A cross-scale scaled model test design method for transient strong nonlinear process

Abstract

The application provides a cross-scale scaled model test design method for a transient strong nonlinear process, belongs to the technical field of structural impact dynamics model test, and is based on a scale similarity conversion model, introduces similarity conversion coefficients and an uncertainty control index therein, and constructs a scale similarity conversion equation from model test results to prototype responses.Combining self-similarity and scale invariance of the strong nonlinear system, discrete constraint is applied to a scaledown ratio of the cross-scale test, scale levels are defined, three types of cross-scale model conversion, i.e., large-middle-large, large-small and middle-small, can still realize cross-scale similarity conversion of strong impact response time histories such as acceleration and strain under the condition that medium parameters, material parameters and boundaries inevitably distort; and the method is suitable for model test data compensation deduction of prototypes of various strong impact response structures such as explosion impact, collision, drop, throwing into water / into soil and impact vibration.

Description

Technical Field

[0001] This invention belongs to the field of structural impact dynamics model testing technology, specifically, it relates to a cross-scale scaled model test design method for transient strongly nonlinear processes. Background Technology

[0002] The structural response characteristics under strong impact loads are a key research focus in impact tests such as underwater explosions, vehicle collisions, and cross-medium launches of aircraft. These impact responses are characterized by high load intensity, short duration, and significant transient features, directly impacting the system's performance, reliability, and lifespan. Due to the high cost, high risk, long organizational cycle, and stringent site and safety conditions associated with full-scale prototype testing, scaled-down model tests are typically used in engineering practice. These tests replicate experimental loads and boundary constraints under controlled conditions to obtain impact response data such as acceleration and strain. The model test results are then converted to the prototype scale for structural design, reinforcement assessment, and blast resistance verification.

[0003] However, strictly satisfying classical similarity theory in scaled-down model tests under strong impact loads often presents objective difficulties. According to Buckingham's Π theorem, phenomena can be characterized by a functional relationship consisting of several dimensionless Π terms. Ideally, the model and prototype should simultaneously satisfy the equality of all key Π terms. However, in actual model tests, dimensional parameters such as elastic modulus, material density, yield strength, gravitational acceleration, structural impedance, and fluid-structure interaction parameters are difficult to scale uniformly at the same scale ratio, inevitably leading to some Π terms being unequal between the model and prototype, resulting in "distortion." Furthermore, the strong impact response is a transient, strongly nonlinear dynamic process; the response may exhibit bifurcation, abrupt changes, and increased uncertainty with parameter variations. This makes relying solely on traditional dimensional analysis to derive a "definite proportional relationship" prone to inaccuracies in engineering. The distortion effect is amplified during cross-scale conversion, thereby reducing the reliability and stability of the model test results converted to the prototype. Therefore, establishing a reliable scaled-down model design method is a fundamental step in the research and engineering application of strong impact tests.

[0004] To address distortion issues in scaled-down model experiments, existing techniques typically employ compensation corrections, empirical coefficient corrections, or fitting transformations within specific parameter ranges. One type of method introduces additional coefficients to correct unmet similarity conditions, while another relies on finite-scale experiments or limited prototype information to calibrate correction relationships. While these methods can improve transformation accuracy under certain conditions, they generally suffer from the following shortcomings: First, correction relationships are often highly dependent on the experimental platform, loading method, material batch, and boundary realization, limiting their versatility. Second, the search for correction coefficients often requires multiple sets of experiments under the same experimental conditions, and is only applicable to a single model type or a single experimental type. Third, existing methods lack a systematic characterization of questions such as "which Π terms cause key distortions, how distortions evolve with scaling ratio, and how to select a more stable scaling ratio," often treating the scaling ratio as a simple proportional constant, making it difficult to provide robust and reproducible cross-scale similarity transformation paths under strongly nonlinear response conditions.

[0005] Therefore, there is an urgent need for a novel cross-scale model test design method that can effectively compensate for distortion effects, is applicable to model tests with different scaling ratios, and achieves high-precision similarity conversion under strong nonlinear impact response conditions. Summary of the Invention

[0006] In structural response systems under strong impact loads, dimensional medium parameters are often greater than 2, which easily leads to distortion phenomena during scaled-down model tests. Furthermore, this impact response exhibits transient, strongly nonlinear, and nonstationary characteristics. To address these issues, this invention proposes a cross-scale scaled-down model test design method for transient strongly nonlinear processes, aiming to overcome the limitations of classical similarity theory in terms of insufficient similarity conversion accuracy and limited applicability in strongly nonlinear impact dynamics systems.

