Shape Memory Alloy Engineering

6.4. Plate and Laminate Models for SMA Applications

An initially flat plate is defined by its reference domain Ω:

Ω={(X1,X2,Z)∈R3/Z∈(−t2,t2),(X1,X2)∈M⊂R2}

(6.41)

where t is the constant thickness of the plate, Z is the transverse coordinate orthogonal to the undeformed mid-plane M identified by Z = 0 and (X₁,X₂) are mid-plane (or simply in-plane) reference coordinates.

6.4.1. Finite Deformation Plate Model

The following displacement field is assumed for the plate:

v(X1,X2,Z)=u(X1,X2)+Zφ(X1,X2)+Z2ψ(X1,X2)

(6.42)

where u = {u₁,u₂,u₃}^T represents the displacement ...