The purpose of this work is to solve governing differential equations of laminated anisotropic plates and shells by using the Chebyshev collocation method. This method yields these results those can not be accomplished easily by both Navier¡¦s and Levy¡¦s methods in the case of any kind of stacking sequence in composite laminates with the variety of boundary conditions subjected to any type of loading. The Chebyshev polynomials have the characteristics of orthogonality and fast convergence. They and Gauss-Lobatto collocation points can be utilized to approximate the solution of these problems in this paper. Meanwhile, these results obtained by the method are presented as some mathematical functions that they are more applicable than some sets of data obtained by other methods. On the other hand, by simply mathematical transformation, it is easy to modify the range of Chebyshev polynomials from the interval [-1,1] into any intervals. In general, the research on laminated anisotropic plates is almost focused on the case of rectangular plate. It is difficult to handle the laminated anisotropic plate problems with the non-rectangular borders by traditional methods. However, through the merits of Chebyshev polynomials, such problems can be overcome as stated in this paper. Finally, some cases in the chapter of examples are illustrated to highlight the displacements, stress resultants and moment resultants of our proposed work. The preciseness is also found in comparison with numerical results by using finite element method incorporated with the software of NASTRAN.

Biomimetic scale-covered systems offer immense potential and applications, particularly in soft robotics, protective armors, wearable materials, and multifunctional aerospace structures. A typical system consists of stiff rectangular plate like scales embedded in a softer media and arranged periodically. Experimentally, these systems indicate pronounced nonlinear strain stiffening behavior even when the underlying substrate strains are small. However, capturing these behaviors using commercial finite element (FE) codes has proved difficult due to multiple sliding contacts between the scales after engagement. Therefore, accurate and reliable analytical models of architecture-property-relationships are needed for analysis and design. This thesis investigates the contact kinematics and mechanics of biomimetic scale-covered plates subjected to bi-directional bending. Both synclastic and anti-clastic deformations of the plate are considered. The mechanical moment-curvature relationships are derived using the work-energy balance principle. The results show that when a plate is bent to a certain curvature, a quasi-rigid locked emerges for both synclastic and anticlastic curvature. Interestingly, while for anticlastic bending, the curvature at locking is nearly the same curvature as a beam with equivalent geometry and configuration, for synclastic bending, locking occurs significantly earlier due to cross-curvature effects. The moment-curvature relationships indicate strongly anisotropic behavior of the plate. The anisotropy itself was not constant, being strongly influenced by the state of deformation. The effect of scale arrangement parameters (lattice geometry) directly influenced the nonlinear behavior including the locked state. The analytical models developed are compared with equivalent FE analysis for validation for select cases and excellent agreements have been found. The outcome of this work would enhance the understanding of the nonlinear and anisotropic behavior of scale-covered plate systems, paving the way for systematic design and integration tailored for specific applications.