• Title, Summary, Keyword: higher order mean curvature

Search Result 8, Processing Time 0.031 seconds

ON A CHARACTERIZATION OF ROUND SPHERES

  • Onat, Leyla
    • Bulletin of the Korean Mathematical Society
    • /
    • v.39 no.4
    • /
    • pp.681-685
    • /
    • 2002
  • It is shown that, an immersion of n-dimensional compact manifold without boundary into (n + 1)-dimensional Euclidean space, hyperbolic space or the open half spheres, is a totally umbilic immersion if for some r, r =2, 3, …, n the r-th mean curvature Hr does not vanish and there are nonnegative constants $C_1$, $C_2$, …, $C_{r}$ such that (equation omitted)d)

Compensation for Elastic Recovery in a Flexible Forming Process Using Predictive Models for Shape Error (성형 오차 예측 모델을 이용한 가변 성형 공정에서의 탄성 회복 보정)

  • Seo, Y.H.;Kang, B.S.;Kim, J.
    • Transactions of Materials Processing
    • /
    • v.21 no.8
    • /
    • pp.479-484
    • /
    • 2012
  • The objective of this study is to compensate the elastic recovery in the flexible forming process using the predictive models. The target shape was limited to two-dimensional shape having only one curvature radius in the longitudinal-direction. In order to predict the shape error the regression and neural network models were established based on the finite element (FE) simulations. A series of simulations were conducted considering input variables such as the elastic pad thickness, the thickness of plate, and the objective curvature radius. Then, at sampling points in the longitudinal-direction, the shape errors between formed and objective shapes could be calculated from the FE simulations as an output variable. These shape errors were expressed to a representative error value by the root mean square error (RMSE). To obtain the correct objective shape the die shape was adjusted by the closed-loop using the neural network model since the neural network model shows a higher capability of estimating the shape error than the regression model. Finally the experimental result shows that the formed shape almost agreed with the objective shape.

Investigation on the Turbulence Structure of Reattaching Separated Shear Layer Past a Two-Dimensional Vetrical Fenc(I) (2次元 垂直壁을 지니는 再附着 剝離 斷層 의 亂流構造 에 관한 硏究 (I))

  • 김경천;정명균
    • Transactions of the Korean Society of Mechanical Engineers
    • /
    • v.9 no.4
    • /
    • pp.403-413
    • /
    • 1985
  • Hot-wire measurements of second and third-order mean products of velocity fluctuations have been made in the separated, reattached, and redeveloping boundary layer behind a vertical fence. Mean velocity, wall static pressure distributions have also been measured in the whole flow field. Upstream of the reattachment point, the separated shear layer developes as a free mixing layer, but the gradient of the maximum slope thickness, turbulent intensities and the Reynolds shear stress are higher than that of the mixing layer due to initial streamline curvature and the effects of highly turbulent recirculating flow region. In the reattachment region, Reynolds shear stress and triple products near the surface is far more rapid than the decrease of the shear stress; that is the presence of the solid wall has a marked effect on the apparent gradient diffusivity of intensity or shear stress and throws doubts upon the usefulness of the simple gradient diffusivity model in this region.

Development and Assessment for Resilient Modulus Prediction Model of Railway Trackbeds Based on Modulus Reduction Curve (탄성계수 감소곡선에 근거한 철도노반의 회복탄성계수 모델 개발 및 평가)

  • Park, Chul-Soo;Hwang, Seon-Keun;Choi, Chan-Yong;Mok, Young-Jin
    • Proceedings of the KSR Conference
    • /
    • /
    • pp.805-814
    • /
    • 2008
  • This study focused on the resilient modulus prediction model, which is the functions of mean effective principal stress and axial strain, for three types of railroad trackbed materials such as crushed stone, weathered soil, and crushed-rock soil mixture. The model is composed with the maximum Young's modulus and nonlinear values for higher strain in parallel with dynamic shear modulus. The maximum values is modeled by model parameters, $A_E$ and the power of mean effective principal stress, $n_E$. The nonlinear portion is represented by modified hyperbolic model, with the model parameters of reference strain, ${\varepsilon}_r$ and curvature coefficient, a. To assess the performance of the prediction models proposed herein, the elastic response of a test trackbed near PyeongTaek, Korea was evaluated using a 3-D nonlinear elastic computer program (GEOTRACK) and compared with measured elastic vertical displacement during the passages of freight and passenger trains. The material types of sub-ballasts are crushed stone and weathered granite soil, respectively. The calculated vertical displacements within the sub-ballasts are within the order of 0.6mm, and agree well with measured values with the reasonable margin. The prediction models are thus concluded to work properly in the preliminary investigation.

