International Journal of Advanced Science and Technology Vol.72 (2014), pp.37-48 http://dx.doi.org/10.14257/ijast.2014.72.04 ISSN: 2005-4238 IJAST Copyright ⓒ 2014 SERSC Verification of Dynamic Relaxation (DR) Method in Isotropic, Orthotropic and Laminated Plates using Small Deflection Theory Osama Mohammed Elmardi Department of Mechanical Engineering, Faculty of Engineering and Technology, Nile Valley University, Atbara - Sudan osamamm64@gmail.com Abstract Dynamic Relaxation (DR) method is presented for the analysis of geometrically linear laterally loaded, rectangular laminated plates. The analysis uses the Mindlin plate theory which accounts for transverse shear deformations. A computer program has been compiled. The convergence and accuracy of the DR solutions of isotropic, orthotropic, and laminated plates for elastic small deflection response are established by comparison with different exact and approximate solutions. The present Dynamic Relaxation (DR) method shows a good agreement with other analytical and numerical methods used in the verification scheme. It was found that: The convergence and accuracy of the DR solution is dependent on several factors which include boundary conditions, mesh size and type, fictitious densities, damping coefficients, time increment and applied load. Also, the DR small deflection program using uniform meshes can be employed in the analysis of different thicknesses for isotropic, orthotropic or laminated plates under uniform loads in a fairly good accuracy. Keywords: Dynamic Relaxation (DR) method, Dynamic Relaxation Solution, Verification of the Dynamic Relaxation, numerical comparisons 1. Introduction There are many situations in engineering applications where no single material will be suitable to meet a particular design requirement. However, two materials in combination may possess the desired properties and provide a feasible solution to the materials selection problem. A composite can be defined as a material that is composed of two or more distinct phases. It is usually a reinforced material that supported in a compatible matrix, assembled in prescribed amounts to give specific physical, mechanical and chemical properties. Many composites used today are at the leading edge of materials technology, with their performance and cost appropriate to overwhelming applications such as that in space industries. Nevertheless, heterogeneous materials combining the best aspect of dissimilar constituents have been used by nature for millions of years ago. Ancient societies, imitating nature, used this approach as well: The book of exodus explains the usage of straw to reinforce mud in brick making without which the bricks would have almost no strength. Here in Sudan, the population from ancient ages dated back to Meroe civilization, and up to now used zibala (i.e., animal dung) mixed with mud as a strong building material. Composites possess two desirable features: the first one is their high strength to weight ratio, and the second is their properties that can be tailored through the variation of the fiber orientation and the stacking sequence which give the designer a wide choice of a suitable composite material. The incorporation of high strength, high modulus and low density fibers in a low strength and a low modulus matrix material result in a structural composite material