• Journal of the Korean Mathematical Society
• /
• v.48 no.6
• /
• pp.1101-1123
• /
• 2011

Numerical schemes are routinely used to predict the behavior of continuous dynamical systems. All such schemes transform flows into maps, which can possess dynamical behavior deviating from their continuous counterparts. Here the common bifurcations of scalar dynamical systems are transformed under a class of algorithms known as linearized one-point collocation methods. Through the use of normal forms, we prove that each such bifurcation in an originating flow gives rise to an exactly corresponding one in its discretization. The conditions for spurious period doubling behavior under this class of algorithm are derived. We discuss the global behavioral consequences of a singular set induced by the discretizing methods, including loss of monotonicity of solutions, intermittency, and distortion of attractor basins.

• Proceedings of the Korea Concrete Institute Conference
• /
• 1992.04a
• /
• pp.47-52
• /
• 1992

The entire nonlinear behavior of reinforced concrete frames up to collapse, is analyzed by the displacement control method and the combined layered and nonlayered method. All of the rigidities of section are calculated approximately by a sum over all the layers for the layered method, are used the integral values over the cross section area for the nonlayered method. The spurious sensitivity to the chosen element size in the result of analysis by finite element method for the materials with strain-softening can be overcome by modifying the strain distribution based on the concept of fracture energy at plastic hinge considering the applied axial load.

• Proceedings of the Korean Institute of Communication Sciences Conference
• /
• 2004.07a
• /
• pp.303-303
• /
• 2004

• Journal of Mechanical Science and Technology
• /
• v.17 no.6
• /
• pp.787-795
• /
• 2003

Mechanical properties of the materials used for transportations and industrial machinery under high strain rate loading conditions such as seismic loading are required to provide appropriate safety assessment to these mechanical structures. The Split Hopkinson Pressure Bar (SHPB) technique with a special experimental apparatus can be used to obtain the material behavior under high strain rate loading conditions. In this paper, dynamic deformation behaviors of the aluminum alloys such as A12024-T4, A1606 IT-6 and A17075-T6 under both high strain rate compressive and tensile loading conditions are determined using the SHPB technique.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.12
• /
• pp.3033-3039
• /
• 2000

Mechanical properties of the materials used for transportations and industrial machinery under high stain rate loading conditions have been required to provide appropriate safety assessment to these mechanical structures. The Split Hopkinson Pressure Bar(SHPB) technique with a special experimental apparatus can be used to obtain the material properties under high strain rate loading condition. There have been many studies on the material behavior under high strain rate compressive loading compared to those under tensile loading. In this paper, mechanical properties of the aluminum alloy, Al6061-T6, under high strain rate tensile loading were determined using SHPB technique.

• Proceedings of the KSME Conference
• /
• 2000.11a
• /
• pp.268-273
• /
• 2000

Mechanical properties of the materials used for transportations and industrial machinery under high strain rate loading conditions are required to provide appropriate safety assessment to these mechanical structures. The Split Hopkinson Pressure Bar(SHPB) technique, a special experimental apparatus, can be used to obtain the material behavior under high strain rate loading condition. In this paper, dynamic deformation behaviors of the aluminum alloys, Al2024-T4, Al6061-T6 and Al7075-T6, under high strain rate compressive and tensile loading are determined using SHPB technique.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1999.04a
• /
• pp.234-241
• /
• 1999

In this study, an improved 8-node flat shell element is presented for the analysis of shell structure, by combining 8-node membrane element with drilling degree-of-freedom and 8-node plate bending element based on the recently presented technique. Firstly, 8-node membrane element designated as CLM8 is presented in this paper. The element has drilling degree-of.freedom in addition to transitional degree-of-freedom. Therefore the element possesses 3 degrees-of-freedom per each node which as well as the improvement of the element behavior, permits an easy connection to other element with rotational degree-of -freedom. Secondly. 8-node flat shell element was composed by adding 8-node Mindlin plate bending element to the membrane element. The behavior of the introduced plate bending element is further improved by combined use of nonconforming displacement modes, selectively reduced integration scheme and assumed shear strain fields. The element passes in the patch test, doesn't show spurious mechanism and doesn't produce shear locking phenomena. Finally, Numerical examples are presented to show the performance of flat shell element developed in the present study.

• Journal of Korean Society of Steel Construction
• /
• v.16 no.3 s.70
• /
• pp.295-303
• /
• 2004

In this paper, an improved four-node Reissner-Mindlin plate-bending element with enhanced assumed strain field is presented for the analysis of isotropic and laminated composite plates. To avoid the shear locking and spurious zero energy modes, the transverse shear behavior is improved by the addition of a new enhanced shear strain based on the incompatible displacement mode approach and bubble function. The "standard" enhanced strain fields (Andelfinger and Ramm, 1993) are also employed to improve the in-plane behaviors of the plate elements. The four-node quadrilateral element derived using the first-order shear deformation theory is designated as "14EASP". Several applications are investigated to assess the features and the performances of the proposed element. The results are compared with other finite element solutions and analytical solutions. Numerical examples show that the element is stable, invariant, passes the patch test, and yields good results especially in highly distorted regimes.

• Bulletin of the Korean Chemical Society
• /
• v.33 no.3
• /
• pp.933-940
• /
• 2012

Recently, it has been shown that quantum coherence appears in energy transfers of various photosynthetic lightharvesting complexes at from cryogenic to even room temperatures. Because the photosynthetic systems are inherently complex, these findings have subsequently interested many researchers in the field of both experiment and theory. From the theoretical part, simplified dynamics or semiclassical approaches have been widely used. In these approaches, the quantum-classical Liouville equation (QCLE) is the fundamental starting point. Toward the semiclassical scheme, approximations are needed to simplify the equations of motion of various degrees of freedom. Here, we have adopted the Poisson bracket mapping equation (PBME) as an approximate form of QCLE and applied it to find the time evolution of the excitation in a photosynthetic complex from marine algae. The benefit of using PBME is its similarity to conventional Hamiltonian dynamics. Through this, we confirmed the coherent population transfer behaviors in short time domain as previously reported with a more accurate but more time-consuming iterative linearized density matrix approach. However, we find that the site populations do not behave according to the Boltzmann law in the long time limit. We also test the effect of adding spurious high frequency vibrations to the spectral density of the bath, and find that their existence does not alter the dynamics to any significant extent as long as the associated reorganization energy is changed not too drastically. This suggests that adopting classical trajectory based ensembles in semiclassical simulations should not influence the coherence dynamics in any practical manner, even though the classical trajectories often yield spurious high frequency vibrational features in the spectral density.

• Journal of Mechanical Science and Technology
• /
• v.19 no.3
• /
• pp.811-819
• /
• 2005

In this study, we present a new efficient hybrid-mixed composite laminated curved beam element. The present element, which is based on the Hellinger-Reissner variational principle and the first-order shear deformation lamination theory, employs consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees in order to resolve the numerical difficulties due to the spurious constraints. The stress parameters are eliminated and the nodeless degrees are condensed out to obtain the ($6{\times}6$) element stiffness matrix. The present study also incorporates the straightforward prediction of interlaminar stresses from equilibrium equations. Several numerical examples confirm the superior behavior of the present composite laminated curved beam element.