[0007] This invention is achieved through the following technical solution: a method for designing multi-scale scaled model experiments for transient strongly nonlinear processes, the method specifically including the following steps: Step 1. Taking the prototype and model of underwater explosion as the object, set the scaling ratio, establish the Π equation of the strong impact dynamic system and introduce the distorted Π term decomposition; unify the dynamic laws of the prototype and model of underwater explosion into a dimensionless Π equation. Step 2. Based on scaling theory, a generalized homogeneity assumption and scaling ratio scaling mapping are given. The generalized homogeneity feature of scaling theory is introduced into the functional relationship related to the distortion Π term. A scaling similarity transformation model between the model and the prototype is constructed, and the similarity transformation coefficients are solved through cross-scale experiments. K ; Step 3. Compare the similarity transformation coefficients under the classical similarity theory framework with the similarity transformation coefficients defined in Step 2. K To evaluate the reliability and effectiveness of different solution strategies; Step 4. Based on the discrete value conditions of the renormalization group theory, set the model scaling ratio, and combine experimental data to output the prototype response through the scaling similarity transformation model, so as to realize the simulation and prediction of transient strong nonlinear processes.

[0008] Furthermore, in step 1, it is assumed that in the Π equations of the model and the prototype, only one Π term is distorted in each, and the remaining Π terms ensure that the model and the prototype are equal. A time-dependent Π term is introduced into both the model and prototype Π equations. These two Π terms may or may not be equal and have no effect on the early stages of the impact response.

[0009] Furthermore, in step 2, based on the satisfaction and distortion of the functions in the model and prototype Π equations, combined with the generalized homogeneous function condition, and focusing only on the early stage of the impact response, the similarity transformation equation between the model and the prototype is obtained. Define similarity transformation coefficients K Cross-scale pilot-scale experiments were conducted on models of different scales. The results of the pilot-scale experiments were used to determine the intercept. Combined with the experimental data of small-scale models, a similarity transformation relationship that can predict the prototype response was constructed, and the scaling exponent was determined. d ; Based on the relationship between the corresponding π terms of the model and prototype in scaling theory, the exponent is determined. d The index d Determined by the environmental conditions, inputs and outputs, and system parameters of the model and prototype tests, it reflects the characteristic of how the distortion of the Π term between the prototype and the model changes with the model scaling ratio.

[0010] Furthermore, in step 3, within the framework of classical similarity theory, the similarity transformation coefficients... K Expressed as the ratio of the dependent variable Π term, i.e., the coefficient. K It is an index d Scale ratio with model β The function is used to predict the behavior of the prototype system through theoretical scaling relations.

[0011] Furthermore, in step 4, the cross-scale model experiment is divided into three scale levels: large, medium, and small. The cross-scale experiment includes at least two model experiment combinations, which are selected from the three scale combinations of large-medium, large-small, and medium-small.

[0012] A multi-scale scaled model test design system for transient strongly nonlinear processes; The system includes an initialization module, a similarity conversion module, a comparison module, and a simulation prediction module; The initialization module takes the prototype and model of underwater explosion as the object, sets the scaling ratio, establishes the Π equation of the strong impact dynamic system and introduces the distorted Π term decomposition; and unifies the dynamic laws of the prototype and model of underwater explosion into a dimensionless Π equation. The similarity transformation module, based on scaling theory, assumes a generalized homogeneity and a scaling ratio scaling mapping. It introduces the generalized homogeneity characteristic of scaling theory into the functional relationship related to the distortion Π term, constructing a scaling similarity transformation model between the model and the prototype. The similarity transformation coefficients are then solved through cross-scale experiments. K ; The comparison module is used to compare the similarity transformation coefficients under the classical similarity theory framework with the similarity transformation coefficients defined in the similarity transformation module. K To evaluate the reliability and effectiveness of different solution strategies; The simulation and prediction module sets the model scaling ratio based on the discrete value conditions of the renormalization group theory, and outputs the prototype response through the scaling similarity transformation model in combination with experimental data, thereby realizing the simulation and prediction of transient strongly nonlinear processes.

[0013] A computer device system includes a memory, a processor, and a computer program stored in the memory, characterized in that the processor executes the computer program to implement the steps of the above-described method. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that the computer program / instructions, when executed by a processor, implement the steps of the above-described method.

