Micro-Mechanical Approach for Spanwise Periodically and Heterogeneously Beam-like Structures

- Journal title : Journal of the Korean Solar Energy Society
- Volume 36, Issue 3, 2016, pp.9-16
- Publisher : The Korean Solar Energy Society
- DOI : 10.7836/kses.2016.36.3.009

Title & Authors

Micro-Mechanical Approach for Spanwise Periodically and Heterogeneously Beam-like Structures

Lee, Chang-Yong;

Lee, Chang-Yong;

Abstract

This paper discusses a refined model for investigating the micro-mechanical behavior of beam-like structures, which are composed of various elastic moduli and complex geometries varying through the cross-section directions and are also periodically-repeated and heterogeneous along the axial direction. Following the previous work (Lee and Yu, 2011), the original three-dimensional static problem is first formulated in a unified and compact form using the concept of decomposition of the rotation tensor. Taking advantage of the smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity, while also performing homogenization along the dimensional reduction simultaneously, the variational asymptotic method is rigorously used to construct a total energy function, which is asymptotically correct up to the second order. Furthermore, through the transformation procedure based on the pure kinematic relations and the linearized equilibrium equations, a generalized Timoshenko model is systematically established. For the purpose of dealing with realistic and complex geometries and constituent materials at the microscopic level, this present approach is incorporated into a commercial analysis package. A few examples available in literature are used to demonstrate the consistency and efficiency of this proposed model, especially for the structures, in which the effects of transverse shear deformations are significant.

Keywords

Homogenization;Dimensional reduction;Variational asymptotic method;Generalized Timoshenko model;Beam-like structures;Transverse shear deformations;

Language

English

References

1.

Hollister, S. J., Kikuchi, N., 1992. A comparison of homogenization and standard mechanics analyses for periodic porous composites. Compu. Mech. 10, pp.73-95.

2.

Kolpakov, A., 1991. Calculation of the characteristics of the thin elastic rods with a periodic structure. J. Appl. Math. Mech. 55 (3), pp.358-365.

3.

Jonnalagadda, Y., Whitcomb, J., 2011. Calculation of effective section properties for wind turbine blades. In: Proc. 52st AIAA/ASME/ASCE/AHS/ASC Struct., Struct. Dyn., Mat. Conf. AIAA, Colorado.

4.

Kolpakov, A., 1991. Calculation of the characteristics of the thin elastic rods with a periodic structure. J. Appl. Math. Mech. 55 (3), pp.358-365.

5.

Lee, C.-Y., Yu, W., 2011. Variational asymptotic modeling of composite beams with spanwise heterogeneity. Comput. Struct. 89, pp.1503-1511.

6.

Danielson, D., Hodges, D., 1987. Nonlinear beam kinematics by decomposition of the rotation tensor. J. Appl. Mech. 54, pp. 258-262.

7.

Berdichevsky, V., 1979. Variational -asymptotic method of constructing a theory of shells. PMM 43 (4), pp.664-687.

8.

Yu, W., Ho, J., Hodges, H. D., 2012. Variational asymptotic beam sectional analysis - an updated version. Int. J. Engrg. Sci. 50, pp.40-64.