C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolati...C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.展开更多
I first met Constantine Dafermos in August 1974, at a meeting at Brown University, where I was invited because my former advisor （Jacques-Louis LIONS） could not come, and he had proposed my name. I was happily surpr...I first met Constantine Dafermos in August 1974, at a meeting at Brown University, where I was invited because my former advisor （Jacques-Louis LIONS） could not come, and he had proposed my name. I was happily surprised that Constantine greeted me as if he knew me well, and since for many years now I have considered him as if he was an older brother, I wonder when this feeling started.展开更多
In this paper, the classical pressure vessel problem for void damage materials is studied from the theory of microstructure in linear elasticity. The solutions are quasi-static. The stress distribution is predicted by...In this paper, the classical pressure vessel problem for void damage materials is studied from the theory of microstructure in linear elasticity. The solutions are quasi-static. The stress distribution is predicted by isotropic linear elasticity. The displacement and damage fields exhibit a volumetric viscoelasticity induced by considering material damage.展开更多
基金supported by the SDUST Spring Bud (2009AZZ021)Taian Science and Technology Development (20112001)
文摘C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.
文摘I first met Constantine Dafermos in August 1974, at a meeting at Brown University, where I was invited because my former advisor （Jacques-Louis LIONS） could not come, and he had proposed my name. I was happily surprised that Constantine greeted me as if he knew me well, and since for many years now I have considered him as if he was an older brother, I wonder when this feeling started.
文摘In this paper, the classical pressure vessel problem for void damage materials is studied from the theory of microstructure in linear elasticity. The solutions are quasi-static. The stress distribution is predicted by isotropic linear elasticity. The displacement and damage fields exhibit a volumetric viscoelasticity induced by considering material damage.
