A segmented empirical prediction method for maximum dynamic deflection of v-shaped armor steel plate under explosive load

Abstract

The present application is a kind of V-shaped armor steel plate under the maximum dynamic deflection of explosion load segmented experience prediction method. Based on the test response data to check the finite element simulation model, the structure, material and explosion load parameters of the steel plate are determined, the parameterized simulation matrix is established, and the maximum dynamic deflection corresponding to each simulation condition is extracted. The simulation results are screened, and the maximum dynamic deflection prediction database is established. The dimensionless parameter group is constructed, and the power law relationship formula between the maximum dynamic deflection and the dimensionless parameter group is established. The solving method of the index coefficient in the power law relationship formula is determined. The effective samples are divided into multiple angle intervals, and the index coefficients in each angle interval are identified respectively to establish the segmented experience prediction model. According to the angle, the segmented experience prediction model is selected, the structure parameters and explosion load parameters of the steel plate to be predicted are input, and the maximum dynamic deflection prediction value is obtained. The present application improves the response prediction accuracy and parameter screening efficiency in the design of armored vehicle bottom protection structure.

Description

Technical Field

[0001] This invention belongs to the technical field of explosion-proof design and explosion dynamics response prediction of the bottom protective structure of armored vehicles, specifically involving a segmented empirical prediction method for the maximum dynamic deflection of V-shaped armor steel plates under explosion load. Background Technology

[0002] Explosive loads are characterized by short duration, high peak pressure, non-uniform spatial distribution, and strong nonlinear structural response, making them one of the extreme loads that must be considered in the design of armored vehicles, ship compartments, and critical protective facilities. For armored vehicles, the bottom structure is the primary path for the transmission of blast impact to the crew compartment, and its transient deformation directly affects the crew's survival space, structural intrusion, and impact transmission level. Therefore, accurately predicting the maximum dynamic deflection of the bottom protective structure under explosive loads is crucial for conducting blast-resistant design, parameter optimization, and safety assessment.

[0003] Existing research on explosion response prediction mainly focuses on flat, rectangular, circular, beam, or stiffened plate structures. Some studies use gas detonation, uniformly distributed impulse, or small-scale specimens to replace the actual TNT explosion load. While these methods can reveal the mechanisms of partial bending, membrane stretching, and localized damage, they differ from actual TNT air explosions in terms of energy density, wavefront evolution, and pressure-impulse coupling. Furthermore, the load transfer paths of flat plate structures and V-shaped structures differ. The inclined surface of a V-shaped plate decomposes, deflects, and redistributes the explosion wave, and its maximum dynamic deflection exhibits a significant non-monotonic characteristic as the angle changes.

[0004] In the design process of V-shaped armor steel plates, relying entirely on live-fire tests to obtain a response database is limited by factors such as safety, site conditions, cost, and charge consistency. Relying solely on high-precision finite element analysis is inefficient in early configuration selection and multi-parameter combination evaluation. Existing single empirical models often struggle to simultaneously cover the different load-bearing mechanisms of deep V-shaped configurations, configuration transition zones, and near-flat plate configurations, easily averaging different response modes into the same set of empirical coefficients, leading to large local prediction errors.

[0005] There is an urgent need for a maximum dynamic deflection prediction method that can integrate a small number of live-fire tests, finite element simulation, dimensional analysis, and data-driven coefficient identification. This method should distinguish the response mechanisms under different V-shaped angles while ensuring physical constraints and engineering interpretability, so as to achieve rapid and accurate prediction of the explosion response of V-shaped armor steel plates. Summary of the Invention

[0006] The purpose of this invention is to provide a segmented empirical prediction method for the maximum dynamic deflection of V-shaped armor steel plates under explosive load, in order to solve the problems of high cost of actual explosion tests, low efficiency of finite element case-by-case calculation, and difficulty in characterizing different angle response mechanisms by a unified empirical model in the existing prediction of explosive response of V-shaped armor steel plates.

[0007] The technical solution to achieve the objective of this invention is: a segmented empirical prediction method for the maximum dynamic deflection of a V-shaped armor steel plate under explosive load, comprising the following steps:

[0008] Step (1): Obtain the test response data of V-shaped armor steel plate under TNT air explosion load, construct a finite element simulation model, and use the test response data to verify the finite element simulation model;

[0009] Step (2): Determine the structural parameters, material parameters and explosion load parameters of the V-shaped armor steel plate, establish a parameterized simulation matrix based on the verified finite element simulation model, and extract the maximum dynamic deflection corresponding to each simulation condition from the displacement time history of the central region of the V-shaped armor steel plate after the simulation is completed.

