Exact Transfer- and Stiffness Matrix for the Composite Beam-column with Refined Zigzag Kinematics

The Refined Zigzag Theory (RZT), developed by Tessler/Di Sciuva/Gherlone is among the most promising approaches for analyzing shear-elastic composite structures today. Since its appearance many contributions have been published dealing with finite elements for laminated structures based on the efficient kinematic of RZT. For composite beam-columns C⁰-elements of different orders as well as p-type approximations are formulated and assessed. In this work a different approach is given. After establishing the governing equations in a first order differential equation system, the transfer matrix is obtained by a matrix series solution and by similarity transformation. The transfer matrix approach, in principle suited for 1D-structural elements such as beams, disks, circular plates and rotational shells, has been successfully applied in the past. Sometimes this approach exhibits numerical instabilities. The well-known relations between the transfer- and stiffness matrix are invoked to circumvent this drawback. The dynamic stiffness matrix and the load vector are obtained by reordering and partially inverting the submatrices of the transfer matrix. The results, which are obtained by one finite element only, are in agreement with available analytical and numerical solutions.