Three Dimensional Analysis Of Thero-Electric-Mechanical Behaviour Of Functionally Gradient Piezoelectric Material Rectangular Plate

In recent years, the study on the behavior of structural mechanics of functional graded piezo material (FGPM) is developed greatly. In this paper, we employ the state variable method for three-dimension analysis of a functionally gradient piezo material plate that is simply supported along its four edges.By introducing two displacement functions and two stress functions and replace the former displacement and stress, two independent state equations are constructed based on the three-dimensional piezoelasticity equations for transverse isotropy. The original differential equations are thus decoupled with the order reduced that will induce the state equations and transmission matrix of functionally gradient thermoelectricity plate that is simply supported along its four edges. Due to the inhomogeneity of functionally gradient piezo material (FCPM), the state equation has the physical performance, which will induce the laminate model for laminate approximation in this paper and obtain the analytical solutions of simply supported transverse isotropic functionally gradient piezoelectric rectangular plate under arbitrary mechanical, electric and thermal loading on the top and bottom surfaces. The Mathematica software is used to compile the relevant calculation programs and the examples are given, the calculated results are same with that given in the former literature. ,Assuming that the properties of materials, such as the mechanics, eletrology, thermology have three different gradient models which are polynomial function, exponent function and sinusoidal function respectively, based on the theories of three Dimensional elasticity and piezoelectricity equations, discuss the effect of differential gradient model distribution on the field variables of functional gradient piezo plate; meanwhile, discuss the effect of differential length breadth ratio and plate thick on the field variables change under the thermal, electric and mechanical loading of functionally gradient piezo plate. Since no assumption concerning with the stress and displacement are introduced due to the state formulation introduced directly from elastic mechanics, the present results can serves as benchmarks for clarifying the reliability of various approximate theories or numerical methods. We find that change inhomogeneity of FGPM will affect the static response of FGPM structures effectively, so in the engineering design, we always change the gradient index (the quantity reflect the distribution situation of FGPM material constant) to meet the design purpose.