[0014] A computer program product includes a computer program / instructions, characterized in that the computer program instructions, when executed by a processor, implement the steps of the above-described method.

[0015] This invention proposes a design method for transient, high-impact, scaled-down, multi-scale model experiments based on scaling theory and similarity models. This method effectively solves the problems of insufficient conversion accuracy and limited applicability of traditional similarity theory under strongly nonlinear and distorted conditions. Compared with existing technologies, this invention has the following significant advantages: (1) By introducing the generalized homogeneity assumption of scaling theory, a similarity transformation coefficient K is constructed and the uncertainty control index d is calculated, forming a scaling similarity transformation equation from model to prototype. This method not only provides the transformation formula, but also clarifies the evolution law of distortion with scaling ratio, making up for the shortcomings of the similarity transformation coefficient K solved under classical similarity theory, and realizing the derivation from "empirical correction" to "theoretical scaling".

[0016] (2) By introducing the renormalization group theory and the scale invariance principle, a three-level cross-scale model design method is proposed. Specifically, the scaled model is divided into three scale levels: large, medium and small (e.g., 1:3.107, 1:6.25, 1:15.625), that is, similarity transformation is performed under three cross-scale conditions: large-to-medium, large-to-small, and medium-to-small.

[0017] (3) This method does not depend on a specific test platform, material batch or loading method. By constructing a unified scaling transformation framework, it can be widely applied to the structural response similarity transformation under various transient strong impact loads such as explosion impact, collision, drop, projectile into water / soil, and impact vibration. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the period-doubling bifurcation of the renormalization theory of the present invention; Figure 2 This is a flowchart illustrating the overall process of the cross-scale similarity transformation method of the present invention. Figure 3 This is a schematic diagram of a prototype reinforced cylindrical shell structure. Figure 4 Schematic diagrams of reinforced cylindrical shell models at scales of 1:3.107 and 1:6.25; Figure 5 The diagram shows the plate frame structure model; (a) is the design drawing of the plate frame structure model, and (b) is the finite element model drawing of the plate frame structure. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Unless otherwise specified, the experimental methods used in the following examples are conventional methods. Unless otherwise specified, the materials, reagents, methods, and instruments used are all conventional materials, reagents, methods, and instruments in the art, and can be obtained commercially by those skilled in the art.

[0021] In structural response systems under strong impact loads, dimensional medium parameters are often greater than 2, which easily leads to distortion phenomena during scaled-down model tests. Furthermore, this impact response exhibits transient, strongly nonlinear, and non-stationary characteristics. Therefore, this invention proposes a scaled-down, multi-scale model test design method suitable for the dynamic response of such structures, belonging to the field of structural impact dynamics model testing technology. This method is based on a scaling similarity transformation model, introducing similarity transformation coefficients. K and its uncertainty control indexd A scaling similarity transformation equation was constructed from model test results to prototype response. Combining the self-similarity and scale invariance of strongly nonlinear systems, discretization constraints were applied to the scaling ratio of cross-scale tests and scale levels were defined. A combination of large, medium, and small scales was adopted to form three types of cross-scale model transformations: large-to-medium, large-to-small, and medium-to-small.

[0022] This invention adopts the following technical approach: using a prototype ( p ) and model ( m i Taking ) as the basic research object, the scaling ratio is set to β By selecting key characteristic quantities such as acceleration and strain as target quantities for model response and constructing cross-scale similarity criteria through scaling theory, a more accurate simulation and prediction of transient strong impact processes can be achieved.

[0023] Step 1: Establish the π equation for the strong impact dynamic system and introduce the distorted π term decomposition. (Subscript...) p ) and model (subscript) m The dynamic laws of ) are uniformly expressed as the dimensionless Π equation.

[0024]

[0025] In model tests, dimensional medium parameters such as elastic modulus, material density, gravitational acceleration, and structural impedance are much greater than 2, which causes distortion in the Π term of the model test even if it is designed according to the classical similarity theory. This leads to distortion in underwater explosion model tests, at which point the conditions for the application of the classical similarity theory are no longer met.

