Verification of Dynamic Relaxation (DR) Method using Small Deflection Theory

What is it about?

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.

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Why is it important?

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.

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