An Impact Strain Monitoring and Simulating Method for Large-Size Composite Skin Panel with Optical Fiber Sensors

Abstract

Structural Health Monitoring (SHM) is now essential for certifying many composite primary structures as it resolves strain redistribution at the moment of impact. Traditional detection methods, including resistive strain gauges, face challenges due to susceptibility to electromagnetic noise, as well as increased mass and wiring complexity proportional to the number of channels. This study proposes an impact strain monitoring and simulating method using optical fiber sensors for composite skin panels. Repeated low-velocity impact tests were conducted on large-size composite skin panels using various impact forces and locations. The 95% confidence interval for unit load strain in the simulation results differs from the experiment by 18%. This method effectively facilitates the monitoring of global impact strain on large-size composite skin panels.

1. Introduction

Over the past decades, fiber-reinforced composite panels have emerged as the primary load-bearing skins of aircraft due to their exceptional mechanical properties, specific strength, and stiffness [1,2]. However, their laminated architecture renders CFRP composites highly susceptible to out-of-plane stresses, particularly impact loading [3,4]. Consequently, online Structural Health Monitoring (SHM) that can detect strain redistribution at the moment of impact has become a certification prerequisite for many primary composite structures [5,6].

Traditional methods of strain monitoring, such as resistive strain gauges, are prone to interference from electromagnetic noise, primarily due to their metallic lead connections [7,8]. Furthermore, as the number of monitoring channels increases, the weight and complexity of wiring increase linearly. Among the various sensing technologies currently available, Fiber Bragg Grating (FBG) sensors have emerged as the most promising for full-field strain mapping in composite panels [9,10,11,12]. Notably, the use of wavelength-division multiplexing allows a single optical fiber to support numerous gratings, effectively transforming the panel into a high-definition strain camera [13]. Recent demonstrations, validated in flight-worthy conditions, have shown that FBG arrays can detect impacts within 1 ms and provide spatially resolved strain maps that evolve during the impact and subsequent compression-after-impact (CAI) loading phases [14,15,16].

The limited deployment of distributed optical fibers (DOFs) poses challenges in capturing the strain state comprehensively across all locations within the aircraft [17]. To address this limitation, refined simulation modeling is employed to compensate for the limitations of distributed fiber optic monitoring [18,19,20]. This optimized and validated simulation model then serves to monitor strain across the entire aircraft structure.

In this study, we propose a simulation modeling methodology for large-sized composite skin panels to calculate the strain responses during low-velocity impacts. We analyze the relationships between strain responses and variables such as impact force and impact location. Additionally, we propose a strain detection method for composite skin panels utilizing FBGs. Repeated low-velocity impact tests are conducted on large-sized composite skin panels with varying impact forces and locations, with the recorded strain responses compared against the simulation results.

2. Methods

2.1. Strain Relationship for Different Impact Loads

The ABAQUS/Explicit simulation software was employed to model the impact test. The composite aircraft skin panel was designed as a curved structure, measuring 3100 mm by 2090 mm with a radius of 2960 mm, as depicted in Figure 1a. This panel consists of four primary components: the skin, stringers, upper frames and lower frames. The rigid2 elements are used to simulate the connection between the upper and lower frame via rivets, forming a combined frame. A tie surface constraint is employed to simulate the bonding between the combined frame and the upper surface of the stringer, as well as the lower surface of the stringer and the skin.

The skin is configured with stacking sequences of [45/−45/45/90/0/0/90/−45/0] s, forming a curved plate with a total thickness of 3.6 mm, where each layer measures 0.2 mm. There are nine stringers spaced 240 mm apart, each configured with stacking sequences of [45/0/0/−45/90/−45/0/0/45] and shaped into a hat profile with a thickness of 1.8 mm; the thickness of each individual layer is 0.2 mm. The assembly includes five frames, spaced 640 mm apart. Each frame is divided into an upper and a lower section. The upper section, shaped into an “S” curve and featuring stacking sequences of [45/−45/0/0/90] s, has a thickness of 2.0 mm with each layer measuring 0.2 mm. The lower section follows stacking sequences of [45/−45/0/0/90/45/−45] s, is shaped into an “L” curve, and has a thickness of 2.7 mm with each layer measuring 0.19 mm, as shown in Figure 1b.

