Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments.The paper considers a linear elasticity system with strongly heterogeneous...Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments.The paper considers a linear elasticity system with strongly heterogeneous coefficients and quasistatic Tresca friction law,and studies the homogenization theories under the frameworks of H-convergence and small ε-periodicity.The qualitative result is based on H-convergence,which shows the original oscillating solutions will converge weakly to the homogenized solution,while the author’s quantitative result provides an estimate of asymptotic errors in H^(1)-norm for the periodic homogenization.This paper also designs several numerical experiments to validate the convergence rates in the quantitative analysis.展开更多
Presents a study which proposed a dual approximate expression of the exact solution for mixed boundary value problems of second order elliptic partial differential equation with small periodic coefficients. Dual appro...Presents a study which proposed a dual approximate expression of the exact solution for mixed boundary value problems of second order elliptic partial differential equation with small periodic coefficients. Dual approximate error estimates; Main results.展开更多
Deals with a study which discussed the mechanical behaviour for subdivided periodic elastic structures of composite materials, from the viewpoint of macro- and meso-scale coupling. Multiscale asymptotic expansion and ...Deals with a study which discussed the mechanical behaviour for subdivided periodic elastic structures of composite materials, from the viewpoint of macro- and meso-scale coupling. Multiscale asymptotic expansion and truncation error estimates; Discussion on multiscale finite element method; Details of higher order difference quotients and total error estimates; Numerical experiments.展开更多
This paper is concerned with the second order elliptic problems with small periodic coefficients on a bounded domain with a curved boundary. A two-scale curved element method which couples linear elements and isoparam...This paper is concerned with the second order elliptic problems with small periodic coefficients on a bounded domain with a curved boundary. A two-scale curved element method which couples linear elements and isoparametric elements is proposed. The error estimate is obtained over the given smooth domain. Furthermore an additive Schwarz method is provided for the isoparametric element method.展开更多
基金supported by the National Natural Science Foundation of China(No.51739007)the Hong Kong RGC General Research Fund(Nos.14305222,14304021)the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDC06030101)。
文摘Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments.The paper considers a linear elasticity system with strongly heterogeneous coefficients and quasistatic Tresca friction law,and studies the homogenization theories under the frameworks of H-convergence and small ε-periodicity.The qualitative result is based on H-convergence,which shows the original oscillating solutions will converge weakly to the homogenized solution,while the author’s quantitative result provides an estimate of asymptotic errors in H^(1)-norm for the periodic homogenization.This paper also designs several numerical experiments to validate the convergence rates in the quantitative analysis.
基金the National Natural Science Foundation of China under grants 19901014 and 19932030 and the GAS K.C.Wong Poet-doctoral Resear
文摘Presents a study which proposed a dual approximate expression of the exact solution for mixed boundary value problems of second order elliptic partial differential equation with small periodic coefficients. Dual approximate error estimates; Main results.
基金The Project Supported by National Natural Science Foundation of China (No.19801006)and SpecialFunds for Major State Basic Rese
文摘Deals with a study which discussed the mechanical behaviour for subdivided periodic elastic structures of composite materials, from the viewpoint of macro- and meso-scale coupling. Multiscale asymptotic expansion and truncation error estimates; Discussion on multiscale finite element method; Details of higher order difference quotients and total error estimates; Numerical experiments.
基金The research was supported by the National Natural Science Foundation of China under grants 19901014 and 19932030 the Special Funds for Major State Basic Research Projects.
文摘This paper is concerned with the second order elliptic problems with small periodic coefficients on a bounded domain with a curved boundary. A two-scale curved element method which couples linear elements and isoparametric elements is proposed. The error estimate is obtained over the given smooth domain. Furthermore an additive Schwarz method is provided for the isoparametric element method.
