• The Pure and Applied Mathematics
• /
• v.6 no.1
• /
• pp.27-32
• /
• 1999

In this paper, we show that the existence of the solutions to the variational-type inequalities for set-valued mappings on normed linear spaces using Fan's section theorem.

• Communications of Mathematical Education
• /
• v.8
• /
• pp.273-278
• /
• 1999

In this paper, we consider the existence of solutions to the variational-type inequalities for single-valued mappings and set-valued mappings on reflexive Banach spaces using Fan's section theorem.

• Advances in aircraft and spacecraft science
• /
• v.1 no.1
• /
• pp.93-123
• /
• 2014

A variational asymptotic composite beam model has been developed for thermoelastic analysis. Composite beams, including sandwich structure and laminates, under different boundary conditions are examined. Previously developed beam model, which is based on variational-asymptotic method, is extended to incorporate temperature-dependent materials experiencing large temperature changes. The recovery relations have been derived so that the temperatures, heat fluxes, stresses, and strains can be recovered over the cross-section. The present theory is implemented into the computer program VABS (Variational Asymptotic Beam Sectional analysis). Numerical results are compared with the 3D analysis for the purpose of demonstrating advantages of the present theory and use of VABS.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
• /
• 1999.10a
• /
• pp.351-356
• /
• 1999

In this study, the characteristics of chip formation of the cold drawn Bi-S free machining steels were assessed. And for comparison, those of the cold drawn Pb-S free machining steel, the hot rolled low carbon steel which has MnS as free machining inclusions and the conventional steels were also investigated. During chip formation, the cold drawn free machining steels show relatively little change in thickness and width of chip compare to those of the conventional carbon steels. And a single parameter which indicates the degree of deformation during chip formation, 'chip cross-section area ratio' is introduced. The chip cross-section area. The variational patterns of cross-section area is divided by undeformed chip cross-section area. The variational patterns of the chip cross-section area ratio of the materials cut are similar to those of the shear strain values. The shear stress, however, seems to be dependent on the carbon content of the materials. The cold drawn BiS and Pb-S steels show nearly the same chip forming behaviors and the energy consumed during chip formation is almost same. A low carbon steel without free machining aids shows poor chip breakability due to its high ductility. By introducing a small amount of non-metallic inclusions such as MnS, Bi, Pb or merely increasing carbon content the chip breakability improves significantly.

• Composites Research
• /
• v.30 no.6
• /
• pp.343-349
• /
• 2017

A multifield variational formulation is developed for the finite element (FE) cross-sectional analysis of composite beams. The cross-sectional warping displacements and sectional stresses are considered to be the primary variables through the application of Reissner's partially mixed principle. The warping displacements are modeled using generic FE shape functions with nonlinear distribution over the beam section. A generalized Timoshenko level stiffness matrix is derived which incorporates the effects of elastic couplings, transverse shear, and Poisson's deformations. The accuracy of the present analysis is validated for the stiffness constants and elastostatic responses of composite box beams which correlate well with the experimental data and other state-of-the-art approaches.

• Bulletin of the Korean Mathematical Society
• /
• v.26 no.2
• /
• pp.139-149
• /
• 1989

pp.Hartman and G. Stampacchia [6] proved the following theorem in 1966: If f:X.rarw. $R^{n}$ is a continuous map on a compact convex subset X of $R^{n}$ , then there exists $x_{0}$ ..mem.X such that $x_{0}$ , $x_{0}$ -x>.geq.0 for all x.mem.X. This remarkable result has been investigated and generalized by F.E. Browder [1], [2], W. Takahashi [9], S. Park [8] and others. For example, Browder extended this theorem to a map f defined on a compact convex subser X of a topological vector space E into the dual space $E^{*}$; see [2, Theorem 2]. And Takahashi extended Browder's theorem to closed convex sets in topological vector space; see [9, Theorem 3]. In Section 2, we obtain some variational inequalities, especially, generalizations of Browder's and Takahashi's theorems. The generalization of Browder's is an earlier result of the first author [8]. In Section 3, using Theorem 1, we improve and extend some known fixed pint theorems. Theorems 4 and 8 improve Takahashi's results [9, Theorems 5 and 9], respectively. Theorem 4 extends the first author's fixed point theorem [8, Theorem 8] (Theorem 5 in this paper) which is a generalization of Browder [1, Theroem 1]. Theorem 8 extends Theorem 9 which is a generalization of Browder [2, Theorem 3]. Finally, in Section 4, we obtain variational inequalities for multivalued maps by using Theorem 1. We improve Takahashi's results [9, Theorems 21 and 22] which are generalization of Browder [2, Theorem 6] and the Kakutani fixed point theorem [7], respectively.ani fixed point theorem [7], respectively.

• Journal of Aerospace System Engineering
• /
• v.2 no.1
• /
• pp.7-12
• /
• 2008

The three-dimensional finite element modeling of a composite rotor blade is very hard and requires much computation effort. The efficient method to model a composite beam is necessary for the dynamic and aeroelastic analyses of rotor blades. In this study, the beam modeling method of a composite rotor blade is studied using VABS. The computer program, VABS (Variational Asymptotic Beam Section Analysis), uses the variational asymptotic method to split a 3-D nonlinear elasticity problem into 2-D cross-sectional analysis and 1-D nonlinear beam problem. The VABS can produce the sectional stiffness coefficients of composite rotor blades with various cross section and initial twist/curvatures, and recover the original 3-D distribution of displacement/strain/stress fields. The results of various cross section beams show that VABS gives us the accurate results comparared to commercial codes and does not need much computation effort. It can be concluded that VABS provides the efficient method to establish the FE model of a composite rotor blade.

• Honam Mathematical Journal
• /
• v.26 no.4
• /
• pp.533-547
• /
• 2004

In this paper, we introduce two kinds of generalized vector quasivariational-like inequalities for multivalued mappings and show the existence of solutions to those variational inequalities under compact and non-compact assumptions, respectively.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.41 no.4
• /
• pp.275-283
• /
• 2013

In this paper, the structural optimum design method of composite rotor blade cross-section was investigated with the genetic algorithm. An auto-mesh generation program was developed for iterative calculations of optimum design, and stresses in the blade cross-section were analyzed by VABS (variational asymptotic beam sectional analysis) program. Minimum mass of rotor blade was defined as an object function, and stress failure index, center mass and blade minimum mass per unit length were chosen as constraints. Finally, design parameters such as the thickness and layup angles of a skin, and the thickness, position and width of a torsion box were determined through the structural optimum design method of composite rotor blade cross-section presented in this paper.

• International Journal of Aeronautical and Space Sciences
• /
• v.18 no.3
• /
• pp.467-473
• /
• 2017

This paper focuses on the investigation of three-dimensional (3D) warping effect on the stiffness constants of composite beams with closed section profiles. A finite element (FE) cross-sectional analysis is developed based on the Reissner's multifield variational principle. The 3D in-plane and out-of-plane warping displacements, and sectional stresses are approximated as linear functions of generalized sectional stress resultants at the global level and as FE shape functions at the local sectional level. The classical elastic couplings are taken into account which include transverse shear and Poisson deformation effects. A generalized Timoshenko level $6{\times}6$ stiffness matrix is computed for closed section composite beams with and without warping. The effect of neglecting the 3D warping on stiffness constants is shown to be significant indicating large errors as high as 93.3%.