Large Elastic Deformation of Moderately Thick, Orthotropic Shells of Revolution

本研究发展渐近解的方程控制 不可压缩旋转壳的轴对称变形 包括：1. 大位移，2. 材料非线性;3. 横向剪切变形; 4.极性正交各向异性。 边界层 行为将被审查的具体问题，夹紧圆形 由材料制成的板、圆柱体和球冠 有橡胶状的生物组织。 渐近分析将 通过开发直接的数字解决方案来验证 方程 轴对称旋转壳的大变形引起了 在过去的5年里，由于 在低重量结构设计中的重要性日益增加， 在生物力学中的潜在应用。 在许多应用中，外壳 材料是正交各向异性的、不可压缩的和非线性的（即心脏， 动脉、增强橡胶和复合材料）。 溶液 涉及壳位移和应力是困难的，因为 材料非线性、各向异性和横向 剪切变形 本构关系的发展，在这个 研究被耦合以适应弯曲和拉伸， 发生大变形和非对称层压的钢筋 材料.

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.