Static structural simulations were performed using ANSYS Workbench to evaluate the mechanical response of both flexure designs and to provide data for subsequent structural optimization. The material properties used in the simulations are listed in Table I. The arch-shaped flexure, fiber, and adhesive were modeled as an integrated assembly. A vertical downward load was applied to the top force-receiving surface in steps from 0 to 10 N (1 N increments), while the bottom surface was fully constrained. For the S-shaped flexure, a horizontal load was applied from 0 to 5 N with one end fixed. The initial simulation results for the arch-shaped clamping force sensor revealed a highly linear load–deformation relationship. The fiber strain distribution along the axial direction exhibited three characteristic zones: Zones I and III at the bonded ends, where strain approaches zero, and Zone II in the central suspended region, where strain is both maximum and highly uniform. This uniform strain field is essential for preventing chirping of the FBG reflection spectrum. The initial strain sensitivity was 239.612 με/N. With a safety factor threshold of 3.0, the theoretical measurement range was 0–12 N. For the S-shaped pulling force sensor, similar linear behavior and uniform strain distribution were observed, with an initial strain sensitivity of 894.764 με/N and a theoretical measurement range of 0–5 N at a safety factor threshold of 2.0. To maximize strain sensitivity while ensuring adequate structural safety, key geometric parameters of both flexure structures were optimized using response surface methodology (RSM) implemented in Design Expert 13. The selected design variables, their initial values, optimization ranges, and optimized values are summarized in Table II. For the arch-shaped structure, three variables were selected: main arch height 𝑋 1 X 1 ​ [1.0, 1.4] mm, main arch thickness 𝑋 2 X 2 ​ [0.3, 0.5] mm, and auxiliary arch width 𝑋 3 X 3 ​ [1.5, 2.0] mm. The optimization objective was to maximize FBG strain sensitivity under a 0–10 N vertical load, subject to the constraint that the fiber safety factor at 10 N must be ≥3.0. The constructed response surfaces revealed that strain sensitivity increases with 𝑋 1 X 1 ​ and 𝑋 3 X 3 ​ but decreases with 𝑋 2 X 2 ​ , while the safety factor exhibits the opposite trends. For the S-shaped structure, the design variables were beam straight segment length 𝑋 1 X 1 ​ [1.6, 3.0] mm, beam thickness 𝑋 2 X 2 ​ [0.6, 1.2] mm, and beam height 𝑋 3 X 3 ​ [1.5, 2.0] mm, with a safety factor constraint of ≥2.0 at a 5 N load. After optimization, the arch-shaped sensor achieved a strain sensitivity of 294.559 με/N (a 22.93% improvement from the initial 239.612 με/N) with a safety factor of 3.0 at 10 N. The S-shaped sensor achieved a strain sensitivity of 958 με/N (a 7.07% improvement from the initial 894.764 με/N) with a safety factor of 2.0 at 5 N. The optimized simulation results are presented in Fig. 4.

Static structural simulations were performed using ANSYS Workbench to evaluate the mechanical response of both flexure designs and to provide data for subsequent structural optimization. The material properties used in the simulations are listed in Table I. The arch-shaped flexure, fiber, and adhesive were modeled as an integrated assembly. A vertical downward load was applied to the top force-receiving surface in steps from 0 to 10 N (1 N increments), while the bottom surface was fully constrained. For the S-shaped flexure, a horizontal load was applied from 0 to 5 N with one end fixed. The initial simulation results for the arch-shaped clamping force sensor revealed a highly linear load–deformation relationship. The fiber strain distribution along the axial direction exhibited three characteristic zones: Zones I and III at the bonded ends, where strain approaches zero, and Zone II in the central suspended region, where strain is both maximum and highly uniform. This uniform strain field is essential for preventing chirping of the FBG reflection spectrum. The initial strain sensitivity was 239.612 με/N. With a safety factor threshold of 3.0, the theoretical measurement range was 0–12 N. For the S-shaped pulling force sensor, similar linear behavior and uniform strain distribution were observed, with an initial strain sensitivity of 894.764 με/N and a theoretical measurement range of 0–5 N at a safety factor threshold of 2.0. To maximize strain sensitivity while ensuring adequate structural safety, key geometric parameters of both flexure structures were optimized using response surface methodology (RSM) implemented in Design Expert 13. The selected design variables, their initial values, optimization ranges, and optimized values are summarized in Table II. For the arch-shaped structure, three variables were selected: main arch height 𝑋 1 X 1 ​ [1.0, 1.4] mm, main arch thickness 𝑋 2 X 2 ​ [0.3, 0.5] mm, and auxiliary arch width 𝑋 3 X 3 ​ [1.5, 2.0] mm. The optimization objective was to maximize FBG strain sensitivity under a 0–10 N vertical load, subject to the constraint that the fiber safety factor at 10 N must be ≥3.0. The constructed response surfaces revealed that strain sensitivity increases with 𝑋 1 X 1 ​ and 𝑋 3 X 3 ​ but decreases with 𝑋 2 X 2 ​ , while the safety factor exhibits the opposite trends. For the S-shaped structure, the design variables were beam straight segment length 𝑋 1 X 1 ​ [1.6, 3.0] mm, beam thickness 𝑋 2 X 2 ​ [0.6, 1.2] mm, and beam height 𝑋 3 X 3 ​ [1.5, 2.0] mm, with a safety factor constraint of ≥2.0 at a 5 N load. After optimization, the arch-shaped sensor achieved a strain sensitivity of 294.559 με/N (a 22.93% improvement from the initial 239.612 με/N) with a safety factor of 3.0 at 10 N. The S-shaped sensor achieved a strain sensitivity of 958 με/N (a 7.07% improvement from the initial 894.764 με/N) with a safety factor of 2.0 at 5 N. The optimized simulation results are presented in Fig. 4.