A method for predicting the ultimate bearing capacity of a stiffened cylindrical shell structure

Abstract

The application provides a kind of stiffened cylindrical shell structure ultimate bearing capacity prediction method, comprising: establishing the three-dimensional model of stiffened cylindrical shell with different stiffener thicknesses;Axial load and radial disturbance at different positions are applied to the model with different stiffener thicknesses;The maximum value of the reaction force of radial disturbance and the data of axial load are fitted twice, and the buckling load prediction value of the designed structure is obtained from the fitting curve;Print samples with different stiffener thicknesses;Axial load is applied to the sample, and radial disturbance is applied to the sample at different positions using a probe;The maximum pressure value of the probe and the data of axial load are fitted twice, and the ultimate bearing pressure of the sample is predicted.The application realizes nondestructive testing of stiffened cylindrical shell with different stiffener heights, obtains the influence of stiffener thickness and radial disturbance position on the accuracy of the prediction result, improves the accuracy of the measurement of the ultimate bearing capacity of the stiffened cylindrical shell, and avoids the loss of the cylindrical shell.

Description

Technical Field

[0001] This invention relates to the fields of non-destructive testing technology and structural design, and in particular to a method for predicting the ultimate bearing capacity of a stiffened cylindrical shell structure. Background Technology

[0002] Thin-walled shell structures are widely used in engineering practice. These structures use relatively little material but possess significant load-bearing capacity. However, due to the large diameter-to-thickness ratio of thin-walled cylindrical shells, they are prone to buckling instability under longitudinal loads. Stiffening them can effectively improve their buckling capacity. Due to initial imperfections, the actual load-bearing capacity of stiffened cylindrical shells is much smaller than the ultimate load-bearing capacity predicted theoretically or numerically based on perfect models. Therefore, how to reasonably and accurately predict the ultimate load-bearing capacity of the designed structure during the design phase of cylindrical shell structures, and to achieve a buckling load design method that combines safety and lightweight characteristics and is suitable for engineering applications, has always been a pressing challenge. Furthermore, selecting the appropriate stiffener thickness is also a problem that needs to be solved.

[0003] Currently, research methods for predicting the ultimate bearing capacity of cylindrical shells mainly combine experiments and numerical simulations. Experiments primarily involve applying different axial pressures to stiffened cylindrical shells until buckling instability to determine their ultimate bearing capacity. However, in each set of experiments, the specimens are disposable and cannot be reused, leading to high experimental costs. Furthermore, for stiffened cylindrical shells with different stiffener thicknesses, it is impossible to determine the effect of stiffener thickness on structural strength without damaging the specimen. Summary of the Invention

[0004] Therefore, it is necessary to provide a method for predicting the ultimate bearing capacity of a reinforced cylindrical shell structure to address the aforementioned technical problems.

[0005] A method for predicting the ultimate bearing capacity of a stiffened cylindrical shell structure includes the following steps: establishing three-dimensional models of stiffened cylindrical shells with different stiffener thicknesses; applying axial loads and radial disturbances at different locations to the models with different stiffener thicknesses based on numerical simulation; performing a second-order fitting of the data composed of the maximum reaction force of the radial disturbance and the axial load obtained from the numerical simulation, and obtaining the predicted buckling load value of the designed structure from the fitted curve; printing stiffened cylindrical shell specimens with different stiffener thicknesses; applying axial loads to the stiffened cylindrical shell specimens, and applying radial disturbances to the stiffened cylindrical shell specimens at different locations using a probe as the axial load changes; performing a second-order fitting of the data composed of the maximum pressure value of the probe and the axial load, and predicting the ultimate bearing pressure of the stiffened cylindrical shell specimens.

[0006] In one embodiment, the step of establishing a three-dimensional model of a reinforced cylindrical shell with different rib thicknesses specifically includes: establishing a three-dimensional model of a reinforced cylindrical shell with different rib thicknesses according to preset cylindrical shell parameters, wherein the cylindrical shell parameters include the thickness of the cylindrical shell ribs, the inner diameter of the cylindrical shell, the wall thickness of the cylindrical shell, the height of the cylindrical shell, and the material of the cylindrical shell.

