Equivalent ThermoElasticity Analysis of 2D Lattice Structures With Periodic Unit Cells

ZHANG Zhaohui; LI Baohui; SHI Jiao

doi:10.21656/1000-0887.390025

Volume 39 Issue 6

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ZHANG Zhaohui, LI Baohui, SHI Jiao. Equivalent ThermoElasticity Analysis of 2D Lattice Structures With Periodic Unit Cells[J]. Applied Mathematics and Mechanics, 2018, 39(6): 714-727. doi: 10.21656/1000-0887.390025

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Equivalent ThermoElasticity Analysis of 2D Lattice Structures With Periodic Unit Cells

doi: 10.21656/1000-0887.390025

¹College of Water Resources and Architectural Engineering, Northwest A & F University, Yangling, Shaanxi 712100, P.R.China;²College of Transportation and Surveying, Yangling Vocational and Technical College, Yangling, Shaanxi 712100, P.R.China

Funds: The National Natural Science Foundation of China（51505388）；The National Key Research and Development Project of China（2017YFC0405102）

Received Date: 2018-01-16
Rev Recd Date: 2018-04-25
Publish Date: 2018-06-15

Abstract

Abstract

The thermo-elasticity of 2D lattice structures with periodic unit cells was studied. The lattice structure was homogenized as a pseudo-membrane (PM) structure and the equivalent thermal expansion coefficients (TECs) of the PM were derived. The TECs were expressed as explicit functions of the geometrical and physical parameters of the links in unit cells. Simultaneously, the elastic properties were re-defined based on the new geometry of the unit cell under thermal load. Numerical results were given to show the difference between the deformations of the structure under different thermo-mechanical loads, and a uniform pressure was applied on the top surface of the cantilever beam with or without thermal loads (the temperature increment was positive, negative or null, respectively). In simulation, the deformations of the lattice structure beams (with different sizes of unit cells) and the corresponding PM beams were calculated numerically. The theoretical solution of the beam deformation was also given with the elasticity of the PM beam. Differences between the solutions verify the correctness of the derived equivalent parameters. Results show the validity of the PM method for equivalent thermo-mechanical analysis of 2D lattice structures with periodic unit cells.
- homogenization,
- lattice structure,
- pseudo-membrane method,
- thermo-elasticity,
- unit cell

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References(20)

References

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