Geometrically Nonlinear Analysis Of Composite Laminated Plates Under Hygrothermal Environments

Three aspects of investigations are paid attention to. Those are geometrically nonlinear problems of orthotropic plates under complicated boundary conditions based on Kirchhoff supposition, geometrically nonlinear problems of composite laminated plates under complicated boundary conditions based on higher-order shear deformation theory, geometrically nonlinear problems of composite laminated plates under hygrothermal environments and elastically restrained boundary conditions based on elastic groundsill. Based on the Kirchhoff supposition, geometrically nonlinear bending of orthotropic rectangular thin plates is analyzed under four kinds of boundary conditions of two adjacent edges simply supported and other two adjacent edges clamped, three edges simply supported and one edge clamped, one edge simply supported and three edges clamped, and all four edges clamped. A General solution for nonlinear bending of these plates is established for the five kinds of different boundary conditions. For the nonlinear governing equations of the above different boundary conditions, the selected displacement functions are beam vibration functions that have rapid convergence speed. They accurately satisfy the boundary conditions and possess orthogonal property. The basic framework keeps the same for different boundary conditions, but different coefficients of the beam vibration functions are needed to change. Large scale of linear sparse equations have been solved by Biconjugate Gradients Stabilized Method and nonlinear algebraic equations solved by Parameter-regulated Iterative Procedures. The value of linear solutions is treated as initial value of the nonlinear solutions for iteration. In the way we can find both the linear solutions and the nonlinear ones and compare them. Making use of Green formula when an ordinate is upward, we have proved the validity of Green formula when ordinate is downward. Three other formulae are derived from them. As a result the planar integration by parts is produced. We use the principle of virtual displacements and the planar integration by parts to derive the geometrically nonlinear equilibrium equations and their boundary conditions of composite laminated plates depended on higher-order shear deformation theory in the form of five generalized displacements. By the higher-order shear deformation theory, geometrically nonlinear bending of composite laminated plates is analyzed for complicated boundary conditions. These boundary conditions include one edge simply supported and three edges clamped, two adjacent edges simply supported and other two adjacent edges clamped, three edges simply supported and one edge clamped, and elastic restraint against rotation that has same elastic coefficients for opposite sides. A General solution for geometrically nonlinear bending of these plates is then set up for the six kinds of different boundary conditions. Large scale of linear sparse equations solved by Biconjugate Gradients Stabilized Method and nonlinear algebraic equations solved by Parameter-regulated Iterative Procedures previously for the Kirchhoff plate theory are now extended for the higher-order shear deformation theory. For the geometrically nonlinear problems under above different boundary conditions, effects of several factors including transverse shear deformation are investigated on bending property of moderate composite plates. Using normal or partial strains of a orthotropic lamina due to moisture and temperature and force of double-parameter groundsill on the plates, we obtain governing equations, boundary conditions, and their force resultants of laminates plates under both hygrothermal environments and elastic groundsill upon higher-order shear deformation theory. Effects of temperature, moisture, elastic coefficients of boundary conditions, elastic parameters of groundsill, and number of laminated plies are studied on the nonlinear bending deflection and moments of composite laminated plates.