The dynamic response is depending on the new higher order shear deformation function which supported simply by the other hand the cross-ply laminated shallow shell. The amount of the solutions of the new displacement is optimized for giving the closest results to the 3D elasticity which depends of the parameter ‘‘m’’. It is obvious that the obtained transient reactions that Navier series use for both types the thick and thin anti-symmetric as well as the symmetric cross ply laminated shallow shell. The results of the several parameters design as the number of laminates, curvature ratio with the thickness ratio on dynamic reaction of the laminated composite (Glass/epoxy) and hybrid (Glass/carbon/epoxy) shallow shell which are underwent to the center point load and the distributed line with different periods of time dependent loading such as sine pulse, triangular pulse and step pulse are all examined and studied. On the other hand, the accuracy of the present codes by using Matlab R2017b is verified by comparing withAnsys 15 software.

Topics
MATLAB, Algebraic geometry
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