A novel size-dependent microbeam element based on Mindlin’s strain gradient theory

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• 作者：R. Ansari ; M. Faghih Shojaei ; F. Ebrahimi ; H. Rouhi…
• 关键词：Microbeam ; Mindlin’s strain gradient theory ; Finite element method ; Euler–Bernoulli beam theory
• 刊名：Engineering with Computers
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：32
• 期：1
• 页码：99-108
• 全文大小：971 KB
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• 作者单位：R. Ansari (1)
  M. Faghih Shojaei (1)
  F. Ebrahimi (1)
  H. Rouhi (1)
  M. Bazdid-Vahdati (1)
  
  1. Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
  
• 刊物类别：Computer Science
• 刊物主题：Computer-Aided Engineering and Design
  Mathematical Applications in Chemistry
  Systems Theory and Control
  Calculus of Variations and Optimal Control
  Mechanics
  Applied Mathematics and Computational Methods of Engineering
  
• 出版者：Springer London
• ISSN：1435-5663

文摘

Based on Mindlin’s strain gradient elasticity and Euler–Bernoulli beam theory, a non-classical beam element capable of considering micro-structure effects is developed. To accomplish this aim, the higher-order tensors of energy pairs in the energy functional are vectorized and written in the quadratic representation, from which the stiffness and mass matrices of the element are obtained. In comparison with the classical Euler–Bernoulli beam element, the new element needs one additional nodal degree of freedom (DOF) which results in a total of three DOFs per node. The formulation of the paper is general so that it can be reduced to that based on the modified couple stress theory, the modified strain gradient theory, and the classical elasticity theory. To show the reliability of the proposed element, the bending and free vibration problems of microbeams under different kinds of end conditions are addressed. It is revealed that the present finite element results are in excellent agreement with the ones achieved through analytical solutions. Keywords Microbeam Mindlin’s strain gradient theory Finite element method Euler–Bernoulli beam theory