Design method of nonlinearly similar scale test model of alternative materials

Abstract

The application relates to a design method of a nonlinear similar scale test model of replaceable material, which comprises the following steps: S1, determining an actual ship stiffened plate structure design original model; S2, determining the density rho ps , yield stress sigma yps , elastic modulus E ps and all geometric properties of the stiffened plate original model, and determining a geometric scale factor beta; S3, determining material properties of a test design model through a design criterion I, and calculating geometric properties of the test design model by using a design criterion II; S4, determining the material density rho ps , rho ts and yield stress sigma yps , sigma yts of the stiffened plate original model and the test design model; S5, calculating a density scale factor alpha ρ through a design criterion III; S6, calculating a time scale factor h by combining the density scale factor alpha ρ through a design criterion IV; and S7, predicting the ultimate load and displacement of the original model by using a load and displacement prediction formula. The method is simple and convenient to use, does not need to derive many parameters, and has high engineering application value.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of test design, more particularly, to a nonlinear similar scale test model design method of replaceable materials. BACKGROUND

[0002] The mechanism of the buckling failure of the hull girder is quite complex, because the stiffened plate frame constituting the hull girder has multiple buckling collapse forms, and the influences of geometric nonlinearity and material nonlinearity exist simultaneously from the buckling to the final collapse stage, so even today with the high-speed development of computer technology, a single solution method cannot accurately evaluate the ultimate bearing capacity of the hull girder. In order to more deeply study the buckling failure mechanism and deformation process of the hull structure, how to use the scale model test to predict the ultimate bearing capacity of the original model structure is particularly important. As a basic unit of the hull girder structure, the bending of the hull girder is actually a process of compression of the horizontal stiffened plate, and the ultimate bearing capacity thereof can be directly evaluated by using an analytical method and a semi-analytical semi-empirical formula method. However, most of the analytical methods are based on the thin plate buckling theory in the linear elastic range, and the coupling influences of geometric nonlinearity and material nonlinearity are not fully considered, and the numerical method based on theoretical derivation also has such a problem, so the experimental study of the ultimate strength of the stiffened plate still occupies an important position, and the test method is still the most reliable means for predicting the ultimate bearing capacity of the original model.

[0003] In the experimental study, the original model structure test has the highest test accuracy, but the cost of the original model processing test is too high, so it is rarely used by researchers. In most cases, researchers will use a certain specific similarity theory to scale the original model structure into a scale model with relatively small geometric size based on a preset scale, to reduce the test cost while ensuring the accuracy of the test results. The similarity theories commonly used in the similarity design of ship structures at present mainly include the full similarity theory and the distortion similarity theory. The full similarity theory requires the structure to be scaled at the same scale in the size dimension and the plate thickness dimension, which is not applicable to thin-walled structures such as the stiffened plate with small plate thickness in many cases. The distortion similarity theory allows different scaling ratios in the size dimension and the plate thickness dimension based on the full similarity theory, but may change the buckling mode of the scale model. In addition, researchers have also derived a number of similarity criteria based on the dimensional analysis method, which can also be used for the similarity design of the stiffened plate structure. According to the dimensional theory, the original model structure and the scale model that meet the same similarity criterion will exhibit similar bearing characteristics.

[0004] When using existing similarity theories or design methods to design scaled models of actual ship stiffened plate structures, most similarity design methods are based on directional dimensional analysis. If only the linear elastic small deformation stage is considered, the scaled model's accuracy in predicting the ultimate strength of the original model is low. If the nonlinear large deformation stage is considered, new similarity criteria must be determined, resulting in a large workload and high operational difficulty. When material replacement is required in the scaled model due to processing or other reasons, traditional methods do not clearly define how to select the replacement material. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for designing a nonlinear similarity scaled test model of replaceable materials. The stiffened plate test design model obtained by the design can exhibit load-bearing characteristics and failure modes that are very similar to the stiffened plate original model, and can predict and monitor the ultimate load-bearing capacity and actual stress state of the original model structure with high accuracy.

[0006] The technical solution adopted by the present invention to solve the technical problem is to construct a nonlinear similarity scaled test model design method for replaceable materials, comprising the following steps:

[0007] S1. Determine the actual original model of the ship stiffened plate structure design;

[0008] S2. Determine the density ρ of the original model material of the stiffened plate ps , yield stress σ yps , elastic modulus E ps , all geometric properties, determine the geometric scale factor β;

[0009] S3. Determine the material properties of the experimental design model using design criteria I, and calculate the geometric properties of the experimental design model using design criteria II;

[0010] S4. Determine the material density ρ of the original model and the experimental design model of the reinforced plate ps , ρ ts and yield stress σ yps , σ yts ;

[0011] S5. Calculate the density proportional factor α using design criteria III ρ ;

[0012] S6. Combined with density proportional factor α through design criterion IV ρ Calculate the time scale factor h;

[0013] S7. Obtain the ultimate load F of the test design model through testing. ts and displacement u ts Finally, the load and displacement prediction formulas are used to predict the ultimate load and displacement of the original model.

