• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.680-685
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• 1992

Solar arrays and antennas of the satellite are usually stowed within the dimensions of the launch-vehicle fairing and deployed in the orbit. To solve such multibody dynamic problems, differential equations and algebraic equations are simultaneously solved, and special solution techniques are required. In this paper, Lagrange multipliers associated with the constraints are iteratively computed by monotonically reducing an appropriately defined constraint error vector, and the resulting equation of motion is solved by a well-established ODE technique. Defomable bodies as well as rigid bodies are treated, and applications to satellite solar arrays are explained.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.27-40
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• 2017

In this paper, we construct exact traveling wave solutions of various kind of partial differential equations arising in mathematical science by the system technique. Further, the $Painlev{\acute{e}}$ test is employed to investigate the integrability of the considered equations. In particular, we describe the behaviors of the obtained solutions under certain constraints.

• Journal of KSNVE
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• v.4 no.4
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• pp.451-457
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• 1994

A numerical method is presented to obtain natural frequencies and mode shapes of uniform elastic beams with static deflections due to dead loads. The differential equation governing the free vibration of beam taken into account the static deflection due to deal loads is derived and solved numerically. The hinged-hinged, clamped-clamped and clamped-hinged end constraints are applied in the numerical examples. As the numerical results, the lowest three nondimensional frequency parameters are reported as functions of nondimensional system parameters; the load parameters, and the slenderness rations. And some typical mode shapes of free vibrations are also presented in figures.

• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.460-464
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• 2002

Multitemporal interferometric SAR has became an useful geodetic tool for monitoring Earth's surface deformation, generation of precise DEM, and land cover classification even though there still exist certain constraints such as temporal and spatial decorrelation effects, atmospheric artifacts and inaccurate orbit information. The Korea where nearly all areas are heavily vegetated, JERS-1 SAR has advantages in monitoring surface deformations and environmental changes in that it uses 4-times longer wavelength than ERS-l/2 or RADARSAT SAR system. For generating differential SAR interferogram and differential coherence image fer deformation mapping and temporal change detection, respectively, topographic phase removal process is required utilizing a reference inteferogram or external DEM simulation. Because the SAR antenna baseline parameter for JERS-1 is less accurate than those of ERS-l/2, one can not estimate topographic phases from an external DEM and the residual phase appears in differential interferogram. In this paper, we examined topographic phase retrieval method utilizing an external DEM. The baseline refinement is carried out by minimizing the differences between the measured unwrapped phase and the reference points of the DEM.

• Structural Engineering and Mechanics
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• v.59 no.6
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• pp.1139-1153
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• 2016

Elastic constraints are usually simplified as "spring forces" exerted on beam ends without considering the "spring deformation". The partial differential equation governing the free vibrations of a cantilever Bernoulli-Euler beam considering the deformation of elastic constraints is firstly established, and is nondimensionalized to obtain two dimensionless factors, $k_v$ and $k_r$, describing the effects of elastically vertical and rotational end constraints, respectively. Then the frequency equation for the above Bernoulli-Euler beam model is derived using the method of separation of variables. A numerical analysis method is proposed to solve the transcendental frequency equation for the continuous change of the frequency with $k_v$ and $k_r$. Then the mode shape functions are given. Finally, effects of $k_v$ and $k_r$ on free vibration characteristics of the beam with different slenderness ratios are calculated and analyzed. The results indicate that the effects of $k_v$ are larger on higher-order free vibration characteristics than on lower-order ones, and the impact strength decreases with slenderness ratio. Under a relatively larger slenderness ratio, the effects of $k_v$ can be neglected for the fundamental frequency characteristics, while cannot for higher-order ones. However, the effects of $k_r$ are large on both higher- and lower-order free vibration characteristics, and cannot be neglected no matter the slenderness ratio is large or small.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.9
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• pp.835-846
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• 2007

This paper deals with the flexural free vibrations of circular strip foundation with the variable breadth on Pasternak soil. The breadth of strip varies with the linear functional fashion, which is symmetric about the mid-arc. Differential equations governing flexural free vibrations of such strip foundation are derived, in which the elastic soil with the shear layer, i.e. Pasternak soil, is considered. Effects of the rotatory and shear deformation are included in the governing equations. Differential equations are numerically solved to calculate the natural frequencies and mode shapes. In the numerical examples, the hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. Four lowest frequency parameters accompanied with their corresponding mode shapes are reported and parametric studies between frequency parameters and various system parameters are investigated.

• Journal of Mechanical Science and Technology
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• v.16 no.8
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• pp.1072-1078
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• 2002

The constrained motion requires the determination of constraint force acting on unconstrained systems for satisfying given constraints. Most of the methods to decide the force depend on numerical approaches such that the Lagrange multiplier method, and the other methods need vector analysis or complicated intermediate process. In 1992, Udwadia and Kalaba presented the generalized inverse method to describe the constrained motion as well as to calculate the constraint force. The generalized inverse method has the advantages which do not require any linearization process for the control of nonlinear systems and can explicitly describe the motion of holonomically and/or nongolonomically constrained systems. In this paper, an explicit equation to describe the constrained motion is derived by minimizing the performance index, which is a function of constraint force vector, with respect to the constraint force. At this time, it is shown that the positive-definite weighting matrix in the performance index must be the inverse of mass matrix on the basis of the Gauss's principle and the derived differential equation coincides with the generalized inverse method. The effectiveness of this method is illustrated by means of two numerical applications.

• Steel and Composite Structures
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• v.27 no.3
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• pp.297-310
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• 2018

A simple and efficient numerical optimization approach for the lightweight optimal design of composite laminated beams is presented in this paper. The proposed procedure is a combination between the finite element method (FEM) and a global optimization algorithm developed recently, namely Jaya. In the present procedure, the advantages of FEM and Jaya are exploited, where FEM is used to analyze the behavior of beam, and Jaya is modified and applied to solve formed optimization problems. In the optimization problems, the objective aims to minimize the overall weight of beam; and fiber volume fractions, thicknesses and fiber orientation angles of layers are selected as design variables. The constraints include the restriction on the first fundamental frequency and the boundaries of design variables. Several numerical examples with different design scenarios are executed. The influence of the design variable types and the boundary conditions of beam on the optimal results is investigated. Moreover, the performance of Jaya is compared with that of the well-known methods, viz. differential evolution (DE), genetic algorithm (GA), and particle swarm optimization (PSO). The obtained results reveal that the proposed approach is efficient and provides better solutions than those acquired by the compared methods.

• Steel and Composite Structures
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• v.51 no.4
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• pp.363-375
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• 2024

Within the optimization field, addressing the intricate posed by fluidic pressure loads on functionally graded structures with frequency-related designs is a kind of complex design challenges. This paper thus introduces an innovative density-based topology optimization strategy for frequency-constraint functionally graded structures incorporating Darcy's law and a drainage term. It ensures consistent treatment of design-dependent fluidic pressure loads to frequency-related structures that dynamically adjust their direction and location throughout the design evolution. The porosity of each finite element, coupled with its drainage term, is intricately linked to its density variable through a Heaviside function, ensuring a seamless transition between solid and void phases. A design-specific pressure field is established by employing Darcy's law, and the associated partial differential equation is solved using finite element analysis. Subsequently, this pressure field is utilized to ascertain consistent nodal loads, enabling an efficient evaluation of load sensitivities through the adjoint-variable method. Moreover, this novel approach incorporates load-dependent structures, frequency constraints, functionally graded material models, and polygonal meshes, expanding its applicability and flexibility to a broader range of engineering scenarios. The proposed methodology's effectiveness and robustness are demonstrated through numerical examples, including fluidic pressure-loaded frequency-constraint structures undergoing small deformations, where compliance is minimized for structures optimized within specified resource constraints.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.548-555
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• 2005

Since soil-structure interactions are one of the most important subjects in the structural/foundation engineering, much study concerning the soil-structure interactions had been carried out. One of typical structures related to the soil-structure interactions is the strip foundation which is basically defined as the beam or strip rested on or supported by the soils. At the present time, lack of studies on dynamic problems related to the strip foundations is still found in the literature. From these viewpoint, this paper aims to theoretically investigate dynamics of the elliptic strip foundations and also to present the practical engineering data for the design purpose. Differential equations governing the free, out-of-plane vibrations of such sap foundations we derived, in which effects of the rotatory and torsional inertias and also shear deformation are included although the warping of the cross-section is excluded. Governing differential equations subjected to the boundary conditions of free-free end constraints are numerically solved for obtaining the natural frequencies and mode shapes by using the numerical integration technique and the numerical method of non-linear equation.