Refined Reddy-Vlasov Higher-order Shear Deformation Laminated Plate Theories Based On Murakami And Tessler Zig-zag Functions

Refined Reddy-Vlasov higher-order shear deformation plate theories for laminated plates are proposed using the Zig-zag functions developed by Murakami and Tessler.The traction-free conditions on the top and bottom surfaces of plates are enforced to reduce the number of unknowns of the present theories.By referring to the Koiter's recommendation,the transverse normal stress has been taken into account,as a consequence,the higher-order terms of transverse displacement are not neglected.Zig-zag functions developed by Murakami and Tessler are employed in the model to emulate the discontinuties of the first order derivatives of the in-plane displacements distributions with respect to the thickness coordinate.The numerical results of laminated plates in varied span-to-thickness ratios and numbers of layers are included to evaluate the accuracy of theories.It is conducted that:(1)Zig-zag theories can always give accurate predications of deflections of laminated plates,and it is deduced that the differences among Zig-zag functions do not effect the results of deflections;(2)Generally the Zig-zag function proposed by Tessler is the preferred one for evaluating the in-plane stresses;(3)For the cases of the present theories,the Zig-zag function developed by Murakami is highly recommended in the analysis of transverse stresses of laminated plates;(4)Enforcing the traction-free conditions generally yield accurate equivalent single layer models,but for Zig-zag theories,this method is unreliable.