[0026] For ease of analysis, it is assumed that only one Π term in each of the model and prototype Π equations is distorted, while the remaining Π terms ensure that the model and prototype are equal. Furthermore, it should be noted that in strongly nonlinear impact dynamics, the similarity between the response time series or the response trajectory in phase space is one of the key differences from linear impact dynamics. This is because in strongly nonlinear impact dynamics, bifurcation and abrupt changes occur on the trajectory, leading to uncertainty characteristics, which are absent in linear impact dynamics. Equation (1) can be decomposed as follows:

[0027] In the formula:

[0028] Π mt Π ptThese represent time-dependent Π terms introduced in the model and prototype Π equations, respectively, to account for the bifurcation and abrupt changes in the trajectory of the strongly nonlinear dynamic system. These two Π terms may or may not be equal and have no critical impact on the early stages of the impact response.

[0029] Step 2: Construct the model—a scaling similarity transformation model of the prototype; Based on scaling theory, a generalized homogeneity assumption and a scaling ratio scaling mapping are given. For the functional relationship related to the distorted Π term, the generalized homogeneity characteristic of scaling theory is introduced.

[0030]

[0031] Under the conditions of equation (2), the functions in the model and prototype Π equations f The desired result can be achieved in model experiments, while the function f , g This will cause distortion in the model experiment. Therefore, let Π in the model experiment system... 1m With Π 1p The following relation is satisfied. Assume Π mi and Π pi If the conditions for a generalized homogeneous function are met, then from equation (4), we know that:

[0032] In the formula: h For a certain undetermined coefficient, if the function f , g It is a function of geometric dimensions (usually) f , g (Related to the dimensional medium parameters of the system and the geometric dimensions of the system), then h It refers to the scaling ratio of the model test. a It is an index.

[0033] For equation (2) of the experimental system, in the model experiment, the function f The function can be satisfied. f and g This will cause distortion. Substituting the above relationship into equation (5), we get:

[0034] According to scaling theory Π mq = h δ Π pq , Π mt = h ν Π pt Furthermore, if we only concern ourselves with the early stages of the impact response, then we can let Π pt= 0, and the similarity transformation equation between the model and the prototype can be obtained.

[0035]

[0036] In the formula f (Π mq ,0) represents the model test results. g (Π pq ,0) is the predicted prototype test result, a For the index to be determined, h For the model test scaling ratio, this equation essentially shows the method of converting the model to the prototype. Π pq Π mq The parameters are determined by the system design parameters and environmental conditions of the prototype and model in the model experiment design, respectively, and can be defined based on the maximum value of the time series.

[0037] Similarity conversion coefficient K Its formula is defined as follows:

[0038] This involves conducting cross-scale experiments on models at different scales, i.e., carrying out pilot-scale experiments. Among these, the function... g (Π pq ,0) is only related to the physical conditions of the prototype, and not to the model scaling ratio. h It is irrelevant and is a definite constant. Taking the logarithm of equation (7) and the corresponding Π term under scaling theory, we can obtain ln g (Π pq ,0) = - d ln β + ln f (Π mq ,0). In this log-linear relationship, the uncertainty control index a It is reflected in the slope, while the intercept corresponds to the results of the pilot test.

[0039] Based on this structure, the pilot-scale test results can be considered as a definite intercept, and then combined with small-scale model test data to construct a similarity transformation relationship that can effectively predict the prototype response. At this point, the scaling exponent... a This can be expressed by the following relation:

[0040] Scaling theory precisely reflects or characterizes Π pq Π mq The expression for the specific relationship, which mathematically indicates that Π pq Π mq The relationship between the two is related to the model scaling ratio and the exponent. d Related. By Π mq =h δ Π pq We can obtain:

[0041] In the formula: h This represents the model scaling ratio. The exponent can be determined from the above formula. d The above formula also shows that the exponent d It is determined by the environmental conditions, inputs and outputs, and system parameters of the model and prototype tests, without requiring model and prototype test data. Furthermore, the index... d Essentially, it reflects the relationship between the differences between the prototype and the model test and the model scaling ratio, that is, the characteristic of the degree of distortion of the Π term between the prototype and the model as the model scaling ratio changes.

[0042] Step 3, Similarity Transformation Coefficients K contrast Within the framework of classical similarity theory, the similarity transformation coefficient K It can be expressed as the ratio of the dependent variable Π term, which reflects the scale relationship between the response signals of the prototype and the model. Specifically, the ratio of the amplitudes of the prototype and model response signals can be described by equation (11).