[0007] In one embodiment, the application of axial load and radial disturbance at different locations to models with different stiffener thicknesses based on numerical simulation specifically includes: applying axial pressure to the three-dimensional model of the stiffened cylindrical shell using the finite element simulation software Abaqus, and continuously increasing the axial pressure. For each different axial pressure loading, a probe is used to apply radial disturbance to the side of the three-dimensional model of the stiffened cylindrical shell, and the probe is controlled by fixed displacement.

[0008] In one embodiment, the axial compression is applied by a concentrated force method, with the concentrated force acting on a reference point, which is coupled to the upper surface of the stiffened cylindrical shell three-dimensional model.

[0009] In one embodiment, the process of performing a second fitting on the data composed of the maximum value of the radial disturbance reaction force obtained from the numerical simulation and the axial load, and obtaining the predicted value of the buckling load of the designed structure from the fitting curve, specifically includes: performing a second fitting on different axial compressions and corresponding reaction force data of the same stiffened cylindrical shell specimen, and the axial compression data and the corresponding reaction force data are in one-to-one correspondence, and the ultimate bearing pressure of the three-dimensional model of the stiffened cylindrical shell is obtained from the intercept of the second fitting curve.

[0010] In one embodiment, the process of printing reinforced cylindrical shell samples with different rib thicknesses specifically includes: using original-color nylon as the material for the reinforced cylindrical shell samples, manufacturing the samples using 3D printing, and designing the parameters of the reinforced cylindrical shell samples required for the experiment, including the inner and outer diameters of the cylindrical shell structure, the shell thickness, the rib thickness, and the height of the cylindrical shell.

[0011] In one embodiment, applying an axial load to the stiffened cylindrical shell sample and applying radial disturbance to the stiffened cylindrical shell sample at different positions using a probe as the axial load changes specifically includes: applying an increasing axial load to the stiffened cylindrical shell sample while simultaneously applying radial pressure using the side of the probe, wherein the probe is controlled by a fixed displacement.

[0012] In one embodiment, the step of performing a second-order fitting of the data composed of the maximum pressure value of the probe and the axial load to predict the ultimate bearing pressure of the stiffened cylindrical shell specimen specifically includes: extracting the maximum pressure value of the probe under each axial load; performing a second-order fitting of the data composed of each axial load and the maximum pressure of the corresponding probe; and predicting the magnitude of the axial load when the probe pressure is 0 based on the result of the second-order fitting, thereby obtaining the ultimate bearing pressure of the stiffened cylindrical shell specimen.

[0013] In one embodiment, after performing a second-order fitting of the data composed of the maximum pressure value of the probe and the axial load to predict the ultimate bearing pressure of the stiffened cylindrical shell specimen, the method further includes: unloading the radial disturbance on the stiffened cylindrical shell specimen, applying an axial load to the stiffened cylindrical shell specimen until the specimen collapses, obtaining the axial load value at the moment of collapse; comparing the ultimate bearing pressure and the axial load value at the moment of collapse; and determining the accuracy of the prediction under different stiffener thicknesses and different radial disturbance positions.

[0014] Compared with existing technologies, the advantages and beneficial effects of this invention are as follows: By establishing a three-dimensional stiffened cylindrical shell model, axial pressure and radial disturbance are simultaneously applied to stiffened cylindrical shells with different stiffener thicknesses. Stiffened cylindrical shell samples with different stiffener thicknesses are manufactured using 3D printing. An axial load is applied to the stiffened cylindrical shell samples, and radial disturbance is applied to different measurement areas of the stiffened cylindrical shell samples using a probe. The maximum pressure value of the probe and the data composed of the axial load are then subjected to a secondary fitting to predict the ultimate bearing pressure of the stiffened cylindrical shell samples. This achieves non-destructive testing of the ultimate bearing capacity of stiffened structures. Simultaneously, the influence of stiffener thickness and different radial disturbance positions on the accuracy of the prediction results is obtained, improving the accuracy of measuring the ultimate bearing capacity of stiffened cylindrical shells, reducing experimental costs, and enhancing measurement accuracy. Attached Figure Description

[0015] Figure 1 This is a flowchart of a method for predicting the ultimate bearing capacity of a reinforced cylindrical shell structure according to an embodiment of the present invention;

[0016] Figure 2 This is a schematic diagram showing different stiffener thicknesses in the model of this invention embodiment;

[0017] Figure 3 This is a schematic diagram illustrating the principle of predicting buckling