[0010] Step (3): Filter the simulation results, retain the valid samples that meet the requirements of energy balance, numerical stability and response mode consistency, and establish a maximum dynamic deflection prediction database;

[0011] Step (4): Based on dimensional analysis, construct a dimensionless parameter set composed of structural geometry, material properties, and explosive load, and establish a power-law relationship formula between the maximum dynamic deflection and the dimensionless parameter set:

[0012] ,

[0013] in, Where H is the maximum dynamic deflection, C is the plate thickness, and p, q, γ, and δ are the exponential coefficients of the dimensionless parameters, respectively. For structural geometry, dimensionless terms The dimensionless term for the V-shaped included angle. The dimensionless term of the explosion load. This is a dimensionless term for material resistance.

[0014] Step (5): Determine the solution method for the exponential coefficients in step (4);

[0015] Step (6): Divide the effective samples into multiple angle intervals according to the response mechanism corresponding to different V-shaped angles. In each angle interval, identify the exponential coefficients according to the method in step (5) and establish a segmented empirical prediction model.

[0016] Step (7): Select the segmented empirical prediction model for the corresponding angle interval according to the V-shaped angle of the V-shaped armor steel plate, input the structural parameters and explosion load parameters of the V-shaped armor steel plate to be predicted, and output the predicted value of the maximum dynamic deflection.

[0017] Compared with the prior art, the significant advantages of this invention are:

[0018] This invention verifies the finite element model through limited experiments and then expands the sample through parametric simulation, thereby reducing the cost and risk of relying entirely on live-fire tests.

[0019] This invention is based on dimensional analysis reconstruction The dimensionless power-law prediction formula in the form of maximum dynamic deflection prediction simultaneously considers the coupling effect of structural geometry, material resistance and explosive load.

[0020] This invention employs logarithmic linearization and singular value decomposition to identify empirical model coefficients, thereby improving the stability of multivariate regression solutions.

[0021] This invention establishes a segmented model based on the response mechanism corresponding to the V-shaped angle, avoiding prediction deviations caused by the mixing of different load-bearing mechanisms.

[0022] This invention can be used for rapid deflection estimation, configuration screening, and preliminary parameter design of the bottom protection structure of armored vehicles. Attached Figure Description

[0023] Figure 1 This is a schematic flowchart of the empirical prediction method for the maximum dynamic deflection of V-shaped armor steel plates under explosive load according to the present invention.

[0024] Figure 2 This is a schematic diagram comparing the predicted values ​​of the single empirical model with the finite element results of this invention.

[0025] Figure 3 This invention compares the predicted values ​​of the piecewise empirical model with the finite element results.

[0026] Figure 4 This is a schematic diagram comparing the prediction performance of the segmented empirical prediction model and the unified empirical model of the present invention.

[0027] Figure 5 The influence of the included angle of the V-shaped plate on the maximum dynamic deflection in this invention. Detailed Implementation

[0028] The following detailed description is provided with reference to embodiments of the present invention. These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0029] like Figures 1-5As shown, this embodiment uses a 6265 armor steel V-shaped plate as the object. The planar dimensions of the V-shaped plate are 500 mm by 500 mm, corresponding to a half-length and half-width of 250 mm. The main parameters considered in the test and simulation include plate thickness H, V-angle θ, TNT charge mass M, and detonation distance R. The plate thickness is taken as 4.5 mm, 5.0 mm, and 6.0 mm; the V-angle is taken as 110 degrees, 120 degrees, 130 degrees, 140 degrees, 150 degrees, 160 degrees, 170 degrees, and 180 degrees; the TNT charge mass is taken as 1 kg and 2 kg; and the detonation distance is taken as 300 mm, 350 mm, 400 mm, 450 mm, and 500 mm.

