Stress analysis of functionally graded plate under different gradient direction

Functionally Graded Materials (FGMs) are advanced engineered materials whereby material composition and properties vary spatially in macroscopic length scales, caused by manufacture process. One approach to produce FGMs is use of additive manufacturing (3D printing), which can control local composition and microstructure. During 3D printing of FGMs, the reliability requirements for the product should be considered to meet desired or application-specific performance criteria. Furthermore, the gradient distribution and its relationship with the loading direction will affect the macro stiffness and mechanical behavior. The purpose of this paper is to investigate the general stress field of an FGM rectangular plate for different gradient directions, perpendicular, parallel and inclined to the loading direction, both analytically and numerically. Also, the influence of different elastic modulus function variation, such as power law and exponential functions, on the stress and displacement fields is studied through a numerical example. The relevant governing equations of elasticity are solved with elastio-static analysis with power law volume fraction, and verified against finite element (FE) solutions. The FE solution is obtained using plane stress elements with spatially graded property distribution (at different gauss points), which is implemented by a user material subroutine (UMAT) in Abaqus FE software. The comparison between the exact solution and numerical simulation shows the efficiency of graded elements in modelling of FGM. Also, the results demonstrate that the direction of material property gradient and the nature of its variation have significant effects on the mechanical behavior of the FGM plate. This paper presents an approach for design of new materials with controlled macro properties.