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Research Papers

On the Analysis of Periodically Heterogenous Beams

[+] Author and Article Information
Shilei Han

University of Michigan-Shanghai
Jiao Tong University Joint Institute,
Shanghai 200240, China
e-mail: shilei.han@outlook.com

Olivier Bauchau

Professor
Fellow ASME
Department of Aerospace Engineering,
University of Maryland,
College Park, MD 20742

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 9, 2015; final manuscript received May 25, 2016; published online June 20, 2016. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 83(9), 091001 (Jun 20, 2016) (13 pages) Paper No: JAM-15-1663; doi: 10.1115/1.4033721 History: Received December 09, 2015; Revised May 25, 2016

Based on the symplectic transfer-matrix method, this paper develops a novel approach for the analysis of beams presenting periodic heterogeneities along their span. The approach, rooted in the Hamiltonian formalism, generalizes developments presented earlier by the authors for spanwise uniform beams. Starting from the kinematics of a unit cell, the approach proceeds through a set of structure-preserving symplectic transformations and decomposes the solution into its central and extremity components. The geometric configuration and material properties of the unit cell may be arbitrarily complex as long as the cell's two end cross sections are identical. The proposed approach identifies an equivalent, homogenized beam with uniform curvatures and sectional stiffness characteristics along its span. Numerical examples are presented to demonstrate the capabilities of the analysis. Predictions are found to be in excellent agreement with those obtained by full finite-element analysis.

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Figures

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Fig. 1

A typical periodically heterogenous beam

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Fig. 2

Configuration of the unit cell

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Fig. 3

The internal and retained DOF of a unit cell

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Fig. 4

Configuration and meshes of a slice of helicoidal beam

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Fig. 5

Configuration and mesh of a pretwisted, ribbed box beam

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Fig. 6

Axial stress flow over the first cell, proposed approach (ne = 0)

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Fig. 7

Axial stress flow over the first cell, proposed approach (ne = 4)

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Fig. 8

Axial stress flow over the first cell, proposed approach (ne = 56)

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Fig. 9

Axial stress flow over the first cell, proposed approach (ne = 59)

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Fig. 10

Axial stress flow over the first cell, abaqus predictions

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Fig. 11

Axial stress flow over the fifth cell, proposed approach (ne = 0)

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Fig. 12

Axial stress flow over the fifth cell, abaqus predictions

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Fig. 13

Axial stress flow over the tenth cell, proposed approach (ne = 0)

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Fig. 14

Axial stress flow over the tenth cell, proposed approach (ne = 4)

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Fig. 15

Axial stress flow over the tenth cell, proposed approach (ne = 56)

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Fig. 16

Axial stress flow over the tenth cell, proposed approach (ne = 59)

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Fig. 17

Axial stress flow over the tenth cell, abaqus predictions

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Fig. 18

Configuration of the spatial frame-cell

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Fig. 19

Configuration of the spatial frame structure

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