[0030] Step 1: Conduct TNT air explosion tests and verify the finite element model. A V-shaped armor plate is mounted on a rigid support frame, with bolts constraining the two side boundaries. The TNT charge is suspended above the geometric center of the V-shaped plate. After the test, the maximum dynamic deflection is obtained using a deformation measurement device, and the residual plastic deformation is obtained through 3D scanning. Eight sets of live-fire test data are used to verify the finite element model. The finite element model must be able to reproduce the measured maximum dynamic deflection and residual plastic deformation, with the maximum dynamic deflection serving as the main response index for subsequent empirical model establishment.

[0031] Step 2: Establish the parametric simulation matrix. Based on the verified finite element model, 240 simulation conditions are formed by combining all factors of plate thickness, V-angle, TNT charge mass, and detonation distance. All simulation conditions use the same material constitutive model, explosive load description, contact algorithm, boundary constraints, mesh generation strategy, and numerical control parameters. After the simulation is completed, the maximum dynamic deflection is extracted from the displacement time history of the V-shaped plate center region as the output response of each condition.

[0032] Step 3: Establish a valid sample database. Each of the 240 simulation results was screened to determine whether the simulation was completed normally, whether the energy evolution was reasonable, whether the structural deformation was stable, and whether the response mode conformed to the overall bending-membrane stretching characteristics. Cases exhibiting severe element distortion, abnormal termination, non-physical oscillations, local tearing, obvious instability, or transition to other failure modes were discarded. After screening, 222 valid samples were retained, covering the maximum dynamic deflection range from 9.1 mm to 237 mm.

[0033] Step 4: Construct the dimensionless reconstruction formula. Using the ratio of maximum dynamic deflection w0 to plate thickness H, w0 / H, as the dimensionless response term, and combining variables such as plate half-length L, plate half-width B, plate thickness H, V-angle θ, TNT charge mass M, detonation distance R, steel plate density ρ, elastic modulus E, and yield strength, construct the dimensionless terms λ for structural geometry, χ for V-angle, π3 for explosive load, and π4 for material resistance. The maximum dynamic deflection prediction relationship is reconstructed into the following power-law formula:

[0034] (1)

[0035] Where w0 is the maximum dynamic deflection, H is the plate thickness, C is the proportionality coefficient, and p, q, γ, and δ are the exponential coefficients of each dimensionless parameter. This formula integrates the structural dimensions, angle effect, explosive load, and material resistance of the V-shaped armor steel plate into a unified dimensionless prediction framework, avoiding the problem of weak model applicability caused by directly using dimensional variable regression.

[0036] Step 5: Identify the coefficients of the formula using logarithmic linearization and singular value decomposition. Taking the natural logarithm of both sides of equation (1) in step 4, we get:

[0037] (2)

[0038] For the i-th valid sample group, let yi be the logarithmic response of the i-th sample group, xi be the logarithmic input row vector of the i-th sample group, and the vector of coefficients to be identified be... Then each group of samples satisfies a linear relationship. Combining the N groups of valid samples yields an overdetermined system of linear equations:

[0039] (3)

[0040] Where A is an N x 5 design matrix, and Y is an N-dimensional response vector. Singular value decomposition is performed on the design matrix A:

[0041] (4)

[0042] Based on the Moore-Penrose pseudoinverse of the singular value matrix, the coefficient vector is solved using the following formula:

[0043] (5)

[0044] C = exp(η) is obtained from η in the coefficient vector x, and p, q, γ, and δ are obtained, thus completing the coefficient identification of the maximum dynamic deflection reconstruction formula.

[0045] Step 6: Establish a segmented empirical prediction model. First, establish a unified empirical model for all 222 valid samples.

[0046] Model with 110° ≤ θ ≤ 180°

[0047] (6)

[0048] A unified model can reflect overall trends, such as Figure 2 As shown, however, the load-bearing mechanism changes significantly when the V-angle changes from 110 degrees to 180 degrees, resulting in a systematic bias in the unified model. Therefore, as... Figure 3As shown, the included angle is divided into three response intervals: 110° to 140°, 150° to 160°, and 170° to 180°. The 110° to 140° interval is the deep V-shaped stable response region, where the V-shaped slope has a significant decomposition and deflection effect on explosive loads. The 150° to 160° interval is the configuration transformation sensitive region, where bending, membrane tension, local instability, and failure modes compete significantly. The 170° to 180° interval is the approximate flat plate response region, where the structure gradually approaches a flat plate response but may still be affected by shallow broken lines, leading to unfavorable load transfer. Singular value decomposition is used to identify empirical model coefficients within each of these three intervals, resulting in a piecewise empirical prediction model.

