• Journal of Elementary Mathematics Education in Korea
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• v.19 no.3
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• pp.305-321
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• 2015

This study started with wondering whether the nonproportional model used in unit assessment for 2nd graders is appropriate or not for them. This study aims to explore the applicability of the nonproportional model to 2nd graders when they learn about numbers. To achieve this goal, we analyzed elementary mathematics textbooks, applied two kinds of tests to 2nd graders who have learned three-digit numbers by using the proportional model, and investigated their cognitive characteristics by interview. The results show that using the nonproportional model in the initial stages of 2nd grade can cause some didactical problems. Firstly, the nonproportional models were presented only in unit assessment without any learning activity with them in the 2nd grade textbook. Secondly, the size of each nonproportional model wasn't written on itself when it was presented. Thirdly, it was the most difficult type of nonproportional models that was introduced in the initial stages related to the nonproportional models. Fourthly, 2nd graders tend to have a great difficulty understanding the relationship of nonproportional models and to recognize the nonproportional model on the basis of the concept of place value. Finally, the question about the relationship between nonproportional models sticks to the context of multiplication, without considering the context of addition which is familiar to the students.

• Journal of Ocean Engineering and Technology
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• v.26 no.4
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• pp.86-91
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• 2012

A new identification method for a nonproportional damping matrix using the finite element (FE) model updating technique is proposed. Mass and stiffness matrices of the undamped system are identified by FE model updating method. Sensitivity analysis is used to update the FE model, and zero frequencies are considered as design parameters to supplement the information of vibration characteristics. The nonproportional damping matrix is identified through the proposed method. A numerical example is considered to verify the performance of the proposed method. As a result, the damping matrix of the nonproportional system is estimated accurately.

• International Journal of Aeronautical and Space Sciences
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• v.9 no.1
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• pp.85-99
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• 2008

The dynamic response analysis for large structures using finite element method requires a large amount of computational resources. This paper presents an efficient vibration analysis procedure by combining node-based substructuring reduction method with a response analysis scheme for structures with undamped, proportional or nonproportional damping. The iterative form of substructuring reduction scheme is derived to reduce the full eigenproblem and to calculate the dynamic responses. In calculating the time response, direct integration scheme is used because it can be applied directly to the reduced model. Especially for the non proportional damping matrix, the transformation matrices defined in the displacement space are used to reduce the system. The efficiency and the effectiveness of the present method are demonstrated through the numerical examples.

• Journal of Advanced Marine Engineering and Technology
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• v.40 no.4
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• pp.369-373
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• 2016

Accurate identification of damping matrix in structures is very important for predicting vibration responses and estimating parameters or other characteristics affected by energy dissipation. In this paper, damping matrix identification method that use normal frequency response functions, which were estimated from complex frequency response functions, is proposed. The complex frequency response functions were obtained from the experimental data of the structure. The nonproportional damping matrix was identified through the proposed method. Two numerical examples (lumped-mass model and cantilever beam model) were considered to verify the performance of the proposed method. As a result, the damping matrix of the nonproportional system was accurately identified.

• Journal of Korean Society of Steel Construction
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• v.14 no.6
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• pp.735-746
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• 2002

The task of plastic theory is twofold: first, to set up relationships between stress and strain that adequately describe the observed plastic deformation of metals, and second, to develop techniques for using these relationships in studying of the mechanics of metal forming processes, and the anlaysis and design of structures. One of the major problems in the theory of plasticity is to describe the behavior of work-hardening materials in the plastic range for complex loading histories. This can be achieved by formulating constitutive laws either in the integral or differential forms. To adequately predict the response of steel members during cyclic loading, the hardening rule must account for the features of cyclic stress-strain behavior. Neithe of the basic isotropic and kinematic hardening rules is suitable for describing cyclic streess-strain behavior, although a kinematic hardening rule describes the nearly linear portions of the stabilized hystersis loops. There is also a limited expansion of the yield surface as predicted by the isotropic hardening rule. Strong ground motions or wind gusts affect the complex and nonproportional loading histories in the inelastic behavior of structues rather than the proportional loading. Nonproportional loading is defined as externally applied forces on the structure, with variable ratios during the entire loading history. This also includes the rate of time-dependency of the loads. For nonproportional loading histories, unloading may take place along a chord instead of the radius of the load surface. In such cases, the shape of the stress-strain curve has to be determined experimentally for all non-radial loading conditions. The plasticity models including two surface models ae surveyed based on a yield surface and a bound surface that represent a state of maximum stress. This paper is concerned with the improvement of a plasticity models of the two-surface type for structural steel. This is follwed by an overview of plasticity models on structural steel. Finally the need for further research is identified.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.04a
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• pp.443-444
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• 2011

