C0 MIXED LAYERWISE QUADRILATERAL PLATE ELEMENT WITH VARIABLE IN AND OUT-OF-PLANE KINEMATICS AND FIXED D.O.F

A quadrilateral, eight-node, mixed plate element based upon a recent 3D, variable kinematics zig-zag plate model by the authors is developed. Representation can be refined across the thickness though the number of unknown does not depend on the number of constituent layers, the nodal variables being fixed. The out-of-plane stress continuity is a priori satisfied at the interfaces and the material properties are allowed to step-vary moving over the plane of the structure. In order to obtain a C0 model, all derivatives of unknowns are converted with a technique that does not introduce additional d.o.f. Equilibrium equations are satisfied just in approximate integral form, mid-plane displacements and interlaminar stresses, the nodal d.o.f., being interpolated using the same standard serendipity shape functions. As shown by numerical results, this does not result in any precision loss. Accuracy, solvability and convergence are assessed considering multi-layered monolithic and sandwich-like structures with different boundary conditions and abruptly changing material properties across the thickness, for which exact solutions are available. Also a bonded joint is studied, which is treated as a laminate with spatially variable properties. In all these cases, the element is shown to be fast convergent and free from spurious, oscillating results.