[0043]

[0044] The similarity conversion coefficient proposed in this invention K Its definition is shown in equation (8). This coefficient is constructed within the framework of scaling theory to establish the response correlation of the system at different geometric scales. Specifically, the coefficient... K It is an index d Scale ratio with model h The core of this function lies in effectively integrating experimental data across scales through theoretical scaling relationships, thereby enabling reliable predictions of the behavior of prototype systems.

[0045] The core of similarity transformation model correction lies in the similarity transformation coefficients. K To improve the accuracy of the solution, a comparative analysis is conducted on the similarity transformation coefficients obtained by the classical method and the method proposed in this invention to evaluate the reliability and effectiveness of different solution strategies.

[0046] Step 4: Scale Constraints and Scale Definition for Multi-Scale Experiments In high-impact testing, due to limitations in testing conditions and cost control, scaled-down models are often used for research, and the results are then converted to the prototype scale. This invention introduces a discrete value condition for the model scaling ratio, based on renormalization group theory, that allows the system to exhibit "macroscopic quantum state" characteristics. Specifically, the scaling ratio can be divided into three scale levels: large, medium, and small, with typical values ​​such as 1:3.107, 1:6.25, and 1:15.625. This scaling ratio sequence stems from the scaling invariance requirement, ensuring stable robustness and universality of similarity transformation between the model and the prototype near the corresponding values.

[0047] This invention divides cross-scale model experiments into three scale categories: large, medium, and small, which satisfy the relationship shown in formula (8) derived from renormalization theory. This scale sequence is used to characterize more stable and more likely cross-scale levels in natural similarity processes, thereby improving the fitting slope from the experimental design perspective. d The accuracy and stability of [the system / mechanism].

[0048]

[0049] Table 1. Scaled-down constraints for model experiment design

[0050] Based on the above technical solution, the overall flowchart is as follows: Figure 2 As shown.

[0051] This invention proposes a cross-scale scaled model test design method that can still achieve cross-scale similarity conversion of time histories of strong impact responses such as acceleration and strain, even under conditions where there are unavoidable distortions in medium parameters, material parameters, and boundary realization. It is applicable to the compensation extrapolation of prototypes from model test data of various strong impact response structures, including explosion impacts, collisions, drops, projectile impacts into water / soil, and impact vibrations.

[0052] To verify the effectiveness and applicability of this method, this invention takes a series of scaled-down model tests of stiffened cylindrical shells and plate frames under underwater explosive loading as an example, and systematically analyzes the evolution of each distortion term Π under different scaling ratios. Based on the similarity transformation model derived from scaling theory, the cross-scale dynamic response transformation from the model to the prototype is calculated.

[0053] Example 1 – Conversion Analysis of a Reinforced Cylindrical Shell Model Taking a stiffened cylindrical shell structure as a prototype, the central section is selected as the research object. The structural dimensions are: length 2.46 m, diameter 1.60 m, rib spacing 0.19 m, and rib height 62.8 mm. To reduce the influence of boundary effects, a rib is extended at each end as a ballast tank, and the end caps are 10 mm thick. The pressure hull thickness is 15.6 mm, and the dimensions of the ribs and longitudinal girder on the pressure hull are as follows: mm. The overall mass is 2332 kg, the material used is Q355B steel, the yield strength is 360 MPa, the density is 7850 kg / m3, the elastic modulus is 2.06E11 Pa, and the Poisson's ratio is 0.3. A two-dimensional planar schematic diagram and a physical image of the structure are shown below. Figure 3 As shown.

[0054] Based on the aforementioned reinforced cylindrical shell structure, a new impact factor is used. C Under the guidance of 3, the impact factors of the model test and the prototype test are equal, as shown in formula (9), that is, the incident load meets the design requirements of similar theory, and then strong impact tests of the stiffened cylindrical shell prototype and models with different scaling ratios are carried out.

[0055]

[0056] Based on the scaling constraints proposed for large- and medium-scale model experiments, a large-scale model structure with a scaling ratio of 1:2.5 is designed, such as... Figure 4 As shown in Table 2. The large-scale model uses the same material properties as the prototype, specifically Q355B steel. The model's structural dimensions and experimental conditions are also shown in Table 2. A medium-scale model with a scale ratio of 1:6.25 was designed, as shown in Table 2. Figure 4 As shown in the figure, the structural dimensions of the model decrease with the gradual decrease in the scaling ratio, which leads to problems such as difficulty in fabricating the medium-scale model structure and difficulty in purchasing materials. In order to carry out medium-scale model tests of stiffened cylindrical shell structures, this paper, under the guidance of similarity theory and based on the principle of equivalent ultimate bending moment, equates the scaled T-section to the thickness of the cylindrical shell, ensuring that the ultimate bending moment of the prototype and the model are equal before and after equivalence. The equivalence principle is shown in formula (10). The material of the medium-scale cylindrical shell model is Q235 steel, and the structural dimensions and test conditions are shown in Table 2.

