported in the available literature and the efficiency of the proposed LMI-based $H_\infty$ control is revealed.

• Coupled systems mechanics
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• 제13권1호
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• pp.73-93
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• 2024

In this work, we propose combining an advanced optimal control algorithm with a geometrically exact beam model. For simplicity, the 2D Reissner beam model is chosen to represent large displacements and rotations. The difficulty pertains to the nonlinear nature of beam kinematics affecting the tangent stiffness matrix, making it non-constant, which compromises direct use of optimal control methods for linear problems. Thus, we seek to accommodate a time varying control using linear-quadratic regulator (LQR) algorithm with the proposed geometrically nonlinear beam model. We provide a detailed theoretical formulation and its numerical implementation in a variational format form. Several illustrative numerical examples are provided to confirm an excellent performance of the proposed methodology.

• 한국해양학회지:바다
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• 제10권1호
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• pp.69-78
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• 2005

본 연구에서는 전구 해양에서 관측되는 ARGO및 TAO해양 자료를 이용하여 해양의 3차원적인 구조를 분석.동화하고 궁극적으로 해양대순환모형을 위한 초기장을 생산하였다. 초기장의 생산을 위하여 전구 해양대순환 모형인 MOM3.1을 이용하였으며 생산한 배경장에, 계산시간과 계산공간을 절약할 수 있는 공간필터를 사용한 변분법(VAF, variational analysis using filter)을 이용하여 ARGO와 TAO 수온 자료를 동화하였다. 또한 본 연구에서는 자료 동화가 미치는 지속적인 영향을 살펴보고자 실험적분을 수행하였는데, 모형의 초기입력 자료를 자료동화 기법을 적용한 경우와 적용하지 않은 두 가지로 나누어 비교 실험을 수행하였다. 본 연구에서 자료 동화된 분석장은 OISST와의 비교를 통해 적절히 생산되었음을 보여주었다. 관측자료를 동화한 분석장을 초기자료로 한 10개월간의 적분결과를 살펴보면, 자료 동화를 통해 제거된 모형의 계통적 bias가 적분이 진행되는 과정에서 관성 중력파 등의 형태로 소멸되지 않고 지속적으로 관측과 유사하게 유지되었다. 이는 본 연구에서 실행한 자료동화가 모형의 역학적인 균형을 유지하면서 적절히 이루어졌음을 의미하며, 전구 대순환 모형을 이용한 중.장기 대기.해양 예측에 이러한 해양 자료동화가 대단히 유용하다는 것을 의미한다.

• 대한기계학회논문집A
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• 제25권9호
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• pp.1376-1383
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• 2001

Meshless methods, developed in various ways over the past decade, have been attractive as new computational methods in that they do not need mesh generation in analyzing procedure. But most of these methods were not truly meshless methods because background meshes were required for the spatial integration of a weak form. Accordingly, in this paper, nodal integration for truly meshless methods has been studied, and an improvement scheme is proposed. To improve stabilization and accuracy, which are the weak points in previous nodal integration methods, the integration area is transformed to circle and then numerically integrated. This method does not need any adding term for stabilization in the variational formulation and then simplifies the integration procedure. Numerical test results show that the proposed method is more accurate, stable, and reasonable than the existed nodal integration methods.

• Steel and Composite Structures
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• 제24권1호
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• pp.65-77
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• 2017

The purpose of this research is to study the nonlinear free vibration and post-buckling analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams resting on a nonlinear elastic foundation. Uniformly and functionally graded distributions of single walled carbon nanotubes as reinforcing phase are considered in the polymeric matrix. The modified form of rule of mixture is used to estimate the material properties of CNTRC beams. The governing equations are derived employing Euler-Bernoulli beam theory along with energy method and Hamilton's principle. Applying von $K\acute{a}rm\acute{a}n's$ strain-displacement assumptions, the geometric nonlinearity is taken into consideration. The developed governing equations with quadratic and cubic nonlinearities are solved using variational iteration method (VIM) and the analytical expressions and numerical results are obtained for vibration and stability analysis of nanocomposite beams. The presented comparative results are indicative for the reliability, accuracy and fast convergence rate of the solution. Eventually, the effects of different parameters, such as foundation stiffness, volume fraction and distributions of carbon nanotubes, slenderness ratio, vibration amplitude, coefficients of elastic foundation and boundary conditions on the nonlinear frequencies, vibration response and post-buckling loads of FG-CNTRC beams are examined. The developed analytical solution provides direct insight into parametric studies of particular parameters of the problem.

• Structural Engineering and Mechanics
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• 제52권1호
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• pp.115-136
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• 2014

In this study, an extended Kantorovich method, employing multi-term displacement functions, is applied to analyze the vibration problem of symmetrically laminated plates with arbitrary boundary conditions. The vibration behaviors of laminated plates are determined based on the variational principle of total energy minimization and the iterative Kantorovich method. The out-of-plane displacement is represented in the form of a series of a sum of products of functions in x and y directions. With a known function in the x or y directions, the formulation for the variation of total potential energy is transformed to a set of governing equations and a set of boundary conditions. The equations and boundary conditions are then numerically solved for the natural frequency and vibration mode shape. The solutions are verified with available solutions from the literature and solutions from the Ritz and finite element analysis. In most cases, the natural frequencies compare very well with the reference solutions. The vibration mode shapes are also very well modeled using the multi-term assumed displacement function in the terms of a power series. With the method used in this study, it is possible to solve the angle-ply plate problem, where the Kantorovich method with single-term displacement function is ineffective.