In pursuit of an optimal balance between computational efficiency and precision in predictions, a mesh convergence analysis is performed prior to finalizing the mesh size. Mesh sizes of 8 mm and 10 mm are evaluated, with the strain contour at the peak moment and strain–time curve shown in Figure 2. It is observed that when the mesh size is reduced from 10 mm to 8 mm, the peak strain error in impact location is smaller than 0.5%, indicating that a mesh size of 10 mm is able to achieve accurate results.

In impact response simulations, the selection of element types follows the “accuracy-efficiency” principle and aligns with experimentally measurable physical quantities. The specimen’s nominal length-to-thickness ratio is approximately 66 (240/3.6), meeting the “thin-walled” criterion (>20). Both traditional shell and continuous shell elements are available. Traditional shells only output sectional stress and cannot provide distribution of shear stress along the thickness direction. Continuous shells can compute interlaminar shear stresses, offering greater accuracy in calculating critical metrics such as matrix shear failure, dent depth prediction, and peak impact contact forces. Although solid elements can compute interlaminar stresses, achieving convergence for shear stresses requires 3–5 layers of mesh along the thickness, drastically increasing computational degrees of freedom. Furthermore, this study aims to obtain in-plane longitudinal strain of the laminate under low-speed impact, without considering interlaminar delamination. Therefore, continuous shell elements are selected.

A mesh size of 10 mm by 10 mm was utilized for the skin, stringers, and frames. The model incorporated 152,276 continuum shell elements, including SC8R and SC6R elements. To accurately simulate the bending stresses in composite laminates, each ply contains three integral points. The simulation covered a physical timeframe of 3.0 ms (0.003 s), with a stable time increment of 2.2 × 10⁻⁴ ms. The hour-glass control of enhanced stiffness was used, and the hour-glass scale factor was 1.2. Bulk viscosity of linear 0.06 and quadratic 1.2 were selected. As shown in Figure 3a, the proportion of viscous energy and hourglass energy in the internal energy is less than 0.6%, satisfying the requirement for calculations to be less than 5%. As shown in Figure 3b, the changes in both the hourglass effect and viscosity remained below 2% after altering the hourglass coefficient and volumetric viscosity coefficient, so the validation of both the hourglass effect and numerical stability are confirmed. No damage or cohesive models were included; validity is therefore restricted to the linear-elastic regime. Six degrees of freedom are constrained. at both ends of the upper frames, and the load was applied along the y-axis, spanning from locations L1 to L9, as illustrated in Figure 4. Detailed material properties of the composites are provided in

Table 1. Mechanical properties of unidirectional composite laminate.

Density	ρ = 1.6 × 10−9 t/mm3
Young’s modulus	E11 = 160 × 103 MPa E22 = E33 = 8.63 × 103 MPa G12 = G13 = 3.0 GPa, G23 = 4.4 GPa
Poisson’s ratio	ν12 = ν13 = 0.33, ν23 = 0.35

.

There are a total of 13 impact locations, designated as L1 through L13. Among these, impact locations L4, L6 and L7 are situated at the skin above the stringers, while the remaining impact locations were positioned at the center of the skin between two adjacent stringers and frames. These locations are delineated in Figure 4a. The impact forces were administered to the skin using a half-sine pulse. Three impacts, differing in force magnitude, were applied at consistent impact locations. The longitudinal strain was monitored at the sensor sites. Since the center of the skin panel has relatively low structural stiffness and a large surface area, making it most susceptible to impact, sensors are all positioned at the center of the skin panel. A total of 11 sensors were arranged on the back of the skin, designated as S1 through S11, as indicated in Figure 4a. The longitudinal spacing between sensors S4, S1, S6, S8, S2 and S3 is, respectively, 480 mm, 640 mm, 640 mm, 640 mm and 480 mm. The vertical spacing between sensors S2, S11 and S7 is 240. The longitudinal strain on the rear surface of the skin panel was monitored using FBG sensors. The sensors are positioned on the backside of the composite aircraft skin panel, as shown in Figure 4b.

Impact location L1 is situated at the center between two adjacent frames and two stringers. The longitudinal strain extremities of the skin panel occur at the impact location. When the impact forces are 152 N, 291 N and 392 N, respectively, the longitudinal strain extremities at this location are 243 με, 477 με and 654 με. As illustrated in Figure 5a–c, despite the variation in impact force, the strain distribution within the skin panel remains consistent: tensile strain appears in the impact zone, while compressive strain is observed in the surrounding extensive area.

