Spline Finite Point Method For Geometrically Nonlinear Bending Of Piezoelectric Functionally Graded Plates Based On Neutral Surface

Functionally graded material has been developed rapidly as a new kind of composite material in recent years,which has many advantages and is better than homogeneous and laminated materials,such as high temperature resistance,corrosion resistance and wear resistance.The material composition of the FGM is continuously distributed in space,so it can avoid the stress concentration phenomenon in the thermal environment.FGM is widely used in aerospace,energy,biology,civil engineering nowadays.The material composition consists of the metal/ceramic,metal/metal,metal/non-metal,non-metal/ceramic and so on.The researches on the mechanical properties of FGM are very active at present.Piezoelectric materials has the unique positive and negative piezoelectric effect,which can be used as a driver or a sensor in practical applications.The combination of FGM and piezoelectric materials as an intelligent structure model is the new direction of the future structure optimization design,which combines the advantages of piezoelectric materials and FGM.The in-depth research and practical application on the mechanical properties of piezoelectric FGM structure have theory and engineering application valueIt is difficult to study the nonlinear mechanical behavior of FGM structures due to the continuous distribution.The neutral surface constitutive equation has simple calculation and good convergence in the analysis of nonlinear problems.The spline finite point method is a meshless method,which has advantages on solving nonlinear problems,It can avoid mesh reconstruction caused by mesh distortion in large deformation.Therefore,in this paper,based on the neutral surface,as well as the classical plate theory and the first order shear theory,the spline finite point method is used to establish the calculation model of geometrically nonlinear bending of FGM plates.MATLAB software is used to analyze the static nonlinear bending behavior of FGM plate in thermal environment and electric field.First of all,The FGM plate bending behavior in the thermal environment and electric field has been carried out.The effect of FGM material composition and gradient,the ratio of span to thickness and other parameters have been discussed.The piezoelectric materials is adopted to control the deformations of FGM plate.Secondly,the stress distribution of FGM plate when considering geometric nonlinearity has been carried.By the analysis of parameters,the plate thickness span ratio,the effects of temperature field,material gradient,aspect ratio on FGM plate geometrically nonlinear bending have been studied.The results show that the spline finite point method is a reliable and simple method and has a good convergence for studying the nonlinear bending of piezoelectric FGM plates.