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Co-rotational Formulation for Sandwich Plates and Shells Yating Liang, Bassam A. Izzuddin C OMPUTATIONAL S TRUCTURAL M ECHANISM G ROUP (CSM) D EPARTMENTAL OF C IVIL AND E NVIRONMENTAL E NGINEERING I MPERIAL C OLLEGE L ONDON 22 ND ACME C ONFERENCE ON C OMPUTATIONAL M ECHANICS - 2-4 A PRIL - E XETER - UK

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Background Sandwich structures in civil engineering: Insulation wallsRoof panelsCurtain wall glazing

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Outline of Presentation

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Zigzag Displacement Fields Four orthogonal through-thickness displacement modes: Seven displacement parameters per node Five basic nodal freedoms Two additional freedoms

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Modulus ratio Transverse Shear Stress Through Thickness R=10 5 R=10 6 R=10 2 R=10

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Bisector Co-rotational Framework Local x- and y- axes are set to be the bisectors of the two element diagonals in both the initial undeformed and the current deformed configuration. Basic freedoms are defined in this co-rotational system. Izzuddin & Li (2004)

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Shell Coordinate System Additional freedoms are defined in local shell coordinate system. Two considerations: Computational efficiency Consideration of composite materials α x y

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Additional freedoms are defined in local shell coordinate system. Shell Coordinate System z x y n

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Additional freedoms are defined in local shell coordinate system. Shell Coordinate System n z x y

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α Consideration of Composite Materials α β x-axis of element coordinate system With the use of the shell coordinate system, the relative orientation of the composite material fiber relative to the element coordinate system is readily determined.

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Layer-wise Theory Hellinger-Reissner Variation Principle

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Numerical Example 1 Sandwich plate under bi-directional sinusoidal transverse loading

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Annular sandwich plate under uniform transverse shear at one end Numerical Example 2 α

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Numerical Example 3 Cylindrical sandwich shell under point load

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Summary

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Thank you! Questions?

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FEA Simulations Usually based on energy minimum or virtual work Component of interest is divided into small parts – 1D elements for beam or truss structures.

FEA Simulations Usually based on energy minimum or virtual work Component of interest is divided into small parts – 1D elements for beam or truss structures.

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