Impact location L7 is directly aligned with the stringers. The longitudinal strain extremities of the skin panel are also at this impact location. When the impact forces are 206 N, 297 N and 507 N, respectively, the longitudinal strain extremities at this location are 331 με, 481 με and 833 με. As depicted in Figure 5d–f, although the impact force varies, the strain distribution in the skin panel remains consistent: significant tensile strain is noted near the impact location, with a minor presence of compressive strain.

The relationship between strain extremums at the sensor locations and the impact forces is demonstrated in Figure 6. At impact locations L1, L2 and L3, the sensors are positioned at the same location as the impact locations. The strain extremums exhibit a positive linear relationship with the impact forces. The degree of linearity was quantified by comparing the simulated strain at impact locations L1, L2 and L3 with the ideal straight line. The Mean Absolute Percentage Difference (MAPD) of L1, L2 and L3 were 2.1%, 7.4% and 3.0%.

At impact locations L4, L6 and L7, which lie between two sensors, the strain extremums measured at the sensors are significantly lower than those recorded in the skin panel. Here, the strain extremums maintain a negative linear relationship with the impact forces. The Mean Absolute Percentage Difference (MAPD) of L4, L6 and L7 were 0.5%, 4.5% and 5.2%. The reasons for variations in strain extremes under identical loads at different locations include differences in local stiffness at various positions, boundary effects such as the impact location L3 and L4, errors in sensor placement and inaccuracies in the impact location during manual tapping.

2.2. Strain Relationship for Different Impact Locations

Impact forces ranging from 227 N to 285 N are applied to various impact locations. The simulation of the longitudinal strain for these different impact locations is shown in Figure 7. As depicted in Figure 7, the strain extremums registered by the sensor at the impact locations L3, L5, L8 and L9 are 326 με, 355 με, 345 με and 411 με, respectively. The strain per unit load at various positions is presented in Figure 8. Across different impact locations, the strain extremums measured by the sensor per unit load range from 1.431 to 1.444. When impacts occur centrally between two adjacent frames and stringers, the mean percentage difference in strain extremums per unit load was 0.34% (SD = 0.01, CV = 0.42%), with the 95% CI of the mean being [1.43, 1.45].

3. Experiments

3.1. Specimens

In this study, a composite aircraft skin panel was manufactured using carbon fiber pre-impregnated tow. The fabrication process involved automated fiber placement followed by autoclave curing at elevated temperatures, as depicted in Figure 9a. The composite layup design adhered to the specifications detailed in Section 2.1. During the preparation phase, sensors were affixed to the rear surface of the skin panel, as shown in Figure 9b. A DOF was positioned between two adjacent stringers, aligned with the direction of the stringers. Each DOF was marked with an FBG, positioned 120 mm from the centerline of the stringer.

FBG sensors operate based on periodic variations in the refractive index within the fiber core. As broadband light traverses the FBG, it reflects narrow-band incident light. The wavelength of the reflected light is contingent upon the effective refractive index of the fiber core and the grating period, as articulated in Equation (1):

λ = 2n_eff × Λ

(1)

The center wavelength of an FBG is subject to variation due to mechanical loading and temperature changes. When an FBG undergoes axial strain Δε or a temperature shift ΔT, alterations in the grating period Λ and effective refractive index n_eff induce a shift in the center wavelength of the FBG. This wavelength shift is quantifiable and is expressed as follows:

Δλ = λ₀[(α + ζ)ΔT + (1 − P_e)ε] = λ₀[K_T × ΔT + K_S × Δε]

(2)

In this equation, α represents the thermal expansion coefficient, ζ denotes the thermo-optical coefficient, P_e symbolizes the photoelastic coefficient, K_T is the temperature sensitivity constant, and K_S stands for the strain sensitivity constant. Based on Equation (2), the relationship between the FBG wavelength change and either strain or temperature is linear. During impact testing, the ambient temperature of the composite material was assumed to be constant, allowing for the FBGs to function primarily as strain sensors. The FBG high-speed demodulation instrument, with a sampling rate of 5 kHz, recorded only discrete data points of the FBG center wavelength changes. The FBG strain sensitivity coefficient was determined to be 1.2 pm/με.

3.2. Impact Tests

A curved composite fuselage skin panel, measuring 3100 mm by 2090 mm with a radius of 2960 mm, was manufactured using the carbon fiber-reinforced composite material. This panel consists of four primary components: the skin, stringers, upper frames and lower frames. The upper and lower frames are connected with rivets. The entire structure is joined to the stringers and skin using high-strength bolts, with structural adhesive and sealant applied between the stringers and skin.

