Modelling of orthorhombic quasicrystal shallow shells

• The MLPG method is applied to shallow shell analysis in orthorhombic quasicrystals.
• Bak and elasto-hydrodynamic models are used for phason governing equation.
• Spatial variations of phonon and phason displacements are approximated by MLS scheme.
• The Houbolt finite-difference scheme is applied for time integration.
• Numerical results show a small influence of coupling parameters on phonon deflection.

The Reissner–Mindlin theory is applied to shallow shells with material properties of orthorhombic quasicrystals (QC). A quasi-periodic arrangement of atoms through the thickness of the shell is considered. Due to the intrinsic characteristics of QCs two excitations need to be described under dynamic loads, namely, phonon (elastic waves) and phason (long wavelength fluctuations) fields. The Bak and elasto-hydrodynamic models are applied for phason governing equation in the elastodynamic case. The phason displacement for the orthorhombic QC in the first-order shear deformation shallow shell theory depends only on the in-plane coordinates on the mid-surface of the shell. A weak formulation for the set of governing equations in the Reissner–Mindlin theory is transformed into local integral equations on local subdomains on the mid-surface of the shell by using a unit-step test function. Nodal points are randomly spread on the mid-surface of the shell and each node is surrounded by a circular subdomain to which local integral equations are applied. The meshless approximation based on the Moving Least-Squares (MLS) method is employed for the implementation. The influences of the shell curvature and the coupling parameter of quasicrystals on the shell deflection are investigated.