• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.12
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• pp.1966-1973
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• 2001

The Jacobian matrix of the equations of motion of a system using velocity transformation technique is derived via variation methods to apply the implicit integration algorithm, DASSL. The concept of generalized coordinate partitioning is used to parameterize the constraint set with independent generalized coordinates. DASSL is applied to determine independent generalized coordinates and velocities. Dependent generalized coordinates, velocities, accelerations and Lagrange multipliers are explicitly retained in the formulation to satisfy all of the governing kinematic and dynamic equations. The derived Jacobian matrix of a system is proved to be valid and accurate both analytically and through solution of numerical examples.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.20 no.41
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• pp.123-134
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• 1997

In this paper we consider the CSP requirements determination problem of new equipment system. The CSP we deal with in the paper are restricted to the demand-based spare parts. For the newly procured equipment systems, mathematical analyses are made for the system which is constructed with the repairable items to derive the associated CSP requirement determination model in mathematical expression, respectively. Based on these analyses, a mathematical model is derived for making an optimal CSP requirement determination subject to the constraint of satisfying any given funds limitation. We assume that the failure of a part follows a Poisson process. Firstly, the operational availability concept in CSP is defined and the relation between the general system availability and the operational availability is established. Secondly, the problem is formulated as the operational availability maximization problem that should satisfy the funds limitation, and then, using the generalized Lagrange multipliers method, the optimal solution procedure is derived.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.48
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• pp.113-122
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• 1998

In this paper we consider the CSP requirements determination problem of new equipment(machine) system. For the newly procured equipment systems, mathematical analyses are made for the system which is constructed with the consumable parts to derive the associated CSP requirement determination model in mathematical expression. Based on these analyses, a mathematical model is derived for making an optimal CSP requirement determination subject to tile constraint of satisfying any given operational availability limitation. We assume that the failure of a part follows a Poisson process. Firstly, the operational availability concept in CSP is defined and the relation between the general system availability and the operational availability is established. Secondly, the problem is formulated as the cost minimization problem that should satisfy the operational availability limitation, and then, using the generalized Lagrange multipliers method, the optimal solution procedure is derived.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.23 no.59
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• pp.53-67
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• 2000

In this paper we consider the CSP requirements determination problem of new equipment(machine) system. For the newly procured equipment systems, mathematical analyses are made for the system which is constructed with the consumable parts and the repairable parts to derive the associated CSP requirement determination model in mathematical expression. Based on these analyses, a mathematical model Is derived for making an optimal CSP requirement determination subject to the constraint of satisfying any given operational availability limitation. We assume that the failure of a part follows a Poisson process and the repair time has an exponential distribution. Firstly, the operational availability concept in CSP is defined and the relation between the general system availability and the operational availability is established. Secondly, the problem is formulated as the cost minimization problem that should satisfy the operational availability limitation, and then, using the generalized Lagrange multipliers method, the optimal solution procedure Is derived.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.2 s.179
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• pp.113-121
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• 2006

This paper established the dynamic model of a flexible Timoshenko beam capable of geometrical nonlinearities subject to large overall motions by using the finite element method. Equations of motion are derived by using Hamilton principle and are formulated in terms of finite elements using CO elements in which the nonlinear constraint equations are adjoined to the system using Lagrange multipliers. In the final formulation are presented Coriolis and Gyroscopic forces as well as linear and nonlinear stiffnesses effects for the forthcoming numerical computation.

• Journal of Korean Society for Quality Management
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• v.9 no.2
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• pp.31-36
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• 1981

This paper deals with the reliability optimization of parallel - in - series system subject to several linear constraints. The model of nonlinear constrained optimization is transformed to a saddle point problem by using Lagrange multipliers. Then Newton - Raphson method is used to solve the resulting problem and these step - by - step solution procedures are programmed in Basic Level II of micro - computer TRS-80. An example which has two linear constraints is solved and the results are analyzed.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.461-477
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• 2017

A dual substructuring method with a penalty term was introduced in the previous works by the authors, which is a variant of the FETI-DP method. The proposed method imposes the continuity not only by using Lagrange multipliers but also by adding a penalty term which consists of a positive penalty parameter ${\eta}$ and a measure of the jump across the interface. Due to the penalty term, the proposed iterative method has a better convergence property than the standard FETI-DP method in the sense that the condition number of the resulting dual problem is bounded by a constant independent of the subdomain size and the mesh size. In this paper, a further study for a dual iterative substructuring method with a penalty term is discussed in terms of its convergence analysis. We provide an improved estimate of the condition number which shows the relationship between the condition number and ${\eta}$ as well as a close spectral connection of the proposed method with the FETI-DP method. As a result, a choice of a moderately small penalty parameter is guaranteed.

• Interaction and multiscale mechanics
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• v.1 no.1
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• pp.1-31
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• 2008

The present paper presents multiscale modelling via coupling of the discrete and finite element methods. Theoretical formulation of the discrete element method using spherical or cylindrical particles has been briefly reviewed. Basic equations of the finite element method using the explicit time integration have been given. The micr-macro transition for the discrete element method has been discussed. Theoretical formulations for macroscopic stress and strain tensors have been given. Determination of macroscopic constitutive properties using dimensionless micro-macro relationships has been proposed. The formulation of the multiscale DEM/FEM model employing the DEM and FEM in different subdomains of the same body has been presented. The coupling allows the use of partially overlapping DEM and FEM subdomains. The overlap zone in the two coupling algorithms is introduced in order to provide a smooth transition from one discretization method to the other. Coupling between the DEM and FEM subdomains is provided by additional kinematic constraints imposed by means of either the Lagrange multipliers or penalty function method. The coupled DEM/FEM formulation has been implemented in the authors' own numerical program. Good performance of the numerical algorithms has been demonstrated in a number of examples.

• International Journal of CAD/CAM
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• v.8 no.1
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• pp.1-10
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• 2009

This paper presents a topology optimization approach using element-free Galerkin method (EFGM) for the optimal design of compliant mechanisms with geometrically non-linearity. Meshless method has an advantage over the finite element method(FEM) because it is more capable of handling large deformation resulted from geometrical nonlinearity. Therefore, in this paper, EFGM is employed to discretize the governing equations and the bulk density field. The sensitivity analysis of the optimization problem is performed by incorporating the adjoint approach with the meshless method. The Lagrange multipliers method adjusted for imposition of both the concentrated and continuous essential boundary conditions in the EFGM is proposed in details. The optimization mathematical formulation is developed to convert the multi-criteria problem to an equivalent single-objective problem. The popularly applied interpolation scheme, solid isotropic material with penalization (SIMP), is used to indicate the dependence of material property upon on pseudo densities discretized to the integration points. A well studied numerical example has been applied to demonstrate the proposed approach works very well and the non-linear EFGM can obtain the better topologies than the linear EFGM to design large-displacement compliant mechanisms.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.44 no.9
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• pp.775-780
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• 2016

In this paper, a computational algorithm of an improved and versatile structural analysis applicable for large-size flexible nonlinear structures is developed. In more detail, nonlinear finite element based on the co-rotational (CR) framework is developed. Then, a finite element tearing and interconnecting method using local Lagrange multipliers (FETI-local) is combined with the nonlinear CR finite element. The resulting computational algorithm is presented and applied for nonlinear static analyses, i.e., cantilevered beam and multibody structure. Finally, the proposed analysis is evaluated with regard to its parallel computation performance, and it is compared with those obtained by serial computation using the sparse matrix linear solver, PARDISO.