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Comprehensive and easy-to-use torsion and bending theories for micropolar beams
- Source :
- International Journal of Mechanical Sciences. 114:71-87
- Publication Year :
- 2016
- Publisher :
- Elsevier BV, 2016.
-
Abstract
- The main goal of this paper is to develop a comprehensive beam model based on the micropolar elasticity theory which is as general, as easy to use, and as convenient as the classical beam theories. Uncomplicated torsion and bending theories for micropolar elastic beams deforming in three-dimensional space and under different types of external loading and boundary conditions are presented in this paper. Unlike the classical beam models, the developed beam model includes the effect of microinertia and contains new material parameters to capture the microstructure-dependent size effects which could be useful when dealing with micro scale beams. The presented micropolar beam model generalizes the Duleau torsion and Timoshenko bending beam models to include the microstructure effects. Hamilton's principle and a variational approach are used to derive the dynamic equations of the micropolar beam with longitudinal, torsional, and bending deformations. Then the governing dynamic equations are solved numerically by using a finite element approach and numerical results for a simply supported micropolar beam are provided. The static and dynamic behaviors of the developed micropolar beam model are studied and compared against the classical beam models. In particular, the conditions for recovery of the results of the classical beam theories, i.e. Duleau and Timoshenko theories, are addressed.
- Subjects :
- Timoshenko beam theory
Materials science
Mechanical Engineering
Finite element approach
Torsion (mechanics)
02 engineering and technology
Mechanics
021001 nanoscience & nanotechnology
Condensed Matter Physics
Bending beam
020303 mechanical engineering & transports
0203 mechanical engineering
Mechanics of Materials
Bending stiffness
Physics::Accelerator Physics
General Materials Science
Boundary value problem
0210 nano-technology
Dynamic equation
Beam (structure)
Civil and Structural Engineering
Subjects
Details
- ISSN :
- 00207403
- Volume :
- 114
- Database :
- OpenAIRE
- Journal :
- International Journal of Mechanical Sciences
- Accession number :
- edsair.doi...........fc3043cfc9adc85fdd947a14fee26557