Bending Analysis Of Functionally Graded Thin Plates With Different Moduli In Tension And Compression

The classic mechanics of elastic theory considers that materials exhibit the same elastic properties in the state of tension and compression. However, experiments indicate that many materials have different elastic properties under the conditions of tension and compression, such as ceramics, rubber, concrete, and some new composite materials etc. C.A.Амбарцумян, the scholar of the former Soviet Union, published the work which was named by Different Modulus Elasticity Theory and promoted the development of bimodular elastic mechanics.With the progress of science and technology, some new materials have emerged such as functionally graded material abbreviated as FGM, which is usually made of different materials with different properties. Since the volume content of each component of FGM is in a continuous change in the spatial position, the material shows a gradient property on the macro level. Thus, FGM exhibits favorable effects on eliminating interface problems and relieving thermal stress concentrations, thus it has been widely used in various fields. Recently, many scholars have studied the mechanical behavior of functionally graded plates. In especial, abundant research results have been achieved about functionally graded plates which are made of ceramic and metal. However, there are few studies regarding the bending response of a functionally graded plate with bimodular effect.In this study, the bending problem of functionally graded thin plate is analyzed. Firstly, based on the classical Kirchhoff hypothesis, a mechanical model of subzones in tension and compression is established and different moduli formulations in tension and compression are applied, and the poisson’s ratio is modeled as two different constants, Then the governing equation of the small deflection bending problem is obtained, and based on classical nonlinear Von Karman plate theory, the governing equations of the large deflection bending problem are obtained. From which the flexural stiffness and the location of the neutral layer of the functionally graded thin plate with bimodular effect can be derived. Next, the approximate analytical solution under lateral loads can be obtained by the Ritz approach. On the other hand, the bending problem under different gradient index has also been simulated by finite element method, which verifies the analytical solution.The results of this paper are meaningful for the fine analysis and design of functionally graded thin plate. The main conclusions are as follows: First, based on the mechanical model of subzones in tension and compression, the approximate analytical solution and the numerical solution are in agreement substantially. Second, when large deformation occurs, the design with a small deflection approach is not economical, if you do not consider the plane strain. Third, when the plate is in high ceramic content and the modulus of the ceramic is higher than that of the metal, the design without considering the bimodular effect of the functionally graded plates is unsafe.