The optimisation methodology was applied to design a specific geometry for a ring-shaped clip gauge as a quasi-static displacement measurement. The gauge was designed to maximise sensitivity under various types of constraints, including working range, strength, and installation. The analytical expressions of the ring gauge’s responses and constraints were derived to formulate an optimisation problem. The optimal solution was determined by an optimisation solver in the MathCAD Prime 4 program. The sensitivity of the objective function with respect to the parameters in the optimisation problem evaluated at the optimal solution was also determined. The sensitivity and linearity of the designed ring gauge is in the range of commercial gauges. The accuracy of the ring gauge was better than 0.1%, complying with ASTM standard E1820. Performance of the ring gauge, i.e. its linearity, hysteresis, and repeatability, was better than the DCB gauge reproduced from the standard. Applying the ring gauge to a tensile test with a cracked specimen yielded an accurate displacement measurement. Limitations of the analytical formulation are highlighted and recommendations for improving the formulation are discussed.

中文翻译：

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环形夹规的优化设计

优化方法被应用于设计特定几何形状的环形夹规作为准静态位移测量。该仪表旨在在各种类型的限制条件下最大限度地提高灵敏度，包括工作范围、强度和安装。推导出环规响应和约束的解析表达式以制定优化问题。最优解由 MathCAD Prime 4 程序中的优化求解器确定。还确定了目标函数相对于在最优解处评估的优化问题中的参数的敏感性。设计的环规的灵敏度和线性度在商业规的范围内。环规精度优于0.1%，符合ASTM标准E1820。环规的性能，即其线性度、滞后性和可重复性，优于从标准再现的 DCB 规。将环规应用于带有裂纹试样的拉伸试验，可得到准确的位移测量值。强调了分析公式的局限性，并讨论了改进公式的建议。