C~0-type Higher-order Zig-zag Theory For Laminated Composite Plates

Previous zig-zag theories can reasonably predict the mechanical behaviors of laminated composite structures. However, the first derivatives of transverse displacement are involved in the displacement field of mentioned zig-zag theories, so their finite element counterparts have to use the C1interpolation functions. Thus, it is difficult to construct higher-order element based on these zig-zag theories. In order to avoid using the C1interpolation functions and improve the accuracy of previous zig-zag theory, this thesis will present the improved zig-zag theories a priori satisfying continuity conditions of transverse shear stresses at interfaces. Advantages of the proposed zig-zag theory are that the first derivatives of transverse displacement have been taken out from in-plane displacement field of the proposed zig-zag theory, so the C0interpolation functions are only required in its finite element counterparts. Therefore, based on the proposed zig-zag theory, it is convenient to construct higher-order plate elements such as six-note triangular element, eight-node quadrilateral element as well as nine-node quadrilateral element. The proposed zig-zag theory, which satisfying the continuity conditions of transverse shear stresses, can accurately calculate interlaminar stresses of multilayer plates, natural frequency and critical loads of soft-core sandwich plates. Studies in the thesis can be summarized as follows1) A C0-type zig-zag theory satisfying the continuity conditions of transverse shear stresses at interfaces is firstly proposed. The number of displacement variables involved in the proposed model is independent of the number of layers in laminates, and the first derivatives of transverse displacement have been taken out from displacement field. Thus, it is convenient to construct higher-order element based on the proposed model. In order to verify the performance of the proposed model, the equilibrium equations for static response have been derived using the principle of virtual displacement. For simply supported composite plates subjected to transverse loads, analytical results are also presented.2) A C0-type zig-zag theory for laminated composite and sandwich plates with general configurations is proposed, which satisfy the continuity conditions of transverse shear stresses at interfaces. Based on the proposed model, a six-node triangular element has been constructed. In order to assess performance of six-node triangular element, these elements are used to analyze bending problems of laminated composite plates with different thickness and materials at each ply, sandwich plates and angle-ply composite plates.3) Based on the proposed C0-type zig-zag theory, finite element formulation of eight-node quadrilateral element is presented to study free vibration of laminated composite and sandwich plate. In order to verify performance of the C0-type zig-zag theory for free vibration, free vibration of soft-core sandwich plate as well as laminated composite plates with different thickness and materials at each ply will be studied.4) Based on the proposed C0-type zig-zag theory, a three-node beam element is firstly proposed. Subsequently, finite element formulation of an eight-node quadrilateral element is also given. These elements are used to study static and buckling problems of soft-core sandwich beams and plates, respectively. Moreover, the effect of continuity conditions of transverse shear stresses at interfaces on accuracy of critical loads of soft-core sandwich structures has been studied.5) A C0-type zig-zag theory considering transverse normal strain is proposed, and effect of transverse normal strain as well as in-plane displacement model on displacement and stresses of laminated composite plates will be studied. In order to extend C0-type zig-zag theory to analyze the bending problems of thick plates, C0-type zig-zag theory considering transverse normal strain is firstly presented. The equilibrium equations for static response have been derived using the principle of virtual displacement. For simply supported composite plates subjected to transverse loads, analytical results are also presented.