• Proceedings of the KSME Conference
• /
• 2001.11a
• /
• pp.341-348
• /
• 2001

A Mixed Volume and Boundary Integral Equation Method is applied for the effective analysis of plane elastostatic problems in unbounded solids containing general anisotropic inclusions and voids or isotropic inclusions. It should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. This new method can also be applied to general two-dimensional elastodynamic and elastostatic problems with arbitrary shapes and number of anisotropic inclusions and voids or isotropic inclusions. Through the analysis of plane elastostatic problems in unbounded isotropic matrix with orthotropic inclusions and voids or isotropic inclusions, it will be established that this new method is very accurate and effective for solving plane elastic problems in unbounded solids containing general anisotropic inclusions and voids or isotropic inclusions.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.2 no.1
• /
• pp.111-129
• /
• 1998

An integral equation representation of cracks was presented, which differs from well-known "dislocation layer" representation. In this new representation, an integral equation representation of cracks was developed and coupled to the direct boundary-element method for treatment of cracks in plane finite bodies. The method was developed for in-plane(modes I and II) loadings only. In this paper, the method is formulated and applied to mode III problems involving smooth or kinked cracks in finite region. The results are compared to exact solutions where available and the method is shown to be very accurate despite of its simplicity.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.183-196
• /
• 2005

In this paper we study the chromatic sum functions for rooted nonseparable near-triangular maps on the projective plane. A chromatic sum equation for such maps is obtained.

• Steel and Composite Structures
• /
• v.21 no.5
• /
• pp.963-980
• /
• 2016

The jib system with middle strut is widely used to achieve the large arm length in the large scale tower crane and the deployability in the mobile construction crane. In this paper, an analytical solution for the out-of-plane buckling of the jib system with middle strut is proposed. To obtain the analytical expression of the buckling characteristic equation, the method of differential equation was adopted by establishing the bending and torsional differential equation of the jib system under the instability critical state. Compared with the numerical solutions of the finite element software ANSYS, the analytical results in this work agree well with them. Therefore, the correctness of the results in this work can be confirmed. Then the influences of the lateral stiffness of the cable fixed joint, the dip angle of the strut, the inertia moment of the strut, and the horizontal position of the cable fixed joint on the out-of-plane buckling behavior of the jib system were investigated.

• Journal of the Korean Mathematical Society
• /
• v.41 no.3
• /
• pp.535-565
• /
• 2004

In this paper we consider the notion of ξ-invariant or (equation omitted)-invariant real hypersurfaces in a complex two-plane Grassmannian $G_2$( $C^{m+2}$) and prove that there do not exist such kinds of real hypersurfaces in $G_2$( $C^{m+2}$) with parallel second fundamental tensor on a distribution ζ defined by ζ = ξ U(equation omitted), where(equation omitted) = Span ｛ξ$_1$, ξ$_2$, ξ$_3$｝.X>｝.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.4
• /
• pp.775-786
• /
• 2002

A Mixed Volume and Boundary Integral Equation Method is applied for the effective analysis of elastic wave scattering problems and plane elastostatic problems in unbounded solids containing general anisotropic inclusions and voids or isotropic inclusions. It should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. This new method can also be applied to general two-dimensional elastodynamic and elastostatic problems with arbitrary shapes and number of anisotropic inclusions and voids or isotropic inclusions. In the formulation of this method, the continuity condition at each interface is automatically satisfied, and in contrast to finite element methods, where the full domain needs to be discretized, this method requires discretization of the inclusions only. Finally, this method takes full advantage of the pre- and post-processing capabilities developed in FEM and BIEM. Through the analysis of plane elastostatic problems in unbounded isotropic matrix with orthotropic inclusions and voids or isotropic inclusions, and the analysis of plane wave scattering problems in unbounded isotropic matrix with isotropic inclusions and voids, it will be established that this new method is very accurate and effective for solving plane wave scattering problems and plane elastic problems in unbounded solids containing general anisotropic inclusions and voids/cracks or isotropic inclusions.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.5
• /
• pp.952-959
• /
• 2002

The natural frequencies of a flexible spinning disk misaligned with the axis of rotation are studied in an analytic manner. The effects of misalignment on the natural frequency need to be investigated, because the misalignment between the axis of symmetry and the axis of relation cannot be avoided in the removable disks such as CD-R, CD-RW or DVD disks. Assuming that the in -plane displacements are in steady state and the out-of-plane displacement is in dynamic state, the equations of motion are derived for the misaligned spinning disk. After the exact solutions are obtained fur the steady -state in-plane displacements, they are plugged into the equation for the dynamic-state out-of-plane motion. The resultant equation is a linear equation for the out -of-plane displacement, which is discretized by the Galerkin method. Based on the discretized dquations, the effects of the misalignment are analyzed on the vibration characteristics of the spinning disk, i.e., the natural frequencies and the critical speed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.11b
• /
• pp.817-825
• /
• 2001

The natural frequencies of a flexible spinning disk misaligned with the axis of rotation are studied in an analytic manner. The effects of misalignment on the natural frequency need to be investigated, because the misalignment between the axis of symmetry and the axis of rotation cannot be avoided in the removable disks such as CD-R, CD-RW or DVD disks. Assuming that the in-plane displacements are in steady state and the out-of-plane displacement is in dynamic state, the equations of motion are derived for the misaligned spinning disk. After the exact solutions are obtained for the steady-state in-plane displacements, they are plugged into the equation for the dynamic-state out-of-plane motion. The resultant equation is a linear equation for the out-of-plane displacement, which is discretized by the Galerkin method. Based on the discretized equations, the effects of the misalignment are analyzed on the vibration characteristics of the spinning disk, i.e., the natural frequencies and the critical speed

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.20 no.2
• /
• pp.127-136
• /
• 2007

In this paper, the equations of the scaled boundary finite element method are derived for non-homogeneous half plane and analyzed numerically In the scaled boundary finite element method, partial differential equations are weaken in the circumferential direction by approximation scheme such as the finite element method, and the radial direction of equations remain in analytical form. The scaled boundary equations of non-homogeneous half plane, its elastic modulus varies as power function, are newly derived by the virtual work theory. It is shown that the governing equation of this problem is the Euler-Cauchy equation, therefore, the logarithm mode used in the half plane problem is not valid in this problem. Two numerical examples are analysed for the verification and the feasibility.

• Journal of KSNVE
• /
• v.10 no.5
• /
• pp.849-858
• /
• 2000

In this paper the chaotic out-of-plane vibrations of the uniformly curved pipe with pulsating flow are theoretically investigated. The derived equations of motion contain the effects of nonlinear curvature and torsional coupling. The corresponding nonlinear ordinary differential equation is a type of nonhomogenous Hill's equation . this is transformed into the averaged equation by averaging theorem. Bifurcation curves of chaotic motion are obtained by Melnikov's method and plotted in several cases of frequency ratios. The theoretically obtained results are demonstrated by numerical simulation. And strange attractors are shown.