Research Journal of Recent Sciences _________________________________________________ ISSN 2277-2502 Vol. 3(12), 99-106, December (2014) Res.J.Recent Sci. International Science Congress Association 99 Static Analysis of Functionally Gradient Material Plate with various Functions Bhandari Manish 1 , Purohit Kamlesh 2 and Sharma Manoj 1 2 Jai Naraine Vyas University, Jodhpur, Rajasthan, INDIA 1 Jodhpur Institute of Technology, Jodhpur, Rajasthan, INDIA Available online at: www.isca.in, www.isca.me Received 9 th December 2013, revised 4 th March 2014, accepted 30 th May 2014 Abstract Functionally gradient materials are one of the most widely used materials in various applications because of their adaptability to different situations by changing the material constituents as per the requirement. Nowadays it is very easy to tailor the properties to serve specific purposes in functionally gradient material. Most structural components used in the field of engineeringcan be classified as beams, plates, or shells for analysis purposes. In this paper static analysis of functionally gradient material plate is carried out by sigmoid law and verified with the published results. The plate is modeled in step wise variation of the properties in thickness direction. The convergence study of the results is optimized by changing the mesh size and layer size. Power law and exponential laware applied for the same material and set of conditions. Results have been presented comparing with each other and the published results. Keyword: Functional composites, elastic properties, finite element analysis (FEA) Introduction A huge amount of published literature has been observed for evaluation of thermomechanical behavior of functionally gradient material plate using finite element techniques. It includes both linearity and non linearity in various areas. A few of published literature highlights the importance of topic. E. J. Barbero and J. N. Reddy introduced a laminate theory for a desired degree of approximation of the displacements through the laminate thickness, allowing for piecewise approximation of the in-plane deformation through individual laminae. The solutions are compared with the 3-D elasticity solutions for the simply supported case 1 . G. Bao and L. Wang found that under mechanical loading the effect ofdifferent gradations on the crack driving force is relatively small 2 . S. Suresh and A. Mortensen focused on the processing of functionally graded metal-ceramic composites and their thermo mechanical behavior. They discussed various approximations for determination of properties and their limitations. They focused on various issues related to functionally gradient material manufacturing 3 . G. N. Praveen and J.N. Reddy reported the static and dynamic response of the functionally graded material plates by varying the volume fraction of the ceramic and metallic constituents using a simple power law distribution. Deflection and stresses under thermomechanical loadinghave been reported 4 . J.N. Reddy reported theoretical formulations and finite element analysis of the thermomechanical transient response of functionally graded cylinders and plates with nonlinearity. Numerical results of the deflections, temperature distributions and stress distributions in the cylinder and plates have beenpresente. The problems were studied by varying the volume fraction of a ceramic and a metal using power law distribution 5 . J. N. Reddy gave Navier'ssolutions of rectangular plates and Finite element models based on the third-order shear deformation plate theory for functionally graded plates. The formulation accounts for the thermomechanical coupling, time dependency and von Karman-type geometric non-linearity to show the effects of volume fractions and modulus ratio of the constituents on deflections and transverse shear stresses 6 . J.N. Reddy reported three-dimensional thermomechanical deformations of simplysupported functionally graded rectangular plates. The temperature, displacements and stresses of the plate were computed for different volume fractions of the ceramic and metallic constituents 7 . Jin and Paulino, Power-law function and exponential function are commonly used to describe the variations of material properties of FGMs 8 . However, in both power-law and exponential functions, the stress concentrations appear in one of the interfaces in which the material is continuous but rapidly changing. Therefore, Chung and Chi proposed a sigmoid FGM which is composed of two power-law functions to define a new volume fraction. They indicated that the use of a sigmoid FGM can significantly reduce the stress intensity factors of a cracked body 9 . Bhavani V. Sankar solved the thermoelastic equilibrium equations for a functionally graded beam in closed-form to obtain the axial stress distribution by keeping the Poisson ratio constant. The stresses were calculated for the cases for which the elastic constants vary in the same manner as the temperature and vice versa. The residual thermal stresses are greatly reduced, when the variation of thermoelastic constants are opposite to that of the temperature distribution 10 . Senthil S. Vel and R.C. Batra developed an analytical solution for three-dimensional thermomechanical deformations of a simply supported functionally graded rectangular plate subjected to time- dependent thermal loads 11 . M. Tahani1, M. A. Torabizadeh and A. Fereidoon, reported analytical method to analyze