Optimal design of Orthotropic Piezoelectric membranes and plates using particle swarms

[摘要] ENGLISH ABSTRACT: Over the past 50 years smart materials have made their appearance in many structures. Thethermopiezoelectric ceramic is one of these smart materials. When thermal e ects are considerednegligible, then the materials are classified as piezo-ceramic and piezoelectric materials.These so called piezo-ceramics are used as actuator and sensor components in many structures.The use of these components with composite materials is significant due to their application inthe aerospace and aeronautics fields. The interaction that the piezoelectric material has with acomposite body can be improved in order to reduce the energy requirement of the material fordeformation. An objective in the optimisation of composite material structures is to minimisecompliance or maximise sti ness uT f, with the laminate ply orientations as design variables,where u and f are displacement and force vectors, respectively.Here, the objective is not the maximisation of sti ness but the maximisation of compliance,with typical constraints being failure criteria. These failure criteria can include theories suchas the maximum principle stress, the Tsai-Hill or Tsai-Wu failure theories. The compliance ismaximised to accentuate any piezoelectric movement and is for theoretical treatment only.Piezoelectric materials once polarized the materials becomes quasi-isotropic. The piezoelectricmaterials are isotropic in the plane normal to the direction of the voltage being applied and havealtered properties normal to this plane. This change in the material properties can be exploitedso that the layup can be altered in orientation to improve performance. The idea is to improvethe mechanical capabilities of the structure subject to an electrical input or vice versa.In the works by both Carrera et al. and Piefort, First Order Shear Deformation Theory (FSDT) isused in finite element analysis to characterise the structural and electrical behaviour of a plate or shell. FSDT, also known as the Mindlin-Reissner theory, is a plate bending theory that assumesa transverse shear distribution through the thickness of the plate. This theory is considered animprovement on the standard theories such as the Kirchoor Timoshenko theories.Many optimisation techniques exist and are classed as either being direct search or gradientbased methods. Particle Swarm Optimisation (PSO) is a direct search method. It mimicsthe behaviour of a flock of birds or school of fish in their attempt to find food. The PSO'smathematical statement characterises a set of initial unknown particles within a designatedsearch space that are compared to a set of local best particles and a single global best particle.This comparison is used to update the swarm each run cycle.Regression is a procedure whereby a set of testing data is used to fit a pseudo-function thatrepresents the form the data should take in practice. The aim of this work is to optimise thepiezoelectric-composite layer interaction to improve the overall compliance of a structure.Extensive modelling is performed and tested with peer reviewed literature to demonstrate itsaccuracy.

[发布机构] Stellenbosch University