• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1365-1374
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• 2023

Let F be a periodic singular fiber of genus g with dual fiber F^*, and let T (resp. T^*) be the set of the components of F (resp. F^*) by removing one component with multiplicity one. We give a formula to compute the determinant | det T | of the intersect form of T. As a consequence, we prove that | det T | = | det T^*|. As an application, we compute the Mordell-Weil group of a fibration f : S → ℙ¹ of genus 2 with two singular fibers.

• Computational Structural Engineering
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• v.9 no.4
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• pp.181-187
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• 1996

This paper concerns the singular thermal stresses at the interface corner between the elastic fiber and the viscoelastic matrix of a two-dimensional unidirectional laminate model induced during cooling from cure temperature down to room temperature. Time-domain boundary element method is employed to investigate the nature of residual thermal stresses at the interface. Numerical results show that very large stress gradients are present at the interface corner and such stress singularity might lead to local yielding or fiber-matrix debonding.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.4
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• pp.887-902
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• 1994

Within the framework of anisotropic thermoelasticity, the problem of an interlaminar crack in a laminated fiber-reinforced composite subjected to a uniform heat flow is investigated. Under a state of generalized plane deformation, dissimilar anisotropic half-spaces with different fiber orientations are considered to be bound together by a matrix interlayer containing the crack. The interlayer models the matrix-rich interlaminar region of the fibrous composite laminate. Based on the flexibility/stiffness matrix approach, formulation of the current crack problem results in having to solve two sets of singular integral equations for temperature and thermal stress analyses. Numerical results are obtained, illustrating the parametric effects of laminate stacking sequence, relative crack size, crack location, crack surface partial insulation, and fiber volume fraction on the values of mixed mode thermal stress intensity factors.

• Structural Engineering and Mechanics
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• v.5 no.6
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• pp.705-713
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• 1997

The residual thermal stresses at the interface corner between the elastic fiber and the viscoelastic matrix of a two-dimensional unidirectional laminate due to cooling from cure temperature down to room temperature were studied. The matrix material was assumed to be thermorheologically simple. The time-domain boundary element method was employed to investigate the nature of stresses on the interface. Numerical results show that very large stress gradients are present at the interface corner and this stress singularity might lead to local yielding or fiber-matrix debonding.

• Journal of Aerospace System Engineering
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• v.1 no.1
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• pp.25-35
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• 2007

In this paper, the interlaminar crack problems of a fiber metal laminate (FML) under generalized plane deformation are studied using the theory of anisotropic elasticity. The crack is considered to be embedded in the matrix interlaminar region (including adhesive zone and resin rich zone) of the FML. Based on Fourier integral transformation and the stress matrix formulation, the current mixed boundary value problem is reduced to solving a system of Cauchy-type singular integral equations of the 1st kind. Within the theory of linear fracture mechanics, the stress intensity factors are defined on terms of the solutions of integral equations and numerical results are obtained for in-plane normal (mode I) crack surface loading. The effects of location and length of crack in the 3/2 and 2/1 ARALL, GLARE or CARE type FML's on the stress intensity factors are illustrated.

• Steel and Composite Structures
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• v.7 no.5
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• pp.355-376
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• 2007

The purpose of this study is to predict and investigate the time-dependent creep behavior of composite materials. For this, firstly the evaluation method for the modulus of elasticity of whole fiber and matrix is presented from the limited information on fiber volume fraction using the singular value decomposition method. Then, the effects of fiber volume fraction on modulus of elasticity of GFRP are verified. Also, as a creep model, the nonlinear curve fitting method based on the Marquardt algorithm is proposed. Using the existing Findley's power creep model and the proposed creep model, the effect of fiber volume fraction on the nonlinear creep behavior of composite materials is verified. Then, for the time-dependent analysis of a composite material subjected to uniaxial tension and simple shear loadings, a user-provided subroutine UMAT is developed to run within ABAQUS. Finally, the creep behavior of center loaded beam structure is investigated using the Hermitian beam elements with shear deformation effect and with time-dependent elastic and shear moduli.

• International Journal of Precision Engineering and Manufacturing
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• v.1 no.2
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• pp.76-83
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• 2000

A study on the robust control of a composite beam with a distributed PVDF sensor and piezo-ceramic actuator is presented in this paper. $1^{st}$ and $2^{nd}$ natural frequencies are considered in the modeling, because robust control theory which has robustness to structured uncertainty is adopted to suppress the vibration. If the controllers designed by $H_{\infty}$ theory do not satisfy control performance, it is improved by $\mu$-synthesis method with D-K iteration so that the $\mu$-controller based on the structured singular value satisfies the nominal performance and robust performance. Simulation and experiment were carried out with the designed controller and the verification of the robust control properties was presented by results.

• Computational Structural Engineering
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• v.10 no.1
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• pp.129-134
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• 1997

Interfacial stress singularity in a unidirectional two-dimensional laminate model consisting of an elastic fiber and a viscoelastic matrix has been investigated using the time-domain boundary element method. First, the interfacial singular stresses between the fiber and the matrix of a unidirectional laminate subjected to a uniform transverse tensile strain have been investigated near the free surface, but without any defect or any edge crack. Such a stress singularity might lead to fiber-matrix debonding or interfacial edge cracks. Then, the overall stress intensity factor for the case of a small interfacial edge crack of length a has been computed.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.11-14
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• 2000

This paper presents the vibration control of a glass-fiber reinforced thermoplastic composite beam with a distributed PVDF sensor and piezo-ceramic achlator. The three types of different controllen which are PID, H$\infty$ , and p-synthesis ontrollcr are employed to achieve vibration suppression in the transient vibration of composite beam. In the H$\infty$ , controller design, 1st and 2nd natural frequencies are considered in the modeling, because robust control theory which has robustness to struchred uncertainty is adopled Lo suppress the vibration. If the controller designed by H$\infty$ , theory does not satisfy control performance, it is improved by $\mu$ -synthesis method with D-K iteration so that the$\mu$-contoller based on the structured singular value satisfies the nominal performance and robust performance Simulations and experiments were carried out with the designed controllers m order to demonstrate the suppression efficiency of each controller.

• Advances in nano research
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• v.9 no.4
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• pp.295-307
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• 2020

The vibrational characteristics of Multi-Phase Nanocomposite (MPC) reinforced annular/circular plate under initially stresses are presented using the state-space formulation based on three-dimensional elasticity theory (3D-elasticity theory) and Differential Quadrature Method (DQM). The MPC reinforced annular/circular plate is under initial lateral stress and composed of multilayers with Carbon Nanotubes (CNTs) uniformly dispersed in each layer, but its properties change layer-by-layer along the thickness direction. The State-Space based Differential Quadrature Method (SS-DQM) is presented to examine the frequency behavior of the current structure. Halpin-Tsai equations and fiber micromechanics are used in the hierarchy to predict the bulk material properties of the multi-scale composite. A singular point is investigated for modeling the circular plate. The CNTs are supposed to be randomly oriented and uniformly distributed through the matrix of epoxy resin. Afterward, a parametric study is done to present the effects of various types of sandwich circular/annular plates on frequency characteristics of the MPC reinforced annular/circular plate using 3D-elasticity theory.