• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.23 no.5
• /
• pp.525-533
• /
• 2010

Direct time integration method such as Newmark method is numerically performed under the assumption that continuous load function such as constant amplitude load can be treated as a discontinuous load fuction. It is due that the load can be treated as a constant value at the given time period regardless of variation of load at the time increment interval. It means the numerical results should be accompanied by the error due to approximation of load fuction. In contrast, the load function is calculated by convolution integral for the given time interval at finite element equation based on Gurtin's variation equation. Therefore. precise numerical results can be obtained by Gurtin's method because of convolution integral for the continuous load fuction curve even at the variation of load function in the given time interval. In this study, we prove that Gurtin's method can be more suitable than Newmark method in the problem of constant amplitude loading, using the numerical results for the free end of the one-dimensional rod. This study also shows that Gurtin's method is more effective in constant amplitude loading than in constant loading. The accuracy and the validity are verified by comparison between the results of in-house FORTRAN code and ADINA, a commercial software supporting Newmark method.

• Archives of Reconstructive Microsurgery
• /
• v.6 no.1
• /
• pp.29-38
• /
• 1997

A peripheral nerve when approximation of the ends imparts tension at the anastomosis and with a relatively long segment defect after excision of neuroma and neurofibroma cannnot be repaired by early primary suture. The one of the optimistic reconstruction method of severed peripheral nerves is to restore tension-free continuity at the repair site putting an autogenous nerve graft into the neural gap despite of ancipating motor or sensory deficit of the donor nerve area. To overcome the deficit of the autogenous nerve graft, several other conduits supplying a metabolically active environment which is able to support axon regeneration and progression, providing protection against scar invasion, and guiding the regrowing axons to the distal stump of the nerve have been studied. An author have used ipsilateral femoral vein, ipsilateral femoral vein filled with fresh thigh muscle, and autogenous sciatic nerve for the sciatic nerve defect of around 10 mm in length to observe the regeneration pattern in rat by light and electron microscopy. The results were as follows. 1. Light microscopically regeneration pattern of nerve fibers in the autogenous graft group was more abundant than vein graft and vein filled with muscle group. 2. On ultrastructural findings, the proxial end of the graft in various groups showed similar regenerating features of the axons, myelin sheaths, and Schwann cells. The fascicular arrangement of the myelinated and unmyelinated fibers was same regardless of the type of conduits. There were more or less increasing tendency in the number and the diameter of myelinated fibers correlated with the regeneration time. 3. In the middle of the graft, myelinated nerve fibers of vein filled with muscle group were more in number and myelin sheath was thinner than in the venous graft, but the number of regenerating axons in autogenous nerve graft was superior to that in both groups of the graft. The amount of collagen fibrils and amorphous materials in the endoneurial space was increased to elapsed time. 4. There was no difference in regenerating patterns of the nerve fibers of distal end of the graft. The size and shape of the myelinated nerve fbers were more different than that of proximal and middle portion of the graft. From the above results, the degree of myelination and regenerating activity in autogenous nerve is more effective and active in other types of the graft and there were no morphological differences in either ends of the graft regardless of regeneration time.

• Nuclear Engineering and Technology
• /
• v.4 no.4
• /
• pp.306-321
• /
• 1972

Molecular reorientation in (NH$_4$)$_2$SO$_4$, has been studied by cold neutron scattering. For T=300$^{\circ}$K data, the isolated quasielastic spectra and form-factors at various scattering angles are compared with four reorientational models based on SKOLD theory. Front these, it is concluded that the NH$_4$ions are performing either 3-fold four axes or 2-fold three axes reorientation with $\tau$$_{c}$=2.0$\times$10$^{-11}$ sec. The temperature dependence of f. is studied over 100$^{\circ}$K-413$^{\circ}$K and for the high-temperature phase, the widths of composite spectra are compared with the results from NMR relaxation measurements. All the results have shown that the neutron scattering method is capable of giving detalis of the reorientational modes in solids and therefore some discussions are given on the application of this method. A study of the form-factor is applied for NH$_4$I (Phase I) by comparing the measurement with the calculation based on free rotation approximation and proposed a reorientation model of NH$_4$ ions in the octahedral potential cage with $\tau$$_{c}$$\leq$10$^{-12}$ sec. Also a brief theoretical prediction for the effect of reorientational motions on the inelastic spectrum is discussed.sed.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.29 no.6
• /
• pp.583-590
• /
• 2016