Impact tests were conducted using an impact hammer and a distributed signal test instrument. The distributed signal test instrument operated at a sampling rate of 5 kHz. The point of impact was located on the front of the composite aircraft skin panel, consistent with the description provided in Section 2.1. The grating sensors were affixed to the wall panel after the wall panel has been machined, so the machining process does not affect the sensor’s performance. The longitudinal strain on the rear surface of the skin panel was monitored using FBG sensors. A series of experiments were designed to explore the relationship between the strain experienced by the panel and the impact load, as well as the impact location on the composite aircraft skin panel. Impact locations designated from L1 to L13 were subjected to forces ranging from 113N to 732N. The experimental design is outlined in

Table 2. Experimental matrix.

Test Number	Impact Force/N	Impact Location	Description
1-1	152	L1	Load–strain relationship verification
1-2	291
1-3	392
2-1	185	L2
2-2	371
2-3	423
3-1	113	L3
3-2	227
3-3	302
4-1	416	L4
4-2	559
4-3	723
5-1	374	L6
5-2	633
5-3	732
6-1	206	L7
6-2	297
6-3	507
7-1	227	L3	Location–strain relationship verification
7-2	248	L5
7-3	239	L8
7-4	285	L9

.

Impact locations (L1–L13) were not uniformly distributed but strategically selected at structural key points (e.g., joints, mid-span, boundaries). The impact force values do not increase in equal increments because the hammer signal is generated by manual striking. The magnitude of the striking force cannot be controlled, and each strike is unique. To obtain data under different impact loads, strike the same location three consecutive times with progressively increasing loads.

4. Results and Discussion

4.1. Simulation Results Verification

This section assesses the computational accuracy of the simulation model by comparing the extremes of strain observed in both the experimental and simulation results.

Table 3. Test results and simulation results.

Test Number	Target Force (N)	Achieved Force (N)	Impact Location	Strain of Experiment (με)	Strain of Simulation (με)
1-1	100~400	152	L1	178	243
1-2		291		330	477
1-3		392		631	654
2-1		185	L2	237	298
2-2		371		526	617
2-3		423		607	710
3-1		113	L3	106	194
3-2		227		263	397
3-3		302		346	534
4-1	400~800	416	L4	−7	−72
4-2		559		−14	−96
4-3		723		−27	−123
5-1		374	L6	−17	−43
5-2		633		−23	−71
5-3		732		−35	−82
6-1		206	L7	−12	−24
6-2		297		−18	−35
6-3		507		−26	−59
7-1	200~300	227	L3	263	326
7-2		248	L5	304	355
7-3		239	L8	291	345
7-4		285	L9	336	411

details the simulation results alongside the experimental results for all conditions where the impact location corresponded with the sensor location. In most conditions, the experimental results were lower than the simulated values. This discrepancy can be attributed to the deviations in the actual impact locations from their theoretical positions during manual tapping, as well as deviations in the actual sensor locations from their theoretical positions. Therefore, the strain data recorded at the sensor locations was generally lower than the strain extremes at the impact locations during the testing process. Overall, the simulation results demonstrated a high level of concordance with the experimental data, thereby validating the computational accuracy of the simulation model.

4.2. Strain Relationship for Different Impact Loads Verification

This section analyzes the strain relationship under varying impact forces. Tests 1-1 through 1-3 were conducted at location L1, with impact forces ranging from 152 N to 392 N. Tests 4 through 6 took place at location L2, with impact forces from 185 N to 423 N. Tests 7 through 9 occurred at location L3, with impact forces between 113 N and 302 N. Figure 10a illustrates the strain extremums at locations L1, L2 and L3, influenced by different impact forces. The data indicate that the strain extremums during impacts at location L2 and L3 exhibit a positive linear relationship with the impact forces. While the strain extremums during impacts at location L1 exhibit visible curvature in the force–strain response. The deviation at the L1 position arises because the three impact points at L1 exhibit positional error. Since the strain gradient is relatively high near the impact locations, the strain results exhibit a curvature relationship with the impact force. To quantify the deviation from linearity, we compared linear and quadratic fits for L1 using least-squares regression. The coefficient of determination (R²) and Akaike Information Criterion (AIC) of linear fits is R² = 0.9242 and AIC = 27.6. The R² and AIC of quadratic fits is R² = 1.0 and AIC = −138.1. The quadratic model yields a higher R² and lower AIC, indicating statistically significant improvement in fit quality.