  • PDF

Stochastic hygrothermoelectromechanical loaded post buckling analysis of piezoelectric laminated cylindrical shell panel

  • Lal, Achchhe;Saidane, Nitesh;Singh, B.N.
    • Smart Structures and Systems
    • /
    • v.9 no.6
    • /
    • pp.505-534
    • /
    • 2012
  • The present work deals with second order statistics of post buckling response of piezoelectric laminated composite cylindrical shell panel subjected to hygro-thermo-electro-mechanical loading with random system properties. System parameters such as the material properties, thermal expansion coefficients and lamina plate thickness are assumed to be independent of the temperature and electric field and modeled as random variables. The piezoelectric material is used in the forms of layers surface bonded on the layers of laminated composite shell panel. The mathematical formulation is based on higher order shear deformation shell theory (HSDT) with von-Karman nonlinear kinematics. A efficient $C^0$ nonlinear finite element method based on direct iterative procedure in conjunction with a first order perturbation approach (FOPT) is developed for the implementation of the proposed problems in random environment and is employed to evaluate the second order statistics (mean and variance) of the post buckling load of piezoelectric laminated cylindrical shell panel. Typical numerical results are presented to examine the effect of various environmental conditions, amplitude ratios, electrical voltages, panel side to thickness ratios, aspect ratios, boundary conditions, curvature to side ratios, lamination schemes and types of loadings with random system properties. It is observed that the piezoelectric effect has a significant influence on the stochastic post buckling response of composite shell panel under various loading conditions and some new results are presented to demonstrate the applications of present work. The results obtained using the present solution approach is validated with those results available in the literature and also with independent Monte Carlo Simulation (MCS).

An Assessment of a Resilient Modulus Model by Comparing Predicted and Measured Elastic Deformation of Railway Trackbeds (철도노반의 탄성변위 예측 및 측정을 통한 회복탄성계수 모델 평가)

  • Park, Chul-Soo;Kim, Eun-Jung;Oh, Sang-Hoon;Kim, Hak-Sung;Mok, Young-Jin
    • Proceedings of the Korean Geotechical Society Conference
    • /
    • /
    • pp.1404-1414
    • /
    • 2008
  • In the mechanistic-empirical trackbed design of railways, the resilient modulus is the key input parameter. This study focused on the resilient modulus prediction model, which is the functions of mean effective principal stress and axial strain, for three types of railroad trackbed materials such as crushed stone, weathered soil, and crushed-rock soil mixture. The model is composed with the maximum Young's modulus and nonlinear values for higher strain in parallel with dynamic shear modulus. The maximum values is modeled by model parameters, $A_E$ and the power of mean effective principal stress, $n_E$. The nonlinear portion is represented by modified hyperbolic model, with the model parameters of reference strain, ${\varepsilon}_r$ and curvature coefficient, a. To assess the performance of the prediction models proposed herein, the elastic response of a test trackbed near PyeongTaek, Korea was evaluated using a 3-D nonlinear elastic computer program (GEOTRACK) and compared with measured elastic vertical displacement during the passages of freight and passenger trains. The material types of sub-ballasts are crushed stone and weathered granite soil, respectively. The calculated vertical displacements within the sub-ballasts are within the order of 0.6mm, and agree well with measured values with the reasonable margin. The prediction models are thus concluded to work properly in the preliminary investigation.

  • PDF

Development and Assessment for Resilient Modulus Prediction Model of Railroad Trackbeds Based on Modulus Reduction Curve (탄성계수 감소곡선에 근거한 철도노반의 회복탄성계수 모델 개발 및 평가)

  • Park, Chul Soo;Hwang, Seon Keun;Choi, Chan Yong;Mok, Young Jin
    • Journal of The Korean Society of Civil Engineers
    • /
    • v.29 no.2C
    • /
    • pp.71-79
    • /
    • 2009
  • This study is to develope the resilient modulus prediction model, which is the function of mean effective principal stress and axial strain, for three types of railroad trackbed materials such as crushed stone, weathered granite soil, and crushed-rock soil mixture. The model consists of the maximum Young's modulus and nonlinear values for higher strain, analogous to dynamic shear modulus. The maximum value is modeled by model parameters, $A_E$ and the power of mean effective principal stress, $n_E$. The nonlinear portion is represented by modified hyperbolic model, with the model parameters of reference strain, ${\varepsilon}_r$ and curvature coefficient, a. To assess the performance of the prediction models proposed herein, the elastic response of a test trackbed near PyeongTaek, Korea, was evaluated using a 3-D elastic multilayer computer program (GEOTRACK). The results were compared with measured elastic vertical displacement during the passages of freight and passenger trains at two locations, whose sub-ballasts were crushed stone and weathered granite soil, respectively. The calculated vertical displacements of the sub-ballasts are within the order of 0.6mm, and agree well with measured values. The prediction models are thus concluded to work properly in the preliminary investigation.

  • PDF