Bi-modulus materials with different mechanical responses in tension and compression are often found in civil,composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and c...Bi-modulus materials with different mechanical responses in tension and compression are often found in civil,composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and convergence is usually a problem for traditional iterative schemes. This paper aims to develop a stabilized computational method for nonlinear analysis of 3D bimodular materials. Based on the parametric variational principle, a unified constitutive equation of 3D bimodular materials is proposed, which allows the eight principal stress states to be indicated by three parametric variables introduced in the principal stress directions.The original problem is transformed into a standard linear complementarity problem（LCP） by the parametric virtual work principle and a quadratic programming algorithm is developed by solving the LCP with the classic Lemke＇s algorithm. Update of elasticity and stiffness matrices is avoided and, thus, the proposed algorithm shows an excellent convergence behavior compared with traditional iterative schemes.Numerical examples show that the proposed method is valid and can accurately analyze mechanical responses of 3D bimodular materials. Also, stability of the algorithm is greatly improved.展开更多
Ultrasmall and monodisperse air-stable colloidal Nd-Fe-B-Na nanoparticles(NPs)have been synthesized by the solution phase colloidal method and characterized by TEM,EXAFS,Mössbauer spectroscopy,and SQUID.Their siz...Ultrasmall and monodisperse air-stable colloidal Nd-Fe-B-Na nanoparticles(NPs)have been synthesized by the solution phase colloidal method and characterized by TEM,EXAFS,Mössbauer spectroscopy,and SQUID.Their size can be controlled in the sub-5 nm regime.The critical temperature(TC)of Nd-Fe-B-Na nanoparticles with 3 nm diameter is surprisingly high,higher than 650 K.EXAFS gives the chemical environmental information of the Fe center,and Mössbauer spectroscopy confirms that the 3 nm Nd-Fe-B-Na nanoparticles contain the Fe nanocluster.A possible magnetic coupling mechanism is proposed.展开更多
基金supported by the National Natural Science Foundation of China (Grants 11232003, 91315302, 11502035)the Open Research Foundation (Grant GZ1404) of State Key Laboratory of Structural Analysis for Industrial Equipment at Dalian University of Technology
文摘Bi-modulus materials with different mechanical responses in tension and compression are often found in civil,composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and convergence is usually a problem for traditional iterative schemes. This paper aims to develop a stabilized computational method for nonlinear analysis of 3D bimodular materials. Based on the parametric variational principle, a unified constitutive equation of 3D bimodular materials is proposed, which allows the eight principal stress states to be indicated by three parametric variables introduced in the principal stress directions.The original problem is transformed into a standard linear complementarity problem（LCP） by the parametric virtual work principle and a quadratic programming algorithm is developed by solving the LCP with the classic Lemke＇s algorithm. Update of elasticity and stiffness matrices is avoided and, thus, the proposed algorithm shows an excellent convergence behavior compared with traditional iterative schemes.Numerical examples show that the proposed method is valid and can accurately analyze mechanical responses of 3D bimodular materials. Also, stability of the algorithm is greatly improved.
基金supported by the National Natural Science Foundation of China(91122003)the Developing Science Funds of Tongji University.
文摘Ultrasmall and monodisperse air-stable colloidal Nd-Fe-B-Na nanoparticles(NPs)have been synthesized by the solution phase colloidal method and characterized by TEM,EXAFS,Mössbauer spectroscopy,and SQUID.Their size can be controlled in the sub-5 nm regime.The critical temperature(TC)of Nd-Fe-B-Na nanoparticles with 3 nm diameter is surprisingly high,higher than 650 K.EXAFS gives the chemical environmental information of the Fe center,and Mössbauer spectroscopy confirms that the 3 nm Nd-Fe-B-Na nanoparticles contain the Fe nanocluster.A possible magnetic coupling mechanism is proposed.