This paper discusses a model order reduction for large order rotor dynamics systems results from the finite element discretization. Typical rotor systems consist of a rotor, built-on parts, and a support system, and require prudent consideration in their dynamic analysis models because they include unsymmetric stiffness, localized nonproportional damping and frequency dependent gyroscopic effects. When the finite element model has a very large number of degrees of freedom because of complex geometry, repeated dynamic analyses to investigate the critical speeds, stability, and unbalanced response are computationally very expensive to finish within a practical design cycle. In this paper, the Krylov-based model order reduction via moment matching significantly speeds up the dynamic analyses necessary to check eigenvalues and critical speeds of a Nelson-Vaugh rotor system. With this approach the dynamic simulation is efficiently repeated via a reduced system by changing a running rotational speed because it can be preserved as a parameter in the process of model reduction. The Campbell diagram by the reduced system shows very good agreement with that of the original system. A 3-D finite element model of the Nelson-Vaugh rotor system is taken as a numerical example to demonstrate the advantages of this model reduction for rotor dynamic simulation.

• Structural Engineering and Mechanics
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• v.50 no.1
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• pp.19-36
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• 2014

This paper focuses on a model order reduction (MOR) for large-scale rotordynamic systems by using finite element discretization. Typical rotor-bearing systems consist of a rotor, built-on parts, and a support system. These systems require careful consideration in their dynamic analysis modeling because they include unsymmetrical stiffness, localized nonproportional damping, and frequency-dependent gyroscopic effects. Because of this complex geometry, the finite element model under consideration may have a very large number of degrees of freedom. Thus, the repeated dynamic analyses used to investigate the critical speeds, stability, and unbalanced response are computationally very expensive to complete within a practical design cycle. In this study, we demonstrate that a Krylov subspace-based MOR via moment matching significantly speeds up the rotordynamic analyses needed to check the whirling frequencies and critical speeds of large rotor systems. This approach is very efficient, because it is possible to repeat the dynamic simulation with the help of a reduced system by changing the operating rotational speed, which can be preserved as a parameter in the process of model reduction. Two examples of rotordynamic systems show that the suggested MOR provides a significant reduction in computational cost for a Campbell diagram analysis, while maintaining accuracy comparable to that of the original systems.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.11
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• pp.1907-1916
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• 2003

During decades, there has been much progress in understanding of the inelastic behavior of the materials and numerous inelastic constitutive equations have been developed. The complexity of these constitutive equations generally requires a stable and accurate numerical method. To obtain the increment of state variable, its evolution laws are linearized by several approximation methods, such as general midpoint rule(GMR) or general trapezoidal rule(GTR). In this investigation, semi-implicit integration schemes using GTR and GMR were developed and implemented into ABAQUS by means of UMAT subroutine. The comparison of integration schemes was conducted on the simple tension case, and simple shear case and nonproportional loading case. The fully implicit integration(FI) was the most stable but amplified the truncation error when the nonlinearity of state variable is strong. The semi-implicit integration using GTR gave the most accurate results at tension and shear problem. The numerical solutions with refined time increment were always placed between results of GTR and those of FI. GTR integration with adjusting midpoint parameter can be recommended as the best integration method for viscoplastic equation considering nonlinear kinematic hardening.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.4 no.2
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• pp.55-64
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• 1984

Presented is a nonlinear constitutive model for progressive tensile fracturing of concrete. The model is incremental, path-dependent, and tensorialy invariant. The total strain tensor is assumed to be a sum of a purely elastic component and an inelastic component. The material is considered to contain weak planes of all directions which characterize the planes of the microcracks. A one-to-one functional dependence is assumed between the normal stress and the normal strain across each of the weak planes. The tangential stiffness of concrete is then derived form the principle of virtual work. The present theory can be applied to loading histories which are nonproportional or during which the principal directions rotate. Good agreement with the available direct tensile test data which cover strain-softening is demonstrated.

• Korean Journal of Social Welfare
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• v.69 no.1
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• pp.33-57
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• 2017

This study examines the effect of working conditions for care workers on the care quality in long-term care facilities, particularly the coexisting perspective on publicness and the marketization of Long-term care services in South Korea brings about. Prior studies have not identified a causal relationship between working conditions and the care quality, only explained cause of a low-wage labor market and low productivity of social services. Theoretical relevance of working conditions and service quality on Long-term care in Korea is to view from a integrated care model by Daly and Lewis(2002). A nonproportional stratified sampling procedure was used to consider Long-term care facility's ownership. A merged dataset combining surveys from 248 Long-Term Care facilities and online resources from NHIC administrative was used and analyzed by multiple regression. The analysis results is showed as follows. Overall, organizations with better working conditions, having higher wage, having greater a fringe benefit, being skills development and training are likely to have good care quality in each area. This research shows that the working conditions, rewards and support to care workers of organizational culture in the normative dimension beyond the minimum standard on labor market policy and evaluation system by government regulations have a positive impact on Long-term care quality.