[0057] (10) In the formula: s For yield strength, W y For the flexural section modulus of the beam with plate, M 0 represents the ultimate bending moment of the beam, a value that is related to the dimensions of the beam with plate and the dynamic yield strength of the material. s related.

[0058] Table 2 Model structural dimensions and impact factor

[0059] For physical systems under strong impact conditions, the medium is similar to Π L = gL / c 2 Only geometric dimensions LIt can be scaled according to a scaling factor, but other related physical quantities cannot synchronously follow the same scaling relationship, causing a deviation in this similarity term. Furthermore, for Π... σ = s s / r w L 2 Because the dynamic mechanical behavior of materials is sensitive to strain rate, there is a complex coupling relationship between the dynamic yield strength and scaling factor of the prototype and the model at different strain rates, which makes it impossible for the strength ratio of the two to meet the condition of complete similarity, thus introducing distortion.

[0060] This study investigates the acceleration signals extracted from measuring points of an underwater explosion-strengthened cylindrical shell structure. Since both the model and prototype tests are conducted on steel structures under normal conditions, the material's impedance is closely related to the structural strength. Therefore, the yield stress, which characterizes the strength of the plate frame structure, is crucial. s It is a distorted physical quantity. Based on the scaling theory analysis results in similar model tests, the relationship between the prototype and model terms of the impact response system of a stiffened cylindrical shell structure under underwater explosive load can be written algebraically as follows:

[0061] In the formula: A For the target structure response acceleration, f The natural frequency of the target structure, L Given the target structure side length, s For the yield stress of steel, W For the quality of the explosive charge.

[0062] To further explore the similarity conversion law of model experiments at different scales, and to analyze the relationship between model experiment results and distortion coefficients... d To understand the relationship between them, this paper conducts model experiments at different scales (1:3.107 and 1:6.25) and calculates the indices in the multi-scale model experiments according to equations (8) and (9), respectively. d and d The calculation results are shown in Table 3: Table 3. Indices in the cross-scale model test of plate frame structure d and d Calculation table

[0063] The distortion coefficients in Table 3 a Sum of Indices dAfter substituting into equation (7), the model test results are introduced into the cross-scale model for similarity transformation. The model test results are then compared with the prototype test results after transformation based on scaling theory and classical similarity theory. The results of the calculation of the maximum peak relative error of the transformed data are shown in Table 4. Table 4. Relative Errors in Span-Scale Model Tests of Plate-Frame Structures

[0064] According to the results in Table 4, the maximum relative error between the predicted values ​​of the prototype experiment obtained based on the similarity transformation equation and the actual measured values ​​is less than 30%. The transformation coefficients obtained by the classical similarity transformation method... K The similarity transformation coefficients are typically slightly lower than those solved in this invention, which is the main reason for the increased prediction error. The similarity transformation results from cross-scale model experiments show that by conducting model experiments at different scales and applying the similarity transformation equations constructed in this study, the model experiment results can be accurately transformed to the prototype scale.

[0065] Example 2 – Transformation Analysis of a Typical Plate Frame Structure Model Based on the typical deck structure of a 10,000-ton ship, a typical stiffened plate frame structure for the hull was designed and numerical model tests were conducted, such as... Figure 5 As shown. The test used spherical TNT. According to equation (9), the impact factor of the model test was calculated to be 0.253. The charge was placed directly above the center of the structure, with a detonation distance of 10m. The plate frame structure model was subjected to fixed support boundary conditions around its perimeter. The homogeneous steel material used in the test had a yield strength of 360MPa and a density of 7850kg / m³. 3 The elastic modulus is 2.06E11 Pa, and the Poisson's ratio is 0.3. The specific geometric dimensions of the prototype stiffened plate frame structure are shown in Table 4.

