平台圆盘对径压缩的一个位移解

A Displacement Solution for Flattened Circular Disc Under Diametral Compression

用半解析半经验的方法推出圆盘对径压缩的一个位移解,该公式可以估算力作用点有微小平台时直径的压缩位移。解析方法采用集中力对径压缩完整圆盘的直径上的应变求积分算压缩位移,但部分项积分的上限离开直径端点有微小距离,这相当于圆盘上有平台。再对所推公式做经验性修正。所推公式不仅形式简单,而且有良好的精度,与有限元计算结果比较误差不大于3.6%。最后给出从材料各向同性到正交异性的推广情况。

A semi-analytical and semi-empirical method is used to formulate a displacement solution for the circular disc with a pair of flattened areas under diametral compression. The fattened areas are usually required to assist testing mechanical properties. The presented formula can be used to estimate the compression displacement of the flattened areas in diameter direction, with a deviation less than 3.6% compared with the results of finite element calculation. When the flattened areas diminish to zero, the formula approaches asymptotically to the situation of complete circular disc applied with concentrated load. Finally, the displacement formula is extended to the condition of orthotropic material when the load is applied along the principal axis of the material.