Mechanics of Beams and Plates with Variable Mechanical Properties

Structures with variable mechanical properties have been attracting increasing attention in engineering. In contrast to conventional homogeneous structures, they are advantaged by variations in mechanical properties. Despite advances in developing such structures, their mechanical behaviour, particularly in the nonlinear regime and when thickness-stretching effects are considered, remains underexplored. To address this gap, the present thesis develops two-dimensional (2D) and quasi-3D theoretical frameworks to investigate the linear and nonlinear mechanics of beams, plates, and shells with variable mechanical properties, focusing on their static and dynamic responses. The thesis is structured using the following peer-reviewed journal papers as outcomes of the research. Paper 1: This paper mathematically investigates the large deformations of mechanical metamaterial beams with initial geometrical imperfections using a higher-order shear deformation theory. Importance of geometrical imperfections, graphene origami content and its distribution patterns, and the folding degree is comprehensively analysed, and the effect of boundary conditions is also examined. Paper 2: This paper investigates mathematically a geometrically imperfect thickness deformable mechanical metamaterial plate, analysing both the large deformations as well as linear vibration characteristics. Using Hamilton’s principle, the governing equations are derived and then discretised with the generalised differential quadrature method. A comprehensive parametric study is carried out to examine the effects of geometrical imperfections, graphene origami content and its distribution patterns, and folding degree on large deformations and natural frequencies. Paper 3: This paper develops a mathematical formulation using a thickness deformable theory for the free vibration response of bi-directional functionally graded viscoelastic plates, modelled within the Kelvin–Voigt framework. Eight governing motion equations are derived via Hamilton’s principle and discretised using a weightedresidual method. The model is used to study the influence of bi-directional material composition, viscoelasticity, and stretching effect on both the real and imaginary parts of natural frequencies, showing the differences between 2D and quasi-3D models, particularly for thick plates. Paper 4: In this study, a modified first-order shear-deformable shell model is developed, in which a logarithmic distribution of porosity is introduced as an imperfection, and the coupled motion equations are solved through a modal decomposition approach. A comprehensive parametric study highlights the roles of porosity, constituent proportion, and size-dependent coefficients in shaping the vibration characteristics of the system for various shell geometries. Paper 5: This paper investigates the nonlinear bending of composite doubly curved shells using a mathematical formulation based on a thickness deformable theory together with the von-K´arm´an-type geometric nonlinearities. Hamilton’s principle and the generalised differential quadrature method are used to derive and discretise the deformation equations, and the resulting nonlinear algebraic system is solved using the Newton–Raphson method. The numerical results highlight the effects of constituent proportion, porosity distributions, and curvature on the nonlinear deformations and stresses distributions. In addition to the core studies summarised above, further investigations on the mechanics of variable-mechanical-property structures (beams, plates, and shells) are presented in Appendices A–F, all of which have been published in peer-reviewed journals. All in one, in this thesis, theoretical models are formulated within computational frameworks and are used to analyse the mechanics of variable-mechanical-property structures.

Author dc:creator

• Karami, Behrouz

Advisors dc:contributor.advisor

• Ghayesh, Mergen
• Hussain, Shahid

• Variable-mechanical-property structures
• Nonlinear mechanics
• Numerical tools
• Viscoelasticity
• Initial geometrical imperfection

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/2440/151029

OAI identifier oai:identifier

oai:digital.library.adelaide.edu.au:2440/151029