This paper introduces an adaptive finite element method （AFEM） using the newest vertex bisection and marking exclusively according to the error estimator without special treatment of oscillation. By the combination ...This paper introduces an adaptive finite element method （AFEM） using the newest vertex bisection and marking exclusively according to the error estimator without special treatment of oscillation. By the combination of the global lower bound and the localized upper bound of the posteriori error estimator, perturbation of oscillation, and cardinality of the marked element set, it is proved that the AFEM is quasi-optimal for linear elasticity problems in two dimensions, and this conclusion is verified by the numerical examples.展开更多
In this paper,we generalize the direct method of lines for linear elasticity problems of composite materials in star-shaped domains and consider its application to inverse elasticity problems.We assume that the bounda...In this paper,we generalize the direct method of lines for linear elasticity problems of composite materials in star-shaped domains and consider its application to inverse elasticity problems.We assume that the boundary of the star-shaped domain can be described by an explicit C 1 parametric curve in the polar coordinate.We introduce the curvilinear coordinate,in which the irregular star-shaped domain is converted to a regular semi-infinite strip.The equations of linear elasticity are discretized with respect to the angular variable and we solve the resulting semidiscrete approximation analytically using a direct method.The eigenvalues of the semi-discrete approximation converge quickly to the true eigenvalues of the elliptic operator,which helps capture the singularities naturally.Moreover,an optimal error estimate of our method is given.For the inverse elasticity problems,we determine the Lam´e coefficients from measurement data by minimizing a regularized energy functional.We apply the direct method of lines as the forward solver in order to cope with the irregularity of the domain and possible singularities in the forward solutions.Several numerical examples are presented to show the effectiveness and accuracy of our method for both forward and inverse elasticity problems of composite materials.展开更多
A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems with Dirichlet and mixed boundary conditions are proposed. Reliability and efficiency of the estimators are p...A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems with Dirichlet and mixed boundary conditions are proposed. Reliability and efficiency of the estimators are proved. Numerical examples are presented to verify the theoretical results.展开更多
As suggested by the title, this extensive book is concerned with crack and contact prob- lems in linear elasticity. However, in general, it is intended for a wide audience ranging from engineers to mathematical physic...As suggested by the title, this extensive book is concerned with crack and contact prob- lems in linear elasticity. However, in general, it is intended for a wide audience ranging from engineers to mathematical physicists. Indeed, numerous problems of both academic and tech- nological interest in electro-magnetics, acoustics, solid and fluid dynamics, etc. are actually related to each other and governed by the same mixed boundary value problems from a unified mathematical standpoint展开更多
In the present paper we investigate linear elastic systems with damping in Hilbert spaces, where A and B ars unbounded positive definite linear operators. We have obtained the most fundamental results for the holomorp...In the present paper we investigate linear elastic systems with damping in Hilbert spaces, where A and B ars unbounded positive definite linear operators. We have obtained the most fundamental results for the holomorphic property and exponential stability of the semigroups associated with these systems via inclusion relation of the domains of A and B.展开更多
Taking hm as the mesh width of a curved edge Гm （m = 1, ..., d ） of polygons and using quadrature rules for weakly singular integrals, this paper presents mechanical quadrature methods for solving BIES of the first...Taking hm as the mesh width of a curved edge Гm （m = 1, ..., d ） of polygons and using quadrature rules for weakly singular integrals, this paper presents mechanical quadrature methods for solving BIES of the first kind of plane elasticity Dirichlet problems on curved polygons, which possess high accuracy O（h0^3） and low computing complexities. Since multivariate asymptotic expansions of approximate errors with power hi^3 （i = 1, 2, ..., d） are shown, by means of the splitting extrapolations high precision approximations and a posteriori estimate are obtained.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.1120115911426102+4 种基金and 11571293)the Natural Science Foundation of Hunan Province(No.11JJ3135)the Foundation for Outstanding Young Teachers in Higher Education of Guangdong Province(No.Yq2013054)the Pearl River S&T Nova Program of Guangzhou(No.2013J2200063)the Construct Program of the Key Discipline in Hunan University of Science and Engineering
文摘This paper introduces an adaptive finite element method （AFEM） using the newest vertex bisection and marking exclusively according to the error estimator without special treatment of oscillation. By the combination of the global lower bound and the localized upper bound of the posteriori error estimator, perturbation of oscillation, and cardinality of the marked element set, it is proved that the AFEM is quasi-optimal for linear elasticity problems in two dimensions, and this conclusion is verified by the numerical examples.
基金This work was partially supported by the NSFC Projects No.12025104,11871298,81930119.
文摘In this paper,we generalize the direct method of lines for linear elasticity problems of composite materials in star-shaped domains and consider its application to inverse elasticity problems.We assume that the boundary of the star-shaped domain can be described by an explicit C 1 parametric curve in the polar coordinate.We introduce the curvilinear coordinate,in which the irregular star-shaped domain is converted to a regular semi-infinite strip.The equations of linear elasticity are discretized with respect to the angular variable and we solve the resulting semidiscrete approximation analytically using a direct method.The eigenvalues of the semi-discrete approximation converge quickly to the true eigenvalues of the elliptic operator,which helps capture the singularities naturally.Moreover,an optimal error estimate of our method is given.For the inverse elasticity problems,we determine the Lam´e coefficients from measurement data by minimizing a regularized energy functional.We apply the direct method of lines as the forward solver in order to cope with the irregularity of the domain and possible singularities in the forward solutions.Several numerical examples are presented to show the effectiveness and accuracy of our method for both forward and inverse elasticity problems of composite materials.
基金supported by National Science Foundation of USA(Grant No.DMS-1418934)the Sea Poly Project of Beijing Overseas Talents,National Natural Science Foundation of China(Grant Nos.11625101,91430213,11421101,11771338,11671304 and 11401026)+1 种基金Zhejiang Provincial Natural Science Foundation of China Projects(Grant Nos.LY17A010010,LY15A010015 and LY15A010016)Wenzhou Science and Technology Plan Project(Grant No.G20160019)
文摘A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems with Dirichlet and mixed boundary conditions are proposed. Reliability and efficiency of the estimators are proved. Numerical examples are presented to verify the theoretical results.
文摘As suggested by the title, this extensive book is concerned with crack and contact prob- lems in linear elasticity. However, in general, it is intended for a wide audience ranging from engineers to mathematical physicists. Indeed, numerous problems of both academic and tech- nological interest in electro-magnetics, acoustics, solid and fluid dynamics, etc. are actually related to each other and governed by the same mixed boundary value problems from a unified mathematical standpoint
文摘In the present paper we investigate linear elastic systems with damping in Hilbert spaces, where A and B ars unbounded positive definite linear operators. We have obtained the most fundamental results for the holomorphic property and exponential stability of the semigroups associated with these systems via inclusion relation of the domains of A and B.
基金Supported by Natioal Science Foundation of China （10171073）.
文摘Taking hm as the mesh width of a curved edge Гm （m = 1, ..., d ） of polygons and using quadrature rules for weakly singular integrals, this paper presents mechanical quadrature methods for solving BIES of the first kind of plane elasticity Dirichlet problems on curved polygons, which possess high accuracy O（h0^3） and low computing complexities. Since multivariate asymptotic expansions of approximate errors with power hi^3 （i = 1, 2, ..., d） are shown, by means of the splitting extrapolations high precision approximations and a posteriori estimate are obtained.
