International Journal of Applied Engineering Research ISSN 0973-4562 Volume 13, Number 11 (2018) pp. 9893-9908 © Research India Publications. http://www.ripublication.com 9893 Displacement and Stress Analysis in Shear Deformable Thick Plate Onyeka F. C. Research Scholar, Department of Civil Engineering,University of Nigeria, Nsukka, Enugu State, Nigeria. Okafor, F. O. Professor, Department of Civil Engineering,University of Nigeria, Nsukka, Enugu State, Nigeria. Onah, H.N. Lecturer, Department of Civil Engineering,University of Nigeria, Nsukka, Enugu State, Nigeria. Abstract This paper presents exact solution of displacement fields of thick rectangular plate which was obtained using traditional third order refined theory for the bending of rectangular plates with different support cases under general boundary conditions. The aim of study is static bending analysis of an isotropic rectangular thick plate using analytical method. Total potential energy equation of a thick plate was formulated from the first principle. This equation was subjected to direct variation to obtain three simultaneous direct governing equations for determination of displacement coefficients. The main assumption here is that the vertical line that is initially normal to the middle surface of the plate before bending is no longer straight nor normal to the middle surface after bending, as a result the shear deformation profile F (z) is used in the place of z. The shear deformation profile equation for vertical shear stress through the thickness of the plate was formulated mathematically in line with Timoshenko work. From this profile equation, the deformation line equation (called function of z or s) was obtained and compared to other four model. These models in comparison includes one polynomial and three trigonometric model. A numerical problem for a rectangular plate simply supported around all the edges was used to test the sufficiency of this study. It was observed that the values of non- dimensional forms of displacements and stresses from the present study agree with the values from previous studies. Also observed is that the values of the in-plane quantities did not vary with span-depth ratio () 6 and above. They are all equal to the values from classical plate theory (CPT) for the values of () 6 and above. However, the out-of-plane quantities varied with span-depth ratio from () equal to 4 up to () equal to 30, after which they become constant and approximately equal to values from CPT. This shows that the present method is reliable and sufficient for thick plate analysis. Keywords: Exact solution, shear deformation, displacement, stress, deflection, total potential energy. INTRODUCTION The use of thick plate materials in engineering is increasing due to their attractive properties such as high strength-to-weight ratio, economy, its ability to withstand heavy loads and ability to tailor the structural properties, etc. Plate structures find numerous applications in the aerospace or aeronautical Engineering, military, structural and mechanical Engineering or automotive industries. In Structural Engineering, plates are widely used in roof and floor slabs, bridge deck slabs, foundation footings, bulkheads, pressure and watertanks, turbine disks, spacecraft panels and ship hulls. Zenkour (2003) in his works on “Exact Mixed-Classical Solution for the Bending Analysis of Shear deformable Rectangular Plates” discovered that thin plate model does not provide a very good analysis of plates in which the thickness-to length ratio is relatively large. The method is very difficult but accurate. This makes analysis of thick plate very imperative. Refined shear deformation theories based on the power series expansion for displacements with respect to the thickness coordinate, and truncating the series at required order of thickness coordinate are called the higher-order shear deformation theories. This type of series expansion was initially proposed by Basset (1890). Refined plate theories have been characterized by the use of trigonometric displacement function. The refined plate theories; first, second and higher order shear deformation theory – HSDT can be obtained through the analogue means to solve the couples governing differential equations, consequently deduce deformation. Reddy’s third-order, and Reissner’s higher-order shear deformation plate theory which have two more unknowns’ variables in comparison with the classical plate theory. To be applied in this work is the higher order shear deformation theory – HSDT (third order shear deformation theory) using polynomial displacement function. Many scholars have obtained the closed form solutions and others have obtained approximate solution by use of energy method. However, one thing is common in them all - the use of trigonometric displacement functions to approximate the deformed shapes of the plates. (Chikalthankar et al., 2013; Sayyad, 2011; Akavci, 2007; Sayyad and Ghugal, 2012; Sadrnejad et al., 2009; Daouadji et al., 2013; Hashemi and Arsanjani, 2005; Reddy, 2014; Shimpi and Patel, 2006; Murthy, 1981; Daouadji, Tounsi, Hadji, Henni and El Abbes, 2012; Zhen-qiang, Xiu:xi and Mao-guang, 1994). Others have applied the polynomial displacement functions in numerical