Reddy-type zig-zag model for multilayered composite plate based on the HW variational theorem

ABSTRACT

Reddy's higher-order theory is quite attractive, but it could not describe a zig-zag shape distribution of in-plane displacement through the thickness direction and violates the continuity of transverse shear stresses at interfaces. This is due to neglect of the zig-zag function in the in-plane displacement field. Thus, a Reddy-type higher-order zig-zag theory is developed for analysis of multilayered composite plates. The developed model differs from existing ones by two features. First, a Reddy-type zig-zag function (RZZF) satisfying the bounding surface free traction condition is constructed. By introducing the RZZF into Reddy's model, a Reddy-type higher-order zig-zag model can be obtained. Second, a functional suitable for composite plate has been presented to obtain improved transverse shear stresses by employing the three-field Hu–Washizu (HW) variational principle. It is significant that the higher-order derivatives of displacement parameters in expression of transverse shear stresses have been eliminated, which is convenient for the model's finite element implementation. Equilibrium equations and analytical solution can be also presented by means of the HW variational principle. The performance of the proposed model is tested with different numerical examples, and numerical results show its accuracy and range of applicability.

KEYWORDS:

• Multilayered composite plates
• Reddy-type higher-order zig-zag model
• three-field Hu–Washizu variational principle
• transverse shear stress
• zig-zag function

Funding

The work described in this paper was supported by the National Natural Sciences Foundation of China [grant nos. 11272217, 11402152, 11572204].