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A simplified strain
gradient Kirchhoff rod model and its applications on
microsprings and microcolumns
Jun Hong, Gongye Zhang, Xiao Wang and Changwen Mi |
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Vol. 15 (2020), No. 2, 203–223
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Abstract |
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The equilibrium equations and boundary conditions of elastic Kirchhoff rods are presented within the theoretical framework of the simplified strain gradient theory. The newly developed Cosserat rod model contains only one intrinsic material length squared parameter to account for the effects of microstructures. Applications of the theory are also presented in this paper. Examples include the equilibrium analysis of a microspring and the buckling behavior of a microcolumn. The first application focuses on estimating the restoring force of a microspring that is deformed from an originally straight rod with uniform cross-sectional area. Semianalytical results show that the restoring force of the microspring predicted by the new strain gradient rod model is always larger than that of its classical counterpart. The restoring force is found to increase with both the intrinsic material length squared parameter and the rod radius. For the stability analysis of a microcolumn, an analytical expression is derived for the critical buckling load. It is found that the critical force predicted by the developed nonclassical Kirchhoff rod model depends linearly on the intrinsic material length squared parameter, quantitatively indicating the significance of strain gradient effects. |
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Keywords
simplified strain gradient theory, Kirchhoff rod,
microstructural effect, microspring, microcolumn
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Milestones
Received: 16 July 2019
Revised: 6 January 2020
Accepted: 13 January 2020
Published: 8 April 2020
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Authors |
| Jun Hong | |
| Jiangsu Key Laboratory of
Engineering Mechanics, School of Civil Engineering Southeast University 2 Sipailou Street Nanjing, 210096 China |
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| Gongye Zhang | |
| Jiangsu Key Laboratory of
Engineering Mechanics, School of Civil Engineering Southeast University 2 Sipailou Street Nanjing, 210096 China |
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| Xiao Wang | |
| Jiangsu Key Laboratory of
Engineering Mechanics, School of Civil Engineering Southeast University 2 Sipailou Street Nanjing, 210096 China |
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| Changwen Mi | |
| Jiangsu Key Laboratory of
Engineering Mechanics, School of Civil Engineering Southeast University 2 Sipailou Street Nanjing, 210096 China |
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