• Korean journal of applied entomology
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• v.49 no.3
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• pp.175-185
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• 2010

The effect of altitude and latitude on biodiversity (or species richness) has been a topic of great interest for many biogeographers for a long time. This study was conducted to examine the dynamics of species richness of aquatic insects along the altitudinal gradient in 24 wetlands on Mt. Halla, Jeju and test the Rapoport's rule. The species richness of aquatic insects monotonically decreased with increasing altitude, showing a significant inverse correlation (r = -0.64). However, the pattern of species richness with altitude showed a hump-shaped relationship, with a peak in species richness at intermediate elevations when the effects of area were removed. The altitudinal range of species tended to increase with increasing altitude, as Rapoport's rule predicts. There was a positive correlation between the altitudinal range size and the midpoint of the range size (Median) except for Hemiptera (Odonata: r = 0.75, Hemiptera: r = -0.22, Coleoptera: r = 0.72, Total: r = 0.55). Also, the extent of average altitudinal range of high-altitude species was 904.3m, and it was significantly wider than a 469.5m of low-altitude species. Consequently, the species richness of aquatic insects in wetlands on Mt. Halla along the altitudinal gradient well supported Rapoport's rule.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.9
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• pp.1562-1570
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• 2003

The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. The complexity of these constitutive equations generally requires a stable and accurate numerical method. The radial return mapping is one of the most robust integration scheme currently used. Nonlinear kinematic hardening model of Armstrong-Fredrick type has recovery term and the direction of kinematic hardening increment is not parallel to that of plastic strain increment. In this case, The conventional radial return mapping method cannot be applied directly. In this investigation, we expanded the radial return mapping method to consider the nonlinear kinematic hardening model and implemented this integration scheme into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using Newton method and bisection method. Using dynamic yield condition derived from linearization of flow rule, the integration scheme for elastoplastic and viscoplastic constitutive model was unified. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method.

• Transactions of Materials Processing
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• v.7 no.3
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• pp.233-245
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• 1998

A new approach has been proposed for the incremental analysis of the nonsteady state large deformation of planar anisotropic elastic-plastic sheet forming. A mathematical brief review of a constitutive law for the incremental deformation theory has been presented from flow theory using the minimum plastic work path for elastic-plastic material. Since the material embedded coordinate system(Lagrangian quantity) is used in the proposed theory the stress integration procedure is completely objective. A new return mapping algorithm has been also developed from the general midpoint rule so as to achieve numerically large strain increment by successive control of yield function residuals. Some numerical tests for the return mapping algorithm were performed using Barlat's six component anisotropic stress potential. Performance of the proposed algorithm was shown to be good and stable for a large strain increment, For planar anisotropic sheet forming updating algorithm of planar anisotropic axes has been newly proposed. In order to show the effectiveness and validity of the present formulation earing simulation for a cylindrical cup drawing and front fender stamping analysis are performed. From the results it has been shown that the present formulation can provide a good basis for analysis for analysis of elastic-plastic sheet metal forming processes.