A flexoelectric spherical microshell model incorporating the strain gradient effect |
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| Institution: | 1. School of Mechanical Engineering, Shandong University, Jinan City, Shandong 250061, People''s Republic of China;2. Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Shandong University, Ministry of Education, Jinan City, Shandong 250061, People''s Republic of China;1. Institute of Mechanics, Beijing Jiaotong University, Beijing, 100044, China;2. Department of Mechanical Engineering, University of Houston, Houston, TX 77204, USA;3. Applied Mechanics of Materials Laboratory, Department of Mechanical Engineering, Temple University, Philadelphia, PA 19122, USA;4. Applied Mechanics of Materials Laboratory, Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA |
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| Abstract: | In this paper, a size-dependent flexoelectric spherical microshell model is proposed considering flexoelectric effect and strain gradient effect. By means of the variation principle, explicit expressions of the governing equations and the boundary conditions are deduced. Solving corresponding governing equations, analytical solutions of both direct and converse flexoelectric responses in static axisymmetric bending problem are obtained. Then, the flexoelectric responses in barium strontium titanate spherical microshells with and without a circular top opening are numerically investigated. Both the direct and converse flexoelectric responses are found to vary non-monotonically as the central angle increases. The converse flexoelectric bending is examined to exist even in clamped spherical microshells, which is different from the case of flat structures. In addition, for all cases, the strain gradient effect will highly reduce the flexoelectric responses, particularly when the thickness approaches the material internal scale constants. |
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