[0014] According to the above scheme, in the step S1, the geometric and arrangement characteristics of the actual ship stiffened plate structure are retained.

[0015] According to the above scheme, in the step S2, the geometric scale factor β is determined according to the test site and actual requirements.

[0016] According to the above scheme, in the step S3, the design criterion I is the basis for selecting the test design model material, and the specific form is: σ yps / E ps = σ yts / E ts ; the design criterion II is the scale relationship between the geometric properties of the original model of the stiffened plate and the test design model of the stiffened plate, and the specific form is: l ps / l ts = β, wherein l represents all geometric properties of the model of the stiffened plate, including the stiffened span a, the longitudinal rib spacing b, the model panel thickness t, the stiffened thickness t w , the stiffened height h w , the stiffened plate is the web plate and the wing plate, and β is the geometric scale factor.

[0017] According to the above scheme, in the step S4, the material density ρ ts and the yield stress σ yts of the test design model are determined by the test design model material selected in the step S3, and the material density ρ ts , the yield stress σ yts , and the geometric scale factor β of the original model of the stiffened plate are determined by the step S2.

[0018] According to the above scheme, in the step S5, the design criterion III is the scale relationship between the material density of the original model of the stiffened plate and the test design model, and the specific form is: ρ ts / β 3 ρ ps = α ρ , wherein α ρ is the density scale factor.

[0019] According to the above scheme, in the step S6, the design criterion IV is the scale relationship between the material yield stress of the original model of the stiffened plate and the test design model, and the specific form is: h , wherein h is the time scale factor.

[0020] According to the above scheme, in the step S7, after the ultimate load and displacement of the test design model are obtained through the test, the ultimate load and displacement of the original model are predicted through the prediction formula, and the specific form is: F ps = βF ts / α ρ h 2 , ups = βu ts , wherein the geometric scale factor β is determined by step S2, the density scale factor α ρ is obtained by step S5, the time scale factor h is obtained by step S6, F ps and F ts are respectively the predicted original model ultimate load of the stiffened plate and the test design model ultimate load of the stiffened plate, u ps and u ts are respectively the predicted original model displacement of the stiffened plate and the test design model displacement of the stiffened plate.

[0021] The nonlinear similar scale test model design method of alternative materials of the present application has the following

[0022] Advantages:

[0023] 1. The present application is based on the finite similarity theory, the relationship between the original model and the test design model is established by the transport equation, and the relationship among the materials, load and displacement of the original model and the test design model is obtained by the constraints of the continuity equation and the mass conservation equation;

[0024] 2. The present application establishes the connection between the original model and the test design model in the whole physical process, so that the test design model and the original model have similar structural responses in the online elastic small deformation stage and the nonlinear large deformation stage;

[0025] 3. The present application can be used for the design of test design models of stiffened plates containing various stiffening types or stiffening sizes such as flat steel, T-shaped section, angle steel, etc. Unlike existing scale model design methods, this method is simple and convenient to use, does not need to derive many parameters, and has strong engineering application value;

[0026] 4. When the original model cannot meet the processing and welding requirements after scaling, the scaled model obtained by using the existing scaled model design method is a distorted model, while the present application can guide the user to select a suitable and processable test design model material, and adopt a scale ratio to make the test design model avoid being a geometric distortion model, which is convenient for welding and processing assembly. BRIEF DESCRIPTION OF DRAWINGS

[0027] The present application will be further described below in combination with the drawings and examples, wherein:

[0028] Fig. 1 is a flowchart of the nonlinear similar scale test model design method of alternative materials of the present application;

[0029] Fig. 2 is a schematic diagram of the original model and the test design model of the embodiment of the present application;

[0030] Fig. 3 is a schematic diagram of the comparison between the axial pressure dimensionless load-displacement curve of the prototype model and the design model of the embodiment of the present application. DETAILED DESCRIPTION

[0031] In order to have a clearer understanding of the technical features, objectives and effects of the present application, the specific embodiments of the present application will be described in detail with reference to the accompanying drawings.

[0032] As shown in the figure, the design method of the nonlinear similarity scale test model of the alternative material of the present application comprises the following steps: Figs. 1-3

[0033] S1, determining the actual ship stiffened plate structure design prototype model;

[0034] The ship stiffened plate structure design prototype should retain the geometric and layout characteristics of the actual ship stiffened plate structure as much as possible.

[0035] S2, determining the density p of the stiffened plate prototype model material ps , the yield stress s yps , the elastic modulus E ps , all geometric properties, and determining the geometric scale factor b; the geometric scale factor b is determined according to the test site and actual requirements.

