• Bulletin of the Korean Chemical Society
• /
• v.33 no.3
• /
• pp.1071-1074
• /
• 2012

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.31 no.1
• /
• pp.34-41
• /
• 2003

A Green's function approach is adopted for analyzing the thermoelastic deformation and stress analysis of a plate made of functionally graded materials (FGMs). The solution to the 3-dimensional steady temperature is obtained by using the laminate theory. The fundamental equations for thermoelastic problems are derived in terms of out-plane deformation and in-plane force, separately. The thermoelastic deformation and the stress distributions due to the bending and in-plane forces are analyzed by using a Green’Às function based on the Galerkin method. The eigenfunctions of the Galerkin Green's function for the thermoelastic deformation and the stress distributions are approximated in terms of a series of admissible functions that satisfy the homogeneous boundary conditions of the rectangular plate. Numerical examples are carried out and effects of material properties on thermoelastic behaviors are discussed.

• Structural Engineering and Mechanics
• /
• v.31 no.6
• /
• pp.737-749
• /
• 2009

The problem of estimating the dynamic response of a distributed parameter system excited by a moving vehicle with random initial velocity and random vehicle body mass is investigated. By adopting the Galerkin's method and modal analysis, a set of approximate governing equations of motion possessing time-dependent uncertain coefficients and forcing function is obtained, and then the dynamic response of the coupled system can be calculated in deterministic sense. The statistical characteristics of the responses of the system are computed by using improved perturbation approach with respect to mean value. This method is simple and useful to gather the stochastic structural response due to the vehicle-passenger-bridge interaction. Furthermore, some of the statistical numerical results calculated from the perturbation technique are checked by Monte Carlo simulation.

• Advances in nano research
• /
• v.7 no.5
• /
• pp.311-324
• /
• 2019

The present study aims to evaluate the nonlinear and post-buckling behaviors of orthotropic graphene sheets exposed to end-shortening strain by implementing a semi-Galerkin technique, as a new approach. The nano-sheets are regarded to be on elastic foundations and different out-of-plane boundary conditions are considered for graphene sheets. In addition, nonlocal elasticity theory is employed to achieve the post-buckling behavior related to the nano-sheets. In the present study, first, out-of-plane deflection function is considered as the only displacement field in the proposed technique, which is hypothesized by an appropriate deflected form. Then, the exact nonlocal stress function is calculated through a complete solution of the von-Karman compatibility equation. In the next step, Galerkin's method is used to solve the unknown parameters considered in the proposed technique. In addition, three different scenarios, which are significantly different with respect to concept, are used to satisfy the natural in-plane boundary conditions and completely attain the stress function. Finally, the post-buckling behavior of thin graphene sheets are evaluated for all three different scenarios, and the impacts of boundary conditions, polymer substrate, and nonlocal parameter are examined in each scenario.

• Journal of the Korean Mathematical Society
• /
• v.61 no.4
• /
• pp.621-657
• /
• 2024

In this study, the numerical solution of a space-fractional Burgers' equation with initial and boundary conditions is considered. This equation is the simplest nonlinear model for diffusive waves in fluid dynamics. It occurs in a variety of physical phenomena, including viscous sound waves, waves in fluid-filled viscous elastic pipes, magneto-hydrodynamic waves in a medium with finite electrical conductivity, and one-dimensional turbulence. The proposed QBS/CNG technique consists of the Galerkin method with a function basis of quadratic B-splines for the spatial discretization of the space-fractional Burgers' equation. This is then followed by the Crank-Nicolson approach for time-stepping. A linearized scheme is fully constructed to reduce computational costs. Stability analysis, error estimates, and convergence rates are studied. Finally, some test problems are used to confirm the theoretical results and the proposed method's effectiveness, with the results displayed in tables, 2D, and 3D graphs.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.19 no.12
• /
• pp.32-40
• /
• 2018

