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 A PRIL - E XETER - UK

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

Outline of Presentation

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

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

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)

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

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

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

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.

Layer-wise Theory Hellinger-Reissner Variation Principle

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

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

Numerical Example 3 Cylindrical sandwich shell under point load

Summary

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