[0049] Model with 110° ≤ θ ≤ 140°

[0050] (7)

[0051] Model with 150° ≤ θ ≤ 160°

[0052] (8)

[0053] Model with 170° ≤ θ ≤ 180°

[0054] (9)

[0055] Step 7: Perform maximum dynamic deflection prediction and engineering application. For the V-shaped armor steel plate to be predicted, input its half-length, half-width, thickness, V-angle, charge mass, and detonation distance. Calculate the corresponding dimensionless parameters and select the appropriate segmented model based on the V-angle. When the angle is between 110 and 140 degrees, the deep V stable response zone model is used. When the angle is between 150 and 160 degrees, the configuration transformation sensitive zone model is used. When the angle is between 170 and 180 degrees, the approximate flat plate response zone model is used. The corresponding model outputs the predicted maximum dynamic deflection value, which is then used for initial configuration selection, plate thickness selection, detonation distance sensitivity analysis, and preliminary anti-blast design of the armored vehicle's bottom structure.

[0056] In this embodiment, when the unified empirical model is used for all 222 valid samples, such as Figure 4 As shown, the coefficient of determination R² is 0.5745, the root mean square error is 34.60 mm, and the mean absolute percentage error is 28.79%. After adopting the piecewise empirical prediction model of this invention, the overall coefficient of determination R² increases to 0.9411, the root mean square error decreases to 12.88 mm, and the mean absolute percentage error decreases to 9.33%. Compared with the uniform model, the piecewise model shows a significant reduction in error, indicating that dividing the model interval according to the response mechanism can effectively avoid prediction bias caused by the mixing of different bearing mechanisms.

[0057] This embodiment also demonstrates that the V-shaped angle is a key geometric parameter controlling the explosion response mechanism. For example... Figure 5 As shown, the average maximum dynamic deflection increases from 22.34 mm at 110 degrees to 149.43 mm at 170 degrees, then decreases to 86.62 mm in the 180-degree flat plate configuration, exhibiting a clear non-monotonic change. The 150-160 degree range shows the highest response sensitivity, and all invalid simulation samples are concentrated in this range. Therefore, in engineering design, a more sufficient safety margin should be set for V-shaped armor steel plates within the 150-160 degree angle range, and verification should be carried out in conjunction with finite element local strain, instability, and failure checks.

[0058] The method of this invention is applicable to the rapid prediction of maximum dynamic deflection within the range of 250 mm half-length and half-width of plate, 6265 armor steel, plate thickness of 4.5 mm to 6.0 mm, TNT charge mass of 1 kg to 2 kg, detonation distance of 300 mm to 500 mm, and V-angle of 110 degrees to 180 degrees. For other materials, dimensions, boundary conditions, or failure modes, the applicable domain of the model should be re-verified and the segmented model coefficients identified based on newly added test or simulation samples.

[0059] This invention solves the problem of the difficulty in quickly and accurately predicting the maximum dynamic deflection of V-shaped armor steel plates under real TNT (Trinitrotoluene) explosive load. Through experimental verification, finite element extension, dimensionless formula reconstruction, and segmented Singular Value Decomposition (SVD) identification, it improves the response prediction accuracy and parameter screening efficiency in the early design of the bottom protection structure of armored vehicles.

Claims

1. A segmented empirical prediction method for the maximum dynamic deflection of a V-shaped armor steel plate under explosive load, characterized in that, Includes the following steps: Step (1): Obtain the test response data of V-shaped armor steel plate under TNT air explosion load, construct a finite element simulation model, and use the test response data to verify the finite element simulation model; Step (2): Determine the structural parameters, material parameters and explosion load parameters of the V-shaped armor steel plate, establish a parameterized simulation matrix based on the verified finite element simulation model, and extract the maximum dynamic deflection corresponding to each simulation condition from the displacement time history of the central region of the V-shaped armor steel plate after the simulation is completed. Step (3): Filter the simulation results, retain the valid samples that meet the requirements of energy balance, numerical stability and response mode consistency, and establish a maximum dynamic deflection prediction database; Step (4): Based on dimensional analysis, construct a dimensionless parameter set composed of structural geometry, material properties, and explosive load, and establish a power-law relationship formula between the maximum dynamic deflection and the dimensionless parameter set: ， in, Where H is the maximum dynamic deflection, C is the plate thickness, and p, q, γ, and δ are the exponential coefficients of the dimensionless parameters, respectively. For structural geometry, dimensionless terms The dimensionless term for the V-shaped included angle. The dimensionless term of the explosion load. This is a dimensionless term for material resistance. Step (5): Determine the solution method for the exponential coefficients in step (4); Step (6): Divide the effective samples into multiple angle intervals according to the response mechanism corresponding to different V-shaped angles. In each angle interval, identify the exponential coefficients according to the method in step (5) and establish a segmented empirical prediction model. Step (7): Select the segmented empirical prediction model for the corresponding angle interval according to the V-shaped angle of the V-shaped armor steel plate, input the structural parameters and explosion load parameters of the V-shaped armor steel plate to be predicted, and output the predicted value of the maximum dynamic deflection.

