For a physically possible deformation field of a continuum, the deformation gradient function F can be decomposed into direct sum of a symmetric tensor S and on orthogonal tensor R, which is called S-R decomposition t...For a physically possible deformation field of a continuum, the deformation gradient function F can be decomposed into direct sum of a symmetric tensor S and on orthogonal tensor R, which is called S-R decomposition theorem. In this paper, the S-R decomposition unique existence theorem is proved, by employing matrix and tensor method. Also, a brief proof of its objectivity is given.展开更多
A connection between Cheng's refined theory and Gregory's decomposed theorem is analyzed. The equivalence of the refined theory and the decomposed theorem is given. Using operator matrix determinant of partial...A connection between Cheng's refined theory and Gregory's decomposed theorem is analyzed. The equivalence of the refined theory and the decomposed theorem is given. Using operator matrix determinant of partial differential equation, Cheng gained one equation, and he substituted the sum of the general integrals of three differential equations for the solution of the equation. But he did not prove the rationality of substitute. There, a whole proof for the refined theory from Papkovich?_Neuber solution was given. At first expressions were obtained for all the displacements and stress components in term of the mid_plane displacement and its derivatives. Using Lur'e method and the theorem of appendix, the refined theory was given. At last, using basic mathematic method, the equivalence between Cheng's refined theory and Gregory's decomposed theorem was proved, i.e., Cheng's bi_harmonic equation, shear equation and transcendental equation are equivalent to Gregory's interior state, shear state and Papkovich_Fadle state, respectively.展开更多
In this paper, we study the convergence rate of two-dimensional Baskakov operators with Jacobi-weights and the approximation equivalence theorem is obtained, making use of multivariate decompose skills and results of ...In this paper, we study the convergence rate of two-dimensional Baskakov operators with Jacobi-weights and the approximation equivalence theorem is obtained, making use of multivariate decompose skills and results of one-dimensional Baskakov operators.展开更多
文摘For a physically possible deformation field of a continuum, the deformation gradient function F can be decomposed into direct sum of a symmetric tensor S and on orthogonal tensor R, which is called S-R decomposition theorem. In this paper, the S-R decomposition unique existence theorem is proved, by employing matrix and tensor method. Also, a brief proof of its objectivity is given.
文摘A connection between Cheng's refined theory and Gregory's decomposed theorem is analyzed. The equivalence of the refined theory and the decomposed theorem is given. Using operator matrix determinant of partial differential equation, Cheng gained one equation, and he substituted the sum of the general integrals of three differential equations for the solution of the equation. But he did not prove the rationality of substitute. There, a whole proof for the refined theory from Papkovich?_Neuber solution was given. At first expressions were obtained for all the displacements and stress components in term of the mid_plane displacement and its derivatives. Using Lur'e method and the theorem of appendix, the refined theory was given. At last, using basic mathematic method, the equivalence between Cheng's refined theory and Gregory's decomposed theorem was proved, i.e., Cheng's bi_harmonic equation, shear equation and transcendental equation are equivalent to Gregory's interior state, shear state and Papkovich_Fadle state, respectively.
基金Supported by the Scientific Research Fund of Zhejiang Province Education Depart-ment(200700190) Supported by the Science Technique Planed Item of Taizhou City(063KY08)Supported by Major Scientific Research Fund of Taizhou University(09ZD08)
文摘In this paper, we study the convergence rate of two-dimensional Baskakov operators with Jacobi-weights and the approximation equivalence theorem is obtained, making use of multivariate decompose skills and results of one-dimensional Baskakov operators.