This paper presents a dynamic crack propagation algorithm with Rayleigh damping effect based on the MLS(Moving Least Squares) Difference Method. Dynamic equilibrium equation and constitutive equation are derived by considering Rayliegh damping and governing equations are discretized by the MLS derivative approximation; the proportional damping, which has not been properly treated in the conventional strong formulations, was implemented in both the equilibrium equation and constitutive equation. Dynamic equilibrium equation including time relevant terms is integrated by the Central Difference Method and the discrete equations are simplified by lagging the velocity one step behind. A geometrical feature of crack is modeled by imposing the traction-free condition onto the nodes placed at crack surfaces and the effect of movement and addition of the nodes at every time step due to crack growth is appropriately reflected on the construction of total system. The robustness of the proposed numerical algorithm was proved by simulating single and multiple crack growth problems and the effect of proportional damping on the dynamic crack propagation analysis was effectively demonstrated.

• Journal of The Korean Astronomical Society
• /
• v.36 no.3
• /
• pp.89-95
• /
• 2003

Observations of dark matter dominated dwarf and low surface brightness disk galaxies favor density profiles with a flat-density core, while cold dark matter (CDM) N-body simulations form halos with central cusps, instead. This apparent discrepancy has motivated a re-examination of the microscopic nature of the dark matter in order to explain the observed halo profiles, including the suggestion that CDM has a non-gravitational self-interaction. We study the formation and evolution of self-interacting dark matter (SIDM) halos. We find analytical, fully cosmological similarity solutions for their dynamics, which take proper account of the collisional interaction of SIDM particles, based on a fluid approximation derived from the Boltzmann equation. The SIDM particles scatter each other elastically, which results in an effective thermal conductivity that heats the halo core and flattens its density profile. These similarity solutions are relevant to galactic and cluster halo formation in the CDM model. We assume that the local density maximum which serves as the progenitor of the halo has an initial mass profile ${\delta}M / M {\propto} M^{-{\epsilon}$, as in the familiar secondary infall model. If $\epsilon$ = 1/6, SIDM halos will evolve self-similarly, with a cold, supersonic infall which is terminated by a strong accretion shock. Different solutions arise for different values of the dimensionless collisionality parameter, $Q {\equiv}{\sigma}p_br_s$, where $\sigma$ is the SIDM particle scattering cross section per unit mass, $p_b$ is the cosmic mean density, and $r_s$ is the shock radius. For all these solutions, a flat-density, isothermal core is present which grows in size as a fixed fraction of $r_s$. We find two different regimes for these solutions: 1) for $Q < Q_{th}({\simeq} 7.35{\times} 10^{-4}$), the core density decreases and core size increases as Q increases; 2) for $Q > Q_{th}$, the core density increases and core size decreases as Q increases. Our similarity solutions are in good agreement with previous results of N-body simulation of SIDM halos, which correspond to the low-Q regime, for which SIDM halo profiles match the observed galactic rotation curves if $Q {\~} [8.4 {\times}10^{-4} - 4.9 {\times} 10^{-2}]Q_{th}$, or ${\sigma}{\~} [0.56 - 5.6] cm^2g{-1}$. These similarity solutions also show that, as $Q {\to}{\infty}$, the central density acquires a singular profile, in agreement with some earlier simulation results which approximated the effects of SIDM collisionality by considering an ordinary fluid without conductivity, i.e. the limit of mean free path ${\lambda}_{mfp}{\to} 0$. The intermediate regime where $Q {\~} [18.6 - 231]Q_{th}$ or ${\sigma}{\~} [1.2{\times}10^4 - 2.7{\times}10^4] cm^2g{-1}$, for which we find flat-density cores comparable to those of the low-Q solutions preferred to make SIDM halos match halo observations, has not previously been identified. Further study of this regime is warranted.