Strozzi A
Dept Scienze dell'Ingegneria, Faculty of Engineering, University of Modena, Italy.
Proc Inst Mech Eng H. 2000;214(1):69-81. doi: 10.1243/0954411001535255.
A mechanical analysis is carried out for a flat deformable layer, firmly anchored to a rigid substrate, and frictionlessly compressed by a rigid spherical indenter, with reference to the design of hip replacements whose cup is covered by an elastomeric layer. An available perturbation solution of differential character, developed for a layer subject to plane strain conditions, indented by a cylinder approximated as parabolic in shape and valid for high contact widths, is here extended to the axisymmetric problem of a layer compressed by a paraboloidal indenter. In addition to the paraboloidal idealization, an accurate mathematical description of the indenter spherical profile is incorporated into the modelling of this contact problem. Perturbed solutions up to the second order are developed for both compressible and incompressible layers. Selected numerical examples addressing actual joint geometries are included to assess the validity of the proposed analytical modelling, to explore the accuracy in describing the spherical profile and to compare the contact pressure profiles activated by paraboloidal and spherical indenters.
针对髋关节置换设计（其髋臼杯由弹性体层覆盖），对牢固锚固在刚性基底上且由刚性球形压头无摩擦压缩的平面可变形层进行了力学分析。为平面应变条件下的层开发的一种可用的微分形式的摄动解，该层由近似抛物线形状的圆柱体压入且适用于高接触宽度，在此扩展到由抛物面压头压缩层的轴对称问题。除了抛物面理想化之外，压头球面轮廓的精确数学描述也被纳入此接触问题的建模中。针对可压缩和不可压缩层都开发了二阶以内的摄动解。包含了针对实际关节几何形状的选定数值示例，以评估所提出的解析模型的有效性，探索描述球面轮廓的准确性，并比较由抛物面压头和球面压头激活的接触压力分布。
