• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.10
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• pp.2457-2466
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• 1993

A simple method is presented for determining transient responses of locally nonlinear structures using substructure eigenproperties and Lagrange multiplier technique. Although the method is based upon the mode synthesis formulation procedure, the equations of the combined whole structure are not constructed compared with the conventional methods. Lagrange multi-pliers are used to enforce the conditions of geometric compatibility between the substructure interfaces and they are treated as external forces on each substructure itself. Substructure eigenvalue problem is defined with the substructure interface free of fixed. The transient analysis is based upon the recurrence discrete-time state equations and offers the simplicity of the Euler integration method without requiring small time increment and iterative solution procedure. Numerical examples reveal that the method is very accurated and efficient in calculating transient responses compared with the direct numerical integration method.

• Interaction and multiscale mechanics
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• v.1 no.3
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• pp.329-337
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• 2008

This paper presents the derivation of the generalized governing equations in theory of elasticity, their weak forms and the some applications in the numerical analysis of structural mechanics. Unlike the differential equations in classical elasticity theory, the generalized equations of the equilibrium and compatibility equations presented here take the form of integral equations, and the generalized equilibrium equations contain the classical differential equations and the boundary conditions in a single equation. By using appropriate test functions, the weak forms of these generalized governing equations can be established. It can be shown that various variational principles in structural analysis are merely the special cases of these weak forms of generalized governing equations in elasticity. The present weak forms of elasticity equations extend greatly the choices of the trial functions for approximate solutions in the numerical analysis of various engineering problems. Therefore, the weak forms of generalized governing equations in elasticity provide a powerful modeling tool in the computational structural mechanics.

• Journal of Powder Materials
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• v.6 no.1
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• pp.18-35
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• 1999

Phase equilibria in the system Si3N4-TiC-TiCxN1-x-C-N were determined by thermodynamic calculations (CALPHAD-method). The reaction peaction paths for Si3N4-TiC and SiC-TiC composites in the Ti-Si-C-n system were simulated at I bar N2-pressure and varying terpreatures. At a temperature of 1923 K two tie-triangles (TiC0.34N0.66+SiC+C and TiC0.13N0.87+SiC+Si3N4) and two 2-phase fieds (TiCxN1-x+SiC; 0.13

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.5
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• pp.1138-1149
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• 1993

A new mode synthesis method using Lagrange multipliers and substructure hybrid interface modes is presented. Substruture governing equations of motion are derived using Lagrange equations and the constraints of geometric compatibility between the substructures are treated with Lagrange multipliers. Fixed, free, and loaded interface modes can be employed for the modal bases of each substructure. In cases of the fixed and loaded interface modes, two successive modal transformation relations are used. Compared with the conventional mode synthesis methods, the suggested method does not construct the equations of motion of the coupled structure and the final characteristic equation becomes a polynomial. Only modal parameters of each substructure and geometric compatibility conditions are needed. The suggested method is applied to a simple lumped mass model and parametric study is performed.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.410-415
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• 2001

An analytical and numerical examination of second-order fractional-step methods and boundary condition for the incompressible Navier-Stokes equations is presented. In this study, the compatibility condition for pressure Poisson equation and its boundary conditions, stability, and numerical accuracy of canonical fractional-step methods has been investigated. It has been found that satisfaction of compatibility condition depends on tentative velocity and pressure boundary condition, and that the compatible boundary conditions for type D method and approximately compatible boundary conditions for type P method are proper for divergence-free velocity for type D and approximately divergence-free for type P method. Instability of canonical fractional-step methods is induced by approximation of implicit viscous term with explicit terms, and the stability criteria have been founded with simple model problems and numerical experiments of cavity flow and Taylor vortex flow. The numerical accuracy of canonical fractional-step methods with its consistent boundary conditions shows second-order accuracy except $D_{MM}$ condition, which make approximately first-order accuracy due to weak coupling of boundary conditions.