[0066] Table 5 Dimensions of Reinforced Plate Frame Structure

[0067] This model employs commercial software based on the CEL algorithm, widely used in underwater explosion impact damage research, to study the impact response of a ship's local plate frame structure under underwater explosion impact loads. Simulation design, mesh size, and other simulation steps strictly adhere to design requirements. Based on classical similarity theory, the main physical quantities characterizing the impact response of a typical local plate frame structure on a ship under underwater explosion loads are analyzed. The yield stress, which characterizes the strength of the plate frame structure, is still considered the primary characteristic. s It is a distorted physical quantity. Based on the scaling theory analysis results in the similar model test, the relationship between the prototype and model Π terms of the impact response system of a typical local plate frame structure of the hull under underwater explosive load can be written as equation (8) after algebraic operation.

[0068] To further explore the similarity transformation law of model experiments at different scales, this paper designs a large-scale model experiment of 1:3.107 based on the compensation and correction method of classical similarity theory using scaling theory. According to the sampling criteria for experimental conditions, a medium-scale model experiment of 1:6.25 and a small-scale model experiment of 1:15.625 were designed. The model experiments designed in this patent strictly adhere to the constraints of the novel impact factor. The size parameters of the 1:3.107, 1:6.25, and 1:15.625 scaled models are shown in Table 6.

[0069] Table 6 Dimensions of Scaled-Down Model of Reinforced Plate Frame Structure

[0070] Further investigation was conducted into the similarity transformation law of model experiments at different scales, and the relationship between model experiment results and distortion coefficients was analyzed. d To understand the relationship between them, this paper conducts model experiments at different scales (1:2.5 and 1:6.25, 1:2.5 and 1:15.625, 1:6.25 and 1:15.625) and calculates the indices in the cross-scale model experiments according to equations (8) and (9). a and d The calculation results are shown in Table 7: Table 7. Indices in the cross-scale model test of plate frame structure d and d Calculation table

[0071] The distortion coefficients in Table 7 a Sum of Indices d After substituting into equation (7), the model test results are substituted into the cross-scale model for similarity transformation. The model test results are then compared with the prototype test results after transformation based on scaling theory and classical similarity theory. The results of the maximum peak relative error of the transformed data are calculated based on the relative error value, as shown in Table 8.

[0072] Table 8. Relative Errors in Span-Scale Model Tests of Plate-Frame Structures

[0073] As shown in Table 8, the relative error between the predicted prototype test results and the actual prototype test results based on the similarity transformation equation and the maximum amplitude during numerical calculation is less than 10%. The transformation coefficients obtained by the classical similarity transformation method... KThe similarity transformation coefficients are typically slightly lower than those solved in this invention, which is the main reason for the increased prediction error. The similarity transformation results from cross-scale model experiments show that by conducting model experiments at different scales and applying the similarity transformation equations constructed in this study, the model experiment results can be accurately transformed to the prototype scale.

[0074] A computer device system includes a memory, a processor, and a computer program stored in the memory, characterized in that the processor executes the computer program to implement the steps of the above-described method. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that the computer program / instructions, when executed by a processor, implement the steps of the above-described method.

[0075] A computer program product includes a computer program / instructions, characterized in that the computer program instructions, when executed by a processor, implement the steps of the above-described method.

[0076] The memory in the embodiments of this application can be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. Non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate synchronous DRAM (DDR SDRAM), enhanced synchronous DRAM (ESDRAM), synchronous linked DRAM (SLDRAM), and direct rambus RAM (DR RAM). It should be noted that the memory of the methods described in this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0077] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired means such as coaxial cable, optical fiber, digital subscriber line, DSL, or wireless means such as infrared, wireless, microwave, etc. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium such as a floppy disk, hard disk, magnetic tape; an optical medium such as a high-density digital video disc, DVD; or a semiconductor medium such as a solid-state disk, SSD, etc.

[0078] In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software. The steps of the method disclosed in the embodiments of this application can be directly implemented by a hardware processor, or by a combination of hardware and software modules in the processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, detailed descriptions are omitted here.

[0079] It should be noted that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied as execution by a hardware decoding processor, or as execution by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0080] The present invention provides a detailed description of a cross-scale scaled model test design method for transient strongly nonlinear processes, and elucidates the principles and implementation methods of the invention. The above description of the embodiments is only for the purpose of helping to understand the method and core ideas of the invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the invention. Therefore, the content of this specification should not be construed as a limitation of the invention.