[0036] S3, determining the material properties of the test design model by design criterion I, and calculating the geometric properties of the test design model by design criterion II;

[0037] Design criterion I is the basis for selecting the material of the test design model, and its specific form is: s yps / E ps = s yts / E ts Since the ratio of the yield stress and the elastic modulus of two materials rarely occurs in real life, a material with a yield stress and an elastic modulus close to that of the prototype model is selected as the test design model; Design criterion II is the proportional relationship between the geometric properties of the stiffened plate prototype model and the stiffened plate test design model, and its specific form is: l ps / l ts = b, wherein l represents all geometric properties of the stiffened plate model, including stiffened span a, longitudinal spacing b, model panel thickness t, stiffened (web, wing plate) thickness t w , stiffened (web, wing plate) height h w , and b is the geometric scale factor.

[0038] S4, determining the material density p of the stiffened plate prototype model, the test design model ps , p ts , and the yield stress s yps , s yts ;​

[0039] material density of the test design model ts , yield stress yts material density of the test design model selected in step S3 ts , yield stress yts , geometric scale factor β determined in step S2.

[0040] S5, calculate the density scale factor α by design criterion III ρ ;

[0041] Design criterion III is the proportional relationship between the material density of the test design model and the original model, which is specifically expressed as ts / β 3 ρ ps = α ρ , in which α ρ is the density scale factor.

[0042] S6, calculate the time scale factor h by design criterion IV combined with the density scale factor α ρ ;

[0043] Design criterion IV is the proportional relationship between the material yield stress of the test design model and the original model, which is specifically expressed as , in which h is the time scale factor.

[0044] S7, after obtaining the ultimate load F ts and displacement u ts of the test design model through testing, the load and displacement prediction formula is used to predict the ultimate load and displacement of the original model.

[0045] After obtaining the ultimate load and displacement of the test design model through testing, the prediction formula is used to predict the ultimate load and displacement of the original model, which is specifically expressed as F ps = βF ts / α ρ h 2 , u ps = βu ts , in which the geometric scale factor β is determined in step S2, the density scale factor α ρ is obtained in step S5, and the time scale factor h is obtained in step S6, F ps and F ts are the predicted ultimate load of the original model and the ultimate load of the test design model, respectively, and u ps and u ts are the predicted displacement of the original model and the displacement of the test design model, respectively.

[0046] The present invention guides the user to select appropriate test model materials and establish a test design model based on the geometric characteristics of the original model. By establishing a connection between the entire physical process of the stiffened plate original model and the test design model, the original model and the test design model have similar structural responses in both the linear elastic small deformation stage and the nonlinear large deformation stage. The present invention uses a certain scale ratio to perform a scaled design on the stiffened plate structure of the original model to obtain a stiffened plate test design model corresponding to the stiffened plate original model. The stiffened plate test design model designed by the present invention can show load-bearing characteristics and failure modes that are very similar to those of the stiffened plate original model, and can predict and monitor the ultimate load-bearing capacity and actual stress state of the original model structure with higher accuracy. The load prediction formula obtained by the present invention can accurately predict the load and displacement of the original model, and the accuracy is generally higher than that of the existing scaled model design method.

[0047] Example

[0048] S1. Select a ship's deck stiffener as design prototype 1. This stiffener contains five longitudinals. Select a ship's bottom stiffener as design prototype 2. This stiffener contains four longitudinals and two longitudinal girders. The panels and stiffeners in both prototypes 1 and 2 are made of 45 steel.

[0049] S2, the material density ρ of the original model 1 and 2 of the stiffened plate ps 7.8×10 -9 t / mm 3 , yield strength σ yps is 507MPa, elastic modulus E ps The longitudinal size of the original model 1 is 30×4, the longitudinal size of the original model 2 is T15×8×4×4, and the longitudinal girder size is T 30×40×4×4. ps is 400mm, longitudinal bone spacing b ps is 200mm, panel thickness t ps They are 6mm and 4mm respectively, and the geometric scale factor β (scale ratio) is determined to be 2.

[0050] S3. The ratio of the yield stress to the elastic modulus of the original models 1 and 2 of the stiffened plate is calculated by design criterion I as σ yps / E ps =2.535×10 -3 , and the yield stress σ of FC-200 gray cast iron yts is 250MPa, elastic modulus E ts is 100 MPa, and the ratio of yield stress to elastic modulus is σ yts / E ts =2.5×10 -3, which is very close to the material of the original model of the stiffened plate, so FC-200 gray cast iron is selected as the material of the experimental design model; using the design criteria II to calculate the geometric properties of the experimental design model, it can be obtained that the longitudinal bone size of the experimental design model 1 is 15×2, the longitudinal bone size of the experimental design model 2 is T 7.5×4×2×2, and the longitudinal girder size is T15×20×2×2. The span a of the experimental design models 1 and 2 ts is 200mm, longitudinal bone spacing b ts is 100mm, panel thickness t ts 3mm and 2mm respectively.

