Keywords: semi-energy approach, finite strip method, post buckling analysis, anti-symmetric angle ply laminates, von Karman's compatibility equation.

The main advantage of the semi-energy finite strip method (FSM) is that it is based on the closed form solution of von Karman's compatibility equation in order to derive the analytical shape functions for the in-plane displacements fields. In the previously developed version of the semi-energy finite strip approach [1], which was suitable for the post-buckling analysis of thin composite plate structures, the out-of-plane displacement field of the finite strip is the only displacement which is postulated by a deflected form due to the application of classic laminated plate theory (CLPT).

In the current paper, a novel semi-energy FSM is developed based on the concept of first order shear deformation theory (FSDT) in order to attempt the post-buckling solution for relatively thick composite plates subjected to uniform end-shortening. In addition to the out-of-plane displacement field of the finite strip, the rotations with respect to x and y axes are also postulated by two deflected forms. The postulated deflected forms are substituted into von Karman's compatibility equation which is solved exactly to obtain the corresponding forms of the mid-plane stresses and displacements. The finite strip method developed is applied to analyze the post buckling behavior of thin and relatively thick anti-symmetric angle-ply composite plates with simply supported boundary conditions. The post buckling load-end shortening and load-maximum out-of-plane deflection path have been obtained by using two versions of semi energy FSM (i.e. the CLPT and FSDT versions). The results are discussed in detail and compared with those obtained using the finite element method (FEM) of analysis that was carried out by employing the general purpose ANSYS package.

It is noted that the theoretical developments of the above mentioned FSDT semi-energy FSM for the same analysis and its application, in the manner described in the current paper, have not been attempted so far elsewhere. The study of the results has revealed that the semi-energy formulations have very good convergence properties and produce very accurate results by incorporating significantly fewer numbers of degrees of freedom than those required by the FEM. The effects of mechanical couplings on the post-buckling behavior of anti-symmetric angle-ply laminated are discussed and highlighted. Moreover, it has been revealed that the formulation of the semi-energy FSM based on the FSDT is generally more accurate than that of the semi energy FSM based on CLPT for the post-buckling analysis of relatively thick laminated plates.

1

H.R. Ovesy, H. Assaee, "Semi-Energy Finite Strip Post-Buckling Analysis of Laminated plates Concerning the Effects of Mechanical Coupling", Composite Structures, 89, 120-125, 2009. doi:10.1016/j.compstruct.2008.07.019

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