A numerical and analytical study of size effects in free vibration of heterogeneous materials

  • Bahman Hassanati

Student thesis: Doctoral Thesis

Abstract

In this thesis, the influence of the periodic microstructure on the dynamic mechanical behaviour of geometrically similar heterogeneous samples, namely 2D beams and 3D plates, with different dimensions and boundary textures but constant aspect ratio has been numerically investigated. Beam samples of a representative material comprised of 2D unit-cells were created using the conventional finite element analysis (FEA) to identify and quantify size effects existing in flexural modal frequencies when the scale of microstructure becomes comparable to the macroscopic dimensions. The unit cells were created so as to keep the overall properties of the material at the macroscopic scale constant despite variations in the void or inclusions volume fraction. The finite element numerical results were then compared against the analytical results obtained from the enhanced nonlocal Timoshenko beam which incorporates the Eringen small length scale coefficients, but the values obtained for the coefficient exhibited size dependency. Accordingly, 2D analysis using a novel finite element method (MPFEM) or, alternatively, the control volume based finite element method (CVFEM) was carried out by incorporating micropolar constitutive behaviour into their formulation. The numerical predictions using either MPFEM or CVFEM were then matched with the FEA results to obtain additional constitutive parameters featuring in planar micropolar elasticity theory. The 2D models were then extruded to form square 3D plates as a straightforward progression. These samples demonstrated a moderate degree of anisotropy, which increased with volume fraction. Nevertheless, the 3D-MPFEM models which assume isotropy agreed with the dynamic behaviour of FEA nonhomogeneous models with low volume fractions, which were mildly anisotropic. Subsequently, to reduce the anisotropy, 3D square plate samples with a square-pyramidal geometry, or a body-centred cubic, arrangement of spherical voids and inclusions were modelled which demonstrated approximately isotropic characteristics for which the 3D-MPFEM results agreed with the finite element results at lower mode numbers.
Date of Award2 Jun 2020
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsUniversity of Strathclyde
SupervisorMarcus Wheel (Supervisor) & Phil Riches (Supervisor)

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