[0051] S4. Determine the density ρ of the original model material of the stiffened plate 45 steel ps 7.8×10 -9 t / mm 3 , yield strength σ yps is 507MPa; the density ρ of the experimental design model material FC-200 gray cast iron ts 7.04×10 -9 t / mm 3 , yield strength σ yts It is 250MPa.

[0052] S5. Calculate the density proportional factor α using design criteria III ρ =0.113.

[0053] S6. Combined with density proportional factor α through design criterion IV ρ The calculated time scale factor h=1.478.

[0054] S7. Obtain the ultimate load F of the test design model through testing ts and displacement u ts Then, use the load and displacement prediction formula F ps =βF ts / α ρ h 2 、u ps =βu ts Predict the ultimate load and displacement of the original model, where the geometric scale factor β is determined by the second step, and the density scale factor α is ρ Obtained from the fifth step, the time proportional factor h is obtained from the sixth step.

[0055] The comparison of the ultimate load and displacement results of the original model and the experimental design model as well as the corresponding prediction accuracy are shown in Table 1. The load unit is kN and the displacement unit is mm.

[0056] Table 1

[0057]

[0058] The embodiments of the present application are described above with reference to the accompanying drawings, but the present application is not limited to the above-described specific embodiments, and the above-described specific embodiments are merely illustrative, but not restrictive, and a person of ordinary skill in the art can make many forms under the inspiration of the present application without departing from the purpose of the present application and the scope protected by the claims, and these all belong to the protection of the present application.

Claims

1. A method for designing a nonlinear similarity scaled test model with replaceable materials, characterized in that: The following steps are involved: S1. Determine the actual original model of the ship stiffened plate structure design; S2. Determine the density of the original model material of the stiffened plate ρ ps , yield stress σ yps , elastic modulus E ps , all geometric properties, determine the geometric scale factor β ; S3. Determine the material properties of the experimental design model using design criteria I, and calculate the geometric properties of the experimental design model using design criteria II; In step S3, the design criterion I is the basis for selecting the experimental design model material, and is specifically expressed in the following form: Design criterion II is the proportional relationship between the geometric properties of the original model of the stiffened plate and the stiffened plate test design model, which is specifically expressed as follows: , where l Represents all geometric properties of the stiffened plate model including the reinforcement span a , longitudinal bone spacing b , Model panel thickness t、 Reinforcement thickness t w , reinforcement height h w , the reinforcement is the web and flange, β is the geometric scale factor; S4. Determine the material density of the original model and the experimental design model of the reinforced plate ρ ps 、 ρ ts and yield stress σ yps 、 σ yts ; In step S4, the material density of the experimental design model ρ ts , yield stress σ yts The material density of the original model of the stiffened plate is determined by the experimental design model material selected in step S3. ρ ts , yield stress σ yts , geometric scale factor β Determined by step S2; S5. Calculate the density proportional factor using design criteria III α ρ ; In step S5, the design criterion III is the proportional relationship between the material density of the original model of the stiffened plate and the experimental design model, and its specific expression is: , where α ρ is the density scaling factor; S6. Combined density scaling factor through design criterion IV α ρ Calculate the time scale factor h ; In step S6, the design criterion IV is the proportional relationship between the material yield stress of the original model of the stiffened plate and the experimental design model, and its specific expression is: , where h is the time scale factor; S7. Obtain the ultimate load of the test design model through testing F ts and displacement u ts Finally, the load and displacement prediction formulas are used to predict the ultimate load and displacement of the original model.

2. The method for designing a nonlinear similarity scaled test model for replaceable materials according to claim 1, characterized in that: In step S1, the geometry and layout features of the actual ship stiffener structure are retained.

3. The method for designing a nonlinear similarity scaled test model for replaceable materials according to claim 1, characterized in that: In step S2, the geometric scale factor β Determined according to the test site and actual needs.

4. The method for designing a nonlinear similarity scaled test model for replaceable materials according to claim 1, wherein: In step S7, after obtaining the ultimate load and displacement of the experimental design model through the experiment, the ultimate load and displacement of the original model are predicted respectively by the prediction formula, which is specifically expressed in the form of 、 , where the geometric scale factor β Determined by step S2, the density scaling factor α ρ The time proportional factor is obtained from step S5. h From step S6, F ps and F ts The predicted ultimate loads of the original model of the stiffened plate and the ultimate loads of the experimental design model of the stiffened plate, u ps and u ts The predicted displacements of the original model of the stiffened plate and the displacements of the experimental design model of the stiffened plate are shown respectively.

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