• Steel and Composite Structures
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• v.35 no.2
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• pp.249-260
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• 2020

The main purpose of this research work is to investigate the free vibration of conical shell structures reinforced by graphene platelets (GPLs) and the elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. To this end, a shell model is developed based on Donnell's theory. To solve the problem, the analytical Galerkin method is employed together with beam mode shapes as weighting functions. Due to importance of boundary conditions upon mechanical behavior of nanostructures, the analysis is carried out for different boundary conditions. The effects of boundary conditions, semi vertex angle, porosity distribution and graphene platelets on the response of conical shell structures are explored. The correctness of the obtained results is checked via comparing with existing data in the literature and good agreement is eventuated. The effectiveness and the accuracy of the present approach have been demonstrated and it is shown that the Donnell's shell theory is efficient, robust and accurate in terms of nanocomposite problems.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.823-824
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• 2018

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.4
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• pp.415-423
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• 2003

The hydrodynamic instability of the three-dimensional boundary-layer over a rotating disk has been numerically investigated for these flows; Ro = -1, -0.5, and 0, using linear stability theory. Detailed numerical values of the disturbance wave number. wave frequency. azimuth angle. radius (Reynolds number, Re) and other characteristics have been calculated for the pre-swirl flows. On the basis of Ekman and Karman boundary layer theory, the instability of the pre-swirl flows have been investigated for the unstable criteria. The disturbance will be relatively fast amplified at small fe and within wide bands of wave number compared with previously known Karman boundary-layer results. The flow (Ro =-0.5) is found to be always stable for a disturbance whose dimensionless wave number is greater than 0.9. It has a larger range of unstable interval than Karman boundary layer and can be unstable at smaller Re.

• Structural Engineering and Mechanics
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• v.72 no.6
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• pp.713-722
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• 2019

Micromechanics is a technique for the analysis of composites or heterogeneous materials which focuses on the components of the intended structure. Each one of the components can exhibit isotropic behavior, but the microstructure characteristics of the heterogeneous material result in the anisotropic behavior of the structure. In this research, the general mechanical properties of a 3D anisotropic and heterogeneous Representative Volume Element (RVE), have been determined by applying periodic boundary conditions (PBCs), using the Asymptotic Homogenization Theory (AHT) and strain energy. In order to use the homogenization theory and apply the periodic boundary conditions, the ABAQUS scripting interface (ASI) has been used along with the Python programming language. The results have been compared with those of the Homogeneous Boundary Conditions method, which leads to an overestimation of the effective mechanical properties. According to the results, applying homogenous boundary conditions results in a 33% and 13% increase in the shear moduli G₂₃ and G₁₂, respectively. In polymeric composites, the fibers have linear and brittle behavior, while the resin exhibits a non-linear behavior. Therefore, the nonlinear effects of resin on the mechanical properties of the composite material is studied using a user-defined subroutine in Fortran (USDFLD). The non-linear shear stress-strain behavior of unidirectional composite laminates has been obtained. Results indicate that at arbitrary constant stress as 80 MPa in-plane shear modulus, G₁₂, experienced a 47%, 41% and 31% reduction at the fiber volume fraction of 30%, 50% and 70%, compared to the linear assumption. The results of this study are in good agreement with the analytical and experimental results available in the literature.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.53-66
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• 2009

We show the existence of a nontrivial periodic solution for the superquadratic parabolic equation with Dirichlet boundary condition and periodic condition with a superquadratic nonlinear term at infinity which have continuous derivatives. We use the critical point theory on the real Hilbert space $L_2({\Omega}{\times}(0 2{\pi}))$. We also use the variational linking theorem which is a generalization of the mountain pass theorem.

• Korean Journal of Mathematics
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• v.20 no.2
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• pp.263-271
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• 2012

We investigate the number of the solutions for the biharmonic boundary value problem with a variable coefficient nonlinear term. We get a theorem which shows the existence of $m$ weak solutions for the biharmonic problem with variable coefficient. We obtain this result by using the critical point theory induced from the invariant function and invariant linear subspace.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.277-288
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• 2010

We consider the nonlinear biharmonic equation with coefficient exponential growth term and Dirichlet boundary condition. We show that the nonlinear equation has at least one bounded solution under the suitable conditions. We obtain this result by the variational method, generalized mountain pass theorem and the critical point theory of the associated functional.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.107-116
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• 2012

We investigate the multiple solutions for a class of the elliptic system with the singular potential nonlinearity. We obtain a theorem which shows the existence of the solution for a class of the elliptic system with singular potential nonlinearity and Dirichlet boundary condition. We obtain this result by using variational method and critical point theory.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.379-391
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• 2015

We investigate the existence of solutions of the nonlinear biharmonic equation with variable coefficient polynomial growth nonlinear term and Dirichlet boundary condition. We get a theorem which shows that there exists a bounded solution and a large norm solution depending on the variable coefficient. We obtain this result by variational method, generalized mountain pass geometry and critical point theory.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.208-213
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• 1992

In this paper we are concerned with optimal control problems whose costs am quadratic and whose states are governed by linear delay equations and general boundary conditions. The basic new idea of this paper is to Introduce a new class of linear operators in such a way that the state equation subject to a starting function can be viewed as an inhomogeneous boundary value problem in the new linear operator equation. In this way we avoid the usual semigroup theory treatment to the problem and use only linear operator theory.