Large Elastic Deformation of Moderately Thick, Orthotropic Shells of Revolution

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This research develops asymptotic solutions to the equations governing axisymmetric deformation of incompressible shells of revolution including: 1. Large displacements, 2. Materials non-linearity;3. Transverse shear deformation; and 4. Polar orthotropy. Boundary layer behavior will be examined for the specific problems of clamped circular plates, circular cylinders, and spherical caps composed of materials with rubber-like and biological tissues. The asymptotic analysis will be validated by developing direct numberical slutions of the governing equations. Large deformation of axisymmetric shells of revolution has attracted the attention of the mechanics community in the past 5 years because of the growing importance in the design of low-weight structures and the potential applications in biomechanics. In many applications, the shell materials are orthotropic, incompressible and non-linear (i.e. heart, arteries, reinforced rubber and composite materials). The solution involving shell displacements and stresses is difficult because of the combined effects of materials non-linearity, anisotropy and transverse shear deformation. The constitutive relations to be developed in this study are coupled to accommodate both bending and stretching which occurs with large deformations and asymmetric lamination of reinforced materials.