• Advances in Computational Design
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• v.2 no.3
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• pp.123-141
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• 2017

Solving a system of linear or non-linear equations is required to analyze any kind of structures. There are many ways to solve a system of equations, and they can be classified as implicit and explicit techniques. The explicit methods eliminate round-off errors and use less memory. The dynamic relaxation method (DR) is one of the powerful and simple explicit processes. The important point is that the DR does not require to store the global stiffness matrix, for which it just uses the residual loads vector. In this paper, a new approach to the DR method is expressed. In this approach, the damping, mass and time steps are similar to those of the traditional method of dynamic relaxation. The difference of this proposed method is focused on the method of calculating the damping. The proposed method is expressed such that the time step is constant, damping is equal to zero except in steps with maximum energy and the concentrated damping can be applied to minimize the energy of system in this step. In this condition, the calculation of damping in all steps is not required. Then the volume of computation is reduced. The DR method for form-finding of membrane structures is employed in this paper. The form-finding of the three plans related to the membrane structures with different loading is considered to investigate the efficiency of the proposed method. The numerical results show that the convergence rate based on the proposed method increases in all cases than other methods.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.175-182
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• 2005

The present study is concerned with the application of dynamic relaxation method in the investigation of the large deflection behavior of spatial structures. This numerical algorithm do not require the computation or formulation of any tangent stiffness matrix. The convergence to the solution is achieved by using only vectorial quantities and no stiffness matrix is required in its overall assembled form. In an effort to evaluate the merits of the methods, extensive numerical studies were carried out on a number of selected structural systems. The advantages of using dynamic relaxation methods, in tracing the post-buckling behavior of spatial structures, are demonstrated.

• Computational Structural Engineering
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• v.11 no.1
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• pp.179-190
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• 1998

A geometrically nonlinear finite element formulation of spatial cable networks is presented using two cable elements. Firstly, derivation procedures of tangent stiffness and mass matrices for the space truss element and the elastic catenary cable element are summarized. The load incremental method based on Newton-Raphson iteration method and the dynamic relaxation method are presented in order to determine the initial static state of cable nets subjected to self-weights and support motions. Furthermore, static non-linear analysis of cable structures under additional live loads are performed based on the initial configuration. Challenging example problems are presented and discussed in order to demonstrate the feasibility of the present finite element method and investigate static nonlinear behaviors of cable nets.

• The KIPS Transactions:PartB
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• v.9B no.6
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• pp.735-744
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• 2002

This paper proposes learning performance improvement of support vector machine using the kernel relaxation and the dynamic momentum. The dynamic momentum is reflected to different momentum according to current state. While static momentum is equally influenced on the whole, the proposed dynamic momentum algorithm can control to the convergence rate and performance according to the change of the dynamic momentum by training. The proposed algorithm has been applied to the kernel relaxation as the new sequential learning method of support vector machine presented recently. The proposed algorithm has been applied to the SONAR data which is used to the standard classification problems for evaluating neural network. The simulation results of proposed algorithm have better the convergence rate and performance than those using kernel relaxation and static momentum, respectively.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.51-58
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• 2000

Dynamic relaxation method is a shape finding analysis method for flexible structures by introducing the dynamic equilibrium equation. However, it is difficult for shape finding to estimate the most appropriate values for the mass and damping on each shape because the values are random one. In this study, the unit mass, the unit damping and the principal direction stiffness are utilized to avoid the random values, and the Newmarks assumption is introduced during the dynamic analysis. By introducing variant time increment method presented, the convergence time is reduced, that is, it can be reduced the total times for analysis.

• Journal of the Korean Magnetic Resonance Society
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• v.21 no.1
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• pp.26-30
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• 2017

Dynamic properties of proteins can present key information on protein-ligand and protein-protein interaction. Despite their usefulness, the properties of protein dynamics have not been obtained easily due to protein stability and short-term measurement. Here, it is shown that combined method for analysis of dynamical properties. It utilizes predicted order parameter and NMR relaxation data such as $T_1$, $T_2$, and heteronuclear NOE. The suggested method could be used to know the flexibility of protein roughly without precise dynamical parameters such as order parameters through model-free analysis.

• Journal of Electrical Engineering and Technology
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• v.3 no.4
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• pp.514-519
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• 2008

The non-separable quadratic penalty terms create an inherent difficulty when applying the standard augmented Lagrangian relaxation(ALR) method for decomposing the unit commitment problem into independent subproblems. This paper presents a separable augmented Lagrangian relaxation method for solving the unit commitment problem. The proposed method is designed to have a separable structure by introducing the quadratic terms with additional auxiliary terms in the augmented Lagrangian function. Numerical results are presented to validate the effectiveness of the proposed method.

• Journal of the Korean Operations Research and Management Science Society
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• v.15 no.1
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• pp.23-35
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• 1990

A mathematical model for a dynamic capacitate facility location problem is formulated by a mixed integer problem. The objective of the model is to minimize total discounted costs that include fixed charges and distributed costs. The Cross Decomposition method of Van Roy is extended and applied to solve the dynamic capacitated facility location problem. The method unifies Benders Decomposition and Lagrangean relaxation into a single framework. It successively solves a transportation problem and a dynamic uncapacitated facility location problem as two subproblems. Computational results are compared with those of general mixed integer programming.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.04a
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• pp.268-275
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• 1999

The purpose of this study is to propose the method of determining the initial pneumatic membrane structures surface and stresses and displacements. Tension structure such as pneumatic membrane structures is stabilized by their initial prestress and air pressure. The process to find initial structural overall shape of tension structures produced by initial prestress called shape finding. One of the most important factor for the design of membrane structures is to search initial smooth surface, because unlike steel or concrete building elements which resist loads in bending, all tension structure forces are carried within the surface by membrane stress. The result for initial surface of pneumatic membrane element and maximum displacement in large deformation in analysis is compared with well-known nonlinear numerical method such as Newton-raphson method and dynamic relaxation method

• Computers and Concrete
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• v.1 no.4
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• pp.371-388
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• 2004

Our objective is to model static multi-cracking processes in concrete. The explicit dynamic relaxation (DR) method, which gives the solutions of non-linear static problems on the basis of the steady-state conditions of a critically damped explicit transient solution, is chosen to deal with the high geometric and material non-linearities stemming from such a complex fracture problem. One of the common difficulties of the DR method is its slow convergence rate when non-monotonic spectral response is involved. A modified concept that is distinct from the standard DR method is introduced to tackle this problem. The methodology is validated against the stable three point bending test on notched concrete beams of different sizes. The simulations accurately predict the experimental load-displacement curves. The size effect is caught naturally as a result of the calculation. Micro-cracking and non-uniform crack propagation across the fracture surface also come out directly from the 3D simulations.