Multi-parameters Perturbation Solution For Functionally Graded Piezoelectric Thin Circular Plates

As a new composited material,functionally graded material has a varied function of volume content of each component in the spatial position.Because of the continuous changes,the macroscopical continuous properties of material can relieve or eliminate the stress concentrations in interfaces and make temperature and stress change uniformly.The past few years has seen the wide application of FGM and many scholars have researched the mechanical performances of functionally graded plates,especially for the FGM plates which are made of ceramics and metal.We know that ceramics shows favorable properties of bearing heat and resisting compression,and,on the other hand,some metals,such as low-carbon steel,own excellent abilities in tension and tenacity.As a result,we can see good performances in both thermology and mechanics in the mixed ceramics-metal materials.Piezoelectric materials will exhibit direct piezoelectric effect and inverse piezoelectric effect because the unique microstructures.Piezoelectric materials are utilized widely in various fields,such as airport,civil engineering and health care.In addition,structure with the piezoelectric effect can detect and repair the damages by itself.However,this kinds of laminated structures generally produced by thin ceramic layers and will generate serious stress concentrations in the combined interfaces.Fortunately,after the designers introduce the concept of FGM into the design of piezoelectric material,we obtain the FGPM which has favorable properties of both materials.FGPM circular plate structures show obvious advantages both in material properties and structural types,but there has few researches for them.In this study,the small deflection bending problem of FGPM circular thin plate with uniformly distributed loading under the clamped boundary is analyzed by perturbation methods.Firstly,When to think about the functionally graded effect,the elastic constants,piezoelectric constants and dielectric constants are modeled as three varied functions of the thickness h of plate.Then we use the stress functions methods to simplify the equations of spatially axisymmetric problem to three governing equations of small deflection bending problem of plate.Next,a set of analytical solutions are obtained by the multi-parameter perturbation methods,as well as solutions of different functionally graded indexes.Finally,the results of laminated model of finite element method verify the validity of analytical solution.The results of this paper provide theoretical reference to fine analysis and design of FGPM thin plate.The main conclusions are as follows: First,this paper considers the elastic constants,piezoelectric constants and dielectric constants to three functions of h,the approximate analytical solution fits the numerical solution well.Second,the deformation of FGPM plate is smaller than the FGM plate which indicates piezoelectric effect has the function of relieving structural deformation.Third,FGPM can realize the transfer between mechanical energy and electric energy,from the energy conservation law we know that the strain energy of FGPM structure is always less than the strain energy of FGM structure when to bear same loadings.