Large Elastic Deformation of Moderately Thick, Orthotropic Shells of Revolution

本研究建立了不可压缩旋转壳轴对称变形方程的渐近解，包括：1.大位移；2.材料非线性；3.横向剪切变形；4.极向各向异性。边界层行为将针对由橡胶状材料和生物组织组成的固定圆板、圆柱体和球帽的特定问题进行研究。渐近分析将通过建立控制方程的直接数值解来验证。近5年来，由于轴对称旋转壳在轻量化结构设计中的重要性及其在生物力学中的潜在应用，轴对称旋转壳体的大变形引起了力学学界的广泛关注。在许多应用中，壳体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)。由于材料的非线性、各向异性和横向剪切变形的共同作用，涉及壳体位移和应力的解是困难的。本研究中将发展的本构关系是耦合的，以适应弯曲和拉伸，这是由于大变形和加筋材料的不对称层合而发生的。

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.