Figure 10b illustrates the strain extremums at locations L10, L11, L12 and L13, influenced by different impact forces. When the impact force is between 177 N and 190 N, the mean peak strain was 279 µε (95% CI: 227–330 µε, n = 4). When the impact force is between 215 N and 245 N, the mean peak strain was 328 µε (95% CI: 241–416 µε, n = 5). When the impact force is between 289 N and 302 N, the mean peak strain was 360 µε (95% CI: 263–456 µε, n = 3). When the impact force is between 371 N and 392 N, the mean peak strain was 610 µε (95% CI: 420–800 µε, n = 3). Within the same impact force range, variations in peak impact strain may result from differences in the distance between the impact location and the sensor, variations in local structural stiffness and boundary effects. The R² and AIC of linear fits of L2 is R² = 1.0000 and AIC = −11.822. The R² and AIC of linear fits of L3 is R² = 0.9967 and AIC = 14.473. The R² and AIC of linear fits of L10 is R² = 0.9994 and AIC = 10.506. The R² and AIC of linear fits of L11 is R² = 0.9959 and AIC = 19.146. The R² and AIC of linear fits of L12 is R² = 0.9989 and AIC = 6.899. The R² and AIC of linear fits of L13 is R² = 0.9843 and AIC = 15.196. The data indicate that the strain extremums during impacts at location L10, L11, L12 and L13 exhibit a positive linear relationship with the impact forces.

Tests 4-1 through 4-3 were performed at location L4, with impact forces ranging from 416 N to 723 N. Tests 5-1 through 5-3 took place at location L6, where the forces varied from 374 N to 732 N. Tests 6-1 through 6-3 occurred at location L7, with impact forces between 206 N and 507 N. Figure 11 displays the strain extremums at locations L4, L6 and L7, influenced by different impact forces. When the impact location is not in the same position as the sensor, such as separated by stringers or frames, the strain extremums during impacts exhibit visible curvature in the force strain response. A possible reason is that far from the impact zone, the magnitude of strain is more than one order of magnitude smaller than at the impact location. This makes the measured results susceptible to influences from boundary conditions, contact non-linearity, and structural damping, leading to pronounced non-linear effects.

4.3. Strain Relationship for Different Impact Locations Verification

This section explores the relationship between strains and various impact locations. Tests 19 through 22 were conducted at locations L3, L5, L8 and L9, each centrally positioned between two adjacent frames and two stringers. Figure 12 presents the strain per unit load at these distinct positions. The strain extremums recorded by the sensors per unit load across these locations varied from 1.180 to 1.227. When impacts occur centrally between two adjacent frames and stringers, the mean percentage difference in strain extremums per unit load was 2.24% (SD = 0.03, CV = 2.68%), with the 95% CI of the mean being [1.15, 1.25].

The proposed diagnostic method is developed for stiffened skin panels, including wing upper/lower panels, fuselage side panels and tail-plane torsion boxes whose in-plane dimensions are 2~6 m, stringer spacing 200~300 mm and radius of curvature ≥ 2 m. Extension to sandwich panels, highly doubly curved doors, or < 1 m control-surface skins is outside the validated envelope and requires re-calibration of the strain–load linearity threshold. Although the linear relation was validated in a carbon fiber/epoxy resin composite, the method itself remains applicable to other carbon fiber-reinforced composite systems.

4.4. The Influence of Sensor Integration on Manufacturing Processes

Although the DOFs in this paper are affixed to the rear surface of composite laminates, practical applications require embedding them within the composite laminates, which impacts both the manufacturing process and mechanical properties.

The conventional autoclave curing temperature ranges from 80 to 120 °C. This exceeds the melting point of standard acrylic coatings. Therefore, secondary encapsulation with polyimide or metal microtubes is required. The post-encapsulation outer diameter increases, leading to an increase in local ply thickness. The resin-rich zone width is bigger than the fiber diameter. A tapered chamfer at the exit section is required to prevent fiber breakage due to stress concentration.

The significant stiffness disparity between optical fibers and carbon fibers causes gaps at fiber positions during automated fiber placement (AFP). Aligning the fiber path parallel to the fiber direction while maintaining a specific spacing preserves the layer porosity required for manufacturing specifications.