• Structural Engineering and Mechanics
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• v.13 no.3
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• pp.329-343
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• 2002

In this research, the dynamic stability of an orthotropic elastic conical shell, with elasticity moduli and density varying in the thickness direction, subject to a uniform external pressure which is a power function of time, has been studied. After giving the fundamental relations, the dynamic stability and compatibility equations of a nonhomogeneous elastic orthotropic conical shell, subject to a uniform external pressure, have been derived. Applying Galerkin's method, these equations have been transformed to a pair of time dependent differential equations with variable coefficients. These differential equations are solved using the method given by Sachenkov and Baktieva (1978). Thus, general formulas have been obtained for the dynamic and static critical external pressures and the pertinent wave numbers, critical time, critical pressure impulse and dynamic factor. Finally, carrying out some computations, the effects of the nonhomogeneity, the loading speed, the variation of the semi-vertex angle and the power of time in the external pressure expression on the critical parameters have been studied.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.28 no.5
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• pp.391-399
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• 2017

At present the general trend of modern electronics is toward smaller packages and high performance. As an antenna requires high powers, the EMC(Electromagnetic Compatibility) problems of the transmission line stage is becoming crucial day by day. In this paper, a transmission line excited by the electromagnetic fields from an infinitesimal electric dipole antenna is analyzed using the modified telegrapher's equations. The analytical equations are derived for arbitrarily positioned electric dipole with reference to a transmission line. To verify our approach, the induced voltage and current at the terminal were computed by the proposed approach and compared with those obtained by the electromagnetic simulation solver. Furthermore, the induced currents at the terminal of a transmission line excited by the electric dipoles at various positions were investigated using our approach.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.1
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• pp.49-60
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• 2014

For simple and accurate analysis for behaviors of multi-span suspension bridges which are expected to be frequently constructed as strait-crossing bridges, the deflection theory as the peculiar theory of a suspension bridge can be applied. This paper performs a structural analysis for four-span suspension bridges using the deflection theory. Simply-supported beams with tension are used for girders and the deflections of the beams due to the vertical loads and moments at supports are calculated. The calculation is performed iteratively until the deflections satisfy the compatibility equations of cables. The results of the deflection theory analysis considering tower rigidity are compared with those of the finite element analysis for verification. Importance of the tower rigidity for four-span suspension bridges is confirmed using various compatibility equations of the cable due to variation of the constraint conditions between main cable and top of towers. In addition, the simple parametric analysis for variation of the center tower rigidity is performed.

• Structural Engineering and Mechanics
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• v.14 no.6
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• pp.661-677
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• 2002

The subject of this investigation is to study the buckling of cross-ply laminated orthotropic cylindrical thin shells with variable elasticity moduli and densities in the thickness direction, under external pressure, which is a power function of time. The dynamic stability and compatibility equations are obtained first. These equations are subsequently reduced to a system of time dependent differential equations with variable coefficients by using Galerkin's method. Finally, the critical dynamic and static loads, the corresponding wave numbers, the dynamic factors, critical time and critical impulse are found analytically by applying a modified form of the Ritz type variational method. The dynamic behavior of cross-ply laminated cylindrical shells is investigated with: a) lamina that present variations in the elasticity moduli and densities, b) different numbers and ordering of layers, and c) external pressures which vary with different powers of time. It is concluded that all these factors contribute to appreciable effects on the critical parameters of the problem in question.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.167-174
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• 2005

Through time-dependent analyses of RC bridges constructed by a movable scaffolding system (MSS) considering the construction sequence and creep deformation of concrete, structural responses related to the member forces are reviewed. On the basis of the compatibility condition and equilibrium equation at every construction stage, basic equations that can describe the moment variation with time in movable scaffolding construction are derived. By using the introduced relations, the design moment and its variation over time can easily be obtained with only the elastic analysis results and without additional time-dependent analyses considering the construction sequences. In addition, the design moments determined by the introduced equations are compared with the results from a rigorous numerical analysis with the objective of establishing the relative efficiencies of the introduced equations.