1. College of Mechanical and Electronic Engineering, Shandong University of Science and Technology, 266510 Qingdao, China;
2. School of Mechanical Engineering, Shandong University, 250061 Jinan, China;
3. Department of Scientific Research, Shandong University of Science and Technology, 266510 Qingdao, China;
4. Jinan Vocational and Technical College in Engineering, 250200 Jinan, China
Abstract C1 natural element method (C1 NEM) is applied to strain gradient linear elasticity, and size effects on microstructures are analyzed. The shape functions in C1 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, C1 NEM for strain gradient linear elasticity is constructed, and several 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.
Received: 23 December 2010
Published: 17 October 2010
Cite this article:
. C1 natural element method for strain gradient linear elasticity and its application to microstructures[J]. Acta Mechanica Sinica, 2012, 28(1): 91-103.
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