During curing, the thermal expansion coefficient difference between the fiber and matrix generates additional tensile residual strain at the interface. Residual strain peaks in the intermediate layer and decreases toward the surface, with the core layer exhibiting higher residual strain than unfilled panels.

When fibers are embedded parallel to the matrix, tensile strength decreases in the 0° direction. Vertical embedding reduces compressive strength due to fiber severing. This requires adopting a parallel, serpentine routing pattern to stagger the load-bearing cross-sections.

Surface-mounting, while circumventing the manufacturing complexities outlined above, introduces its own performance ceiling when the component is exposed to temperatures, pressures or complex stress states. Because the optical fiber is bonded to only one side of the laminate, the strain transfer coefficient becomes a strong function of the adhesive glass-transition temperature (Tg). Once the Tg is exceeded, the shear modulus drops and the measured wavelength shift under-reports the true laminate strain. Similarly, external pressure compresses the adhesive, producing an additional compression that is indistinguishable from mechanical load. Under combined bending and torsion, the sensor lies outside the neutral axis, so the recorded spectrum convolutes membrane, bending and local peel stresses. Finally, long-term monitoring in hot–wet environments is precluded unless the fiber is re-encapsulated or relocated inside the stack. These limitations underscore that the present surface-bonded approach is best suited to qualification-level tests at modest temperature and primarily in-plane loading; any extrapolation to embedded, thermo-pressurized or triaxial stress states must re-validate the strain-transfer law and, ideally, migrate the sensor inside the laminate using the encapsulation strategies.

4.5. The Applicability Limits of the Method with Respect to Laminate Thickness and Structural Configuration

The applicability envelope of the method, specifying that reliable strain detection is assured for laminates up to approximately 5 mm thick and for structural configurations where the dominant strain fields are transmitted to the rear surface (e.g., thin-walled panels, sandwich cores and moderately stiff composites). Beyond this thickness range, the sensor’s sensitivity to deep-lying defects diminishes due to strain attenuation and stress redistribution.

To mitigate the identified limitations, we propose a hybrid monitoring strategy that combines surface sensors with embedded fiber-optic or piezoelectric transducers, as well as data-fusion algorithms that extrapolate internal damage states from surface measurements. This approach will be outlined as a prospective extension of the current framework, thereby enhancing its robustness for thicker laminates and more complex structural geometries.

The linear strain-load relationship proposed in this paper is developed for carbon fiber pre-impregnated tow. For glass fiber/resin systems and hybrid laminates subjected to small impacts, the linear-strain load relationship remains valid provided that all strains (tensile, compressive, shear) within the laminate remain within the elastic range. However, the load magnitude at which different material types enter the linear region varies, and specific evaluation is required.

5. Conclusions

This study introduces a simulation modeling approach for analyzing large-size composite skin panels, focusing on calculating the strain responses during low-velocity impacts. The relationships between strain and various parameters such as impact force and location have been systematically analyzed. Additionally, a strain detection methodology employing FBGs for composite skin panels is proposed. Repeated low-velocity impact tests were performed on large-size composite skin panels using different impact forces and locations, with strain responses recorded and subsequently compared with simulation outcomes. Key findings include the following:

(1)

The proposed simulation modeling approach for large-size composite skin panels accurately predicts the strain responses of these structures under low-speed impacts. The experimental measurement yielded a 95% confidence interval for strain per unit load of 1.15–1.25 µε/N, while the simulation predicted an interval of 1.43–1.45 µε/N. The two intervals do not overlap, with a percentage difference of 18%. Although the simulation overestimates, the deviation remains within the upper limit of the 20% engineering tolerance acceptable for verifying low-speed impact response in composite materials [21].

(2)

The strain extremums during impacts exhibit a linear relation with the impact forces. The demonstrated linear relation allows designers to reduce the complex low-velocity impact problem to an elastic beam/plate calculation, enabling rapid down-selection, load extrapolation and field inversion while maintaining engineering accuracy—thus significantly improving the efficiency and economy of the entire chain from design and certification to maintenance of composite structures.

(3)

At impact positions located centrally between two adjacent frames and two stringers, the mean absolute percentage differences in strain extremums per unit load of experimental and simulation results were 0.34% and 2.24%. The reasons for variations include differences in local stiffness at various positions, boundary effects, errors in sensor placement and inaccuracies in the impact location during manual tapping.