2. The method according to claim 1, characterized in that, The experiment in step (1) specifically involves fixing the V-shaped armor steel plate to a rigid support frame, suspending the TNT charge above the geometric center of the V-shaped armor steel plate, and obtaining the explosion response under different working conditions by changing the charge mass, detonation distance, and plate thickness.

3. The method according to claim 2, characterized in that, The test response data in step (1) includes the maximum dynamic deflection, which is obtained by a deformation measuring device set under the V-shaped armor plate.

4. The method according to claim 3, characterized in that, The finite element simulation model uses the maximum dynamic deflection as the verification index. When the error between the maximum dynamic deflection calculated by the finite element method and the experimental measurement value is less than the preset threshold, the finite element simulation model is deemed to meet the requirements.

5. The method according to claim 4, characterized in that, The structural parameters in step (2) include half-length of the plate, half-width of the plate, thickness of the plate and V-angle, the explosive load parameters include the mass of TNT charge and detonation distance, and the material parameters include density, elastic modulus and yield strength.

6. The method according to claim 5, characterized in that, In step (3), all simulation conditions use the same material constitutive model, explosive load description, contact algorithm, boundary constraints, mesh generation strategy and numerical control parameters.

7. The method according to claim 6, characterized in that, In step (4), "constructing a dimensionless parameter set composed of structural geometry, material properties, and explosive load based on dimensional analysis" specifically involves using the ratio of maximum dynamic deflection w0 to plate thickness H, w0 / H, as the dimensionless response term. Combined with plate half-length L, plate half-width B, plate thickness H, V-angle θ, TNT charge mass M, detonation distance R, steel plate density ρ, elastic modulus E, and yield strength, the following dimensionless terms are constructed: λ for structural geometry, χ for V-angle, π3 for explosive load, and π4 for material resistance. The expressions are as follows: ， ， ， 。 8. The method according to claim 7, characterized in that, Step (5) specifically involves taking the natural logarithm of both sides of the power law formula from step (4) to obtain: ， For the i-th valid sample group, let yi be the logarithmic response of the i-th sample group, xi be the logarithmic input row vector of the i-th sample group, and the vector of coefficients to be identified be... Then each group of samples satisfies a linear relationship; the combination of N groups of valid samples yields an overdetermined system of linear equations: ， Where A is an N-row, 5-column design matrix, and Y is an N-dimensional response vector; singular value decomposition is performed on the design matrix A: ， Based on the Moore-Penrose pseudoinverse of the singular value matrix, the coefficient vector is solved using the following formula. : ， In the formula, Singular value matrix The generalized inverse of a matrix is ​​a matrix The left singular vector matrix, It is a singular value matrix; composed of coefficient vectors By obtaining C=exp(η) from η, and obtaining the values ​​of p, q, γ, and δ, the exponential coefficient identification can be achieved.

9. The method according to claim 8, characterized in that, Step (6) specifically involves: The included angle was divided into three response intervals: 110° to 140°, 150° to 160°, and 170° to 180°. The angle variables of the sampled samples were all multiples of 10. The sample predictions in the intervals of 140° to 150° and 160° to 170° can be evaluated by the model's generalization ability. The empirical model exponential coefficients are identified in three intervals using the method in step (5) to obtain the piecewise empirical prediction model: Model with 110°≤θ≤140°: ， Model with 150°≤θ≤160°: ， Model with 170°≤θ≤180°: 。

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