Claims

1. A method for designing multi-scale scaled model experiments for transient strongly nonlinear processes, characterized in that: The method specifically includes the following steps: Step 1. Taking the prototype and model of underwater explosion as the object, set the scaling ratio, establish the Π equation of the strong impact dynamic system and introduce the distorted Π term decomposition; unify the dynamic laws of the prototype and model of underwater explosion into a dimensionless Π equation. Step 2. Based on scaling theory, a generalized homogeneity assumption and scaling ratio scaling mapping are given. The generalized homogeneity feature of scaling theory is introduced into the functional relationship related to the distortion Π term. A scaling similarity transformation model between the model and the prototype is constructed, and the similarity transformation coefficients are solved through cross-scale experiments. K ; Step 3. Compare the similarity transformation coefficients under the classical similarity theory framework with the similarity transformation coefficients defined in Step 2. K To evaluate the reliability and effectiveness of different solution strategies; Step 4. Based on the discrete value conditions of the renormalization group theory, set the model scaling ratio, and combine experimental data to output the prototype response through the scaling similarity transformation model, so as to realize the simulation and prediction of transient strong nonlinear processes.

2. The method according to claim 1, characterized in that: In step 1, assume that in the Π equations of the model and the prototype, only one Π term in each is distorted, and the remaining Π terms ensure that the model and the prototype are equal. A time-dependent Π term is introduced into both the model and prototype Π equations. These two Π terms may or may not be equal and have no effect on the early stages of the impact response.

3. The method according to claim 2, characterized in that: In step 2, based on the satisfaction and distortion of the functions in the model and prototype Π equations, combined with the generalized homogeneous function conditions, and focusing only on the early stage of the impact response, the similarity transformation equations between the model and the prototype are obtained.

4. The method according to claim 3, characterized in that: In step 2, the similarity transformation coefficients are defined. K Cross-scale pilot-scale experiments were conducted on models of different scales. The results of the pilot-scale experiments were used to determine the intercept. Combined with the experimental data of small-scale models, a similarity transformation relationship that can predict the prototype response was constructed, and the scaling exponent was determined. a ; Based on the relationship between the corresponding π terms of the model and prototype in scaling theory, the exponent is determined. δ The index δ Determined by the environmental conditions, inputs and outputs, and system parameters of the model and prototype tests, it reflects the characteristic of how the distortion of the Π term between the prototype and the model changes with the model scaling ratio.

5. The method according to claim 4, characterized in that: In step 3, within the framework of classical similarity theory, the similarity transformation coefficients... K Expressed as the ratio of the dependent variable Π term, i.e., the coefficient. K It is an index δ Scale ratio with model h The function is used to predict the behavior of the prototype system through theoretical scaling relations.

6. The method according to claim 5, characterized in that: In step 4, the cross-scale model experiment is divided into three scale levels: large, medium, and small. The cross-scale experiment includes at least two model experiment combinations, which are selected from the three scale combinations of large-medium, large-small, and medium-small.

7. A multi-scale scaled model test design system for transient strongly nonlinear processes, characterized in that: The system is used to perform the cross-scale scaled model test design method for the transient strongly nonlinear process described in any one of claims 1 to 6; The system includes an initialization module, a similarity conversion module, a comparison module, and a simulation prediction module; The initialization module takes the prototype and model of underwater explosion as the object, sets the scaling ratio, establishes the Π equation of the strong impact dynamic system and introduces the distorted Π term decomposition; and unifies the dynamic laws of the prototype and model of underwater explosion into a dimensionless Π equation. The similarity transformation module, based on scaling theory, assumes a generalized homogeneity and a scaling ratio scaling mapping. It introduces the generalized homogeneity characteristic of scaling theory into the functional relationship related to the distortion Π term, constructing a scaling similarity transformation model between the model and the prototype. The similarity transformation coefficients are then solved through cross-scale experiments. K ; The comparison module is used to compare the similarity transformation coefficients under the classical similarity theory framework with the similarity transformation coefficients defined in the similarity transformation module. K To evaluate the reliability and effectiveness of different solution strategies; The simulation and prediction module sets the model scaling ratio based on the discrete value conditions of the renormalization group theory, and outputs the prototype response through the scaling similarity transformation model in combination with experimental data, thereby realizing the simulation and prediction of transient strongly nonlinear processes.

8. A computer device system, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 6.

10. A computer program product comprising a computer program / instructions, characterized in that, When executed by a processor, the computer program instructions implement the steps of the method according to any one of claims 1 to 6.

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