In order to avoid excessive vibration, it is required to carry out a vibration analysis of heat-exchanger/nuclear-reactor at the design stage. Information of eigen-frequency in the vibration problem is required to evaluate safety of heat-exchange/nuclear reactor. This paper describes a numerical method, Galerkin's method, to solve the eigenvalue problem occurred in a cantilever beam. The beam is restrained with added mass and spring at the free end or a node point of a mode shape. The numerical results of eigen-frequency were compared with simple analytical and experimental results given by simple approach and simple test, respectively. It is found that Galerkin's method is applicable to estimate the eigen-frequency of the cantilever beam. The frequencies become lower with increasing the added mass and the frequencies increase with the spring force. It is shown the heavy added mass has a role of support on the flexible tube. The eigen-frequency of the first mode, for the system with the added mass mounted at the free end, can be calculated by the approximate analytical method existing with more or less accuracy.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.35 no.3
• /
• pp.95-101
• /
• 1986

This paper describes two methods for analyzing distributed parameter systems (DPS) via Walsh series expansions. Firstly, a Walsh-Galerkin expansion approach technique (WGA) introduced by S.G. Tzafestas. is considered. The method which is based on Galerkin scheme, is well established by using Walsh series. But then, there are some difficulty in finding the proper basic functions at each systems. Secondly, a double Walsh series approach technique (DWA) is developed. The essential feature of DWA propoesed here is that it reduces the analysis problem of DPS to that of solving a set of linear algebraic equation which is extended in double Walsh series.

• Computers and Concrete
• /
• v.23 no.4
• /
• pp.235-243
• /
• 2019

The discontinuous Galerkin method (DGM) has become widely used as it possesses several qualities, such as a natural ability to dealing with discontinuities. DGM has its major success related to fluid mechanics. Its major importance is the ability to deal with discontinuities and still provide high order of approximation. That is an important advantage when simulating cracking propagation. No remeshing is necessary during the propagation, since the crack path follows the interface of elements. However, DGM comes with the drawback of an increased number of degrees of freedom when compared to the classical continuous finite element method. Thus, it seems a natural approach to combine them in the same simulation obtaining the advantages of both methods. This paper proposes the application of the combined continuous-discontinuous Galerkin method (CDGM) to crack propagation. An important engineering problem is the simulation of crack propagation in concrete structures. The problem is characterized by discontinuities that evolve throughout the domain. Crack propagation is simulated using CDGM. Discontinuous elements are placed in regions with discontinuities and continuous elements elsewhere. The cohesive zone model describes the fracture process zone where softening effects are expressed by cohesive zones in the interface of elements. Two numerical examples demonstrate the capacities of CDGM. In the first example, a plain concrete beam is submitted to a three-point bending test. Numerical results are compared to experimental data from the literature. The second example deals with a full-scale ground slab, comparing the CDGM results to numerical and experimental data from the literature.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.32 no.8
• /
• pp.91-100
• /
• 2004

A Green's function approach is adopted for analyzing the thermoelastic deformations and stresses of a plate made of functionally graded materials(FGMs). The solution to the 3-dimensional unsteady temperature is obtained by using the laminate theory. The fundamental equations for thermoelastic problems are derived in terms of out-plane deformation and in-plane force, separately. The thermoelastic deformation and the stress distributions due to the bending and in-plane forces are analyzed by using a Green's function based on the Galerkin method. The eigenfunctions of the Galerkin Green's function for the thermoelastic deformation and the stress distributions are approximated in terms of a series of admissible functions that satisfy the homogeneous boundary conditions of the rectangular plate. Numerical analysis for a simply supported plate is carried out and effects of material properties on unsteady thermoclastic behaviors are discussed.

• 한국전산유체공학회:학술대회논문집
• /
• 2011.05a
• /
• pp.311-317
• /
• 2011

The present paper deals with the continuous works of extending the multi-dimensional limiting process (MLP) for compressible flows, which has been quite successful in finite volume methods, into discontinuous Galerkin (DG) methods. From the series of the previous, it was observed that the MLP shows several superior characteristics, such as an efficient controlling of multi-dimensional oscillations and accurate capturing of both discontinuous and continuous flow features. Mathematically, fundamental mechanism of oscillation-control in multiple dimensions has been established by satisfaction of the maximum principle. The MLP limiting strategy is extended into DG framework, which takes advantage of higher-order reconstruction within compact stencil, to capture detailed flow structures very accurately. At the present, it is observed that the proposed approach yields outstanding performances in resolving non-compressive as well as compressive flaw features. In the presentation, further numerical analyses and results are going to be presented to validate that the newly developed DG-MLP methods provide quite desirable performances in controlling numerical oscillations as well as capturing key flow features.