Laminated Composite Plate Theories Accounting For Interlaminar Continuity And Its Accurate, Efficient Plate Elements

The laminated composite plate-like structures are finding increasing applications in various industries, such as aircraft and aerospace industry, automotive and marine industry, construction, sport goods etc. The most attractive mechanical properties of the laminated composite plates are the high specific modulus, high specific strength, high fatigue strength and designability. However, because of the inhomogeneous and anisotropic nature across the thickness, the mechanical properties of the laminated plates are much more complicated than the isotropic plates. The transverse strength of laminated plates is very weak, especially at the interlaminar interfaces between two adjacent laminae with different fiber orientations, which could lead to delamination damage easily. At the interlaminar interface, the transverse shear stress across the plate thickness plays a very important role in the delamination damage. Meanwhile, the Zig-zag form of the displacement field in the plate thickness direction and the interlaminar continuity of transverse shear and normal stresses should be considered. Therefore, the study of accurate and efficient laminated composite plate theories that are capable of predicting accurate transverse stresses at the interlaminar interfaces is very necessary and important.A number of laminated plate theories have been proposed in the past four decades, as the rapid increase in the usages of the laminated composite plates has attracted many researchers for the development of mathematical models to characterize the mechanical behavior of laminated composite plates. These laminated plate theories are able to yield good global results of laminated plates, such as deflections, fundamental frequencies, buckling load etc. However, there are two common major shortcomings among these various laminated plate theories. The one is that the existing plate theories are not able to predict the accurate stresses of laminated composite plates especially the transverse shear stress at the interfaces, because the interlaminar transverse shear stress continuity conditions are not taken into account. The other one is that the field variables used in some complicated plate theories that could yield good results are dependent on the number of the laminae, which leads to the extensive computation in the analysis.This dissertation has two-folded main objectives, one is to propose accurate and efficient laminated plate and sandwich theories with five independent global field variables but accounting for the interlaminar stress continuity conditions, and the other is to develop simple, reliable, accurate and efficient composite beam and plate elements based on the new laminated plate theories. The following are the detailed topics studied in this dissertation.(1) The properties of different shear functions used in various plate theories are studied by reducing the plate theories to the corresponding beam theories, and the boundary layer solutions of the beams with displacement boundary conditions given by Shi’s shear function are presented. By making a comprehensive analysis and evaluation of displacements and stresses of different beam theories, the result shows that Shi’s shear function can correctly characterize the boundary layer effect induced by displacement boundary conditions and capable of yielding accurate boundary layer solutions and stress predictions. Furthermore, Shi and Voyiadjis beam theory correctly predicts both the fundamental natural frequency and also the higher-mode frequencies in dynamic analysis of laminated composite beams.(2) The new laminated composite plate theory with only five independent field variables and accounting for interlaminar continuity conditions are presented in this dissertation. Based on the shear function given by Shi’s plate theory, the displacement field of the higher-order shear deformation plate theory can be modified to satisfy the Zig-zag effect of displacements at laminae interfaces by using the Heaviside step function. The transverse shear stresses continuity conditions at interlaminar interfaces can be enforced by the constraints of interlaminar stress continuity and continuity coefficients. The new laminated plate theory is applied to solve the bending problems of some typical laminated composite plates to evaluate its reliability and accuracy. The resulting analytical solutions of both deflections and stresses agree well with the 3D elasticity solutions and the numerical results of 3D finite element analysis.(3) The transverse normal strain effect in the sandwich plates with soft core is modeled by the consideration of the distributed load acting on the sandwich surface, and a sandwich plate theory with only five independent variables taking account of the interlaminar continuity of three transverse stresses is proposed. Because the stiffness ratio of face to core is high, sandwich plates are of high transverse shear and normal deformability. To take account of the transverse normal strain effect, a layer-wised quadratic transverse displacement in terms of the thickness coordinate and distributed load can be used to replace constant deflection through the thickness of the present laminated plate theory. The accuracy of the sandwich plate theory is demonstrated by its applications to the bending analyses of the sandwich plates with different aspect ratios and face to core stiffness ratios. The accuracy evaluation shows that the present sandwich plate theory is very accurate and simple.(4) By using the quasi-conforming element technique, a two-noded laminated composite beam element based on Shi and Voyiadjis beam theory is presented. The performance and excellent features of this beam element are evaluated by the numerical results of static and dynamic analysis.(5) A four-noded quadrilateral laminated composite plate element based on the present laminated plate theory accounting for interlaminar continuity is also presented by using the quasi-conforming element technique. The explicit element stiffness matrices are derived by a suitable assumed element strain field accounting for the elasticity basic solutions. The explicit element stiffness matrix leads to the present composite beam elelemnt possesses computational efficiency. The numerical results indicate hat the new composite beam element is locking-free, accurate and efficient.The accuracy evaluations of analytical solutions and finite element results presented in this dissertation show that:(1) The use of the averaged rotation across the plate thickness as basic displacement field variable can provide some advantages, as it illustrates by Shi and Voyiadjis beam theory that the use of the average rotation as basic displacement field variable together with the proper boundary conditions can correctly characterize the boundary layer effect induced by the pure displacement boundary conditions.(2) The present laminated plate theory with only five independent displacement variables and accounting for interlaminar continuity is very accurate and yields more reliable displacements and stresses than other laminated plate theories.(3) The enforcement of the interlaminar continuity condition significantly improves the accuracy of the displacement and stress distributions across the thickness of laminated composite plates.(4) The present sandwich plate theory accounting for the transverse normal strain effect and interlaminar continuity is not only simple, but also capable of achieving the accuracy of layerwise sandwich plate theories.(5) The present two-noded composite beam and four-noded composite plate elements based on the new laminated plate theory and the quasi-conforming element technique are not only free from locking problems as well as free from the time consuming numerical integration, but also very accurate in the static and dynamic analysis of laminated composite beams and plates.The present laminated plate theories and the four-noded quadrilateral composite plate element provide a simple, accurate and efficient mathematical model and computational model for the analysis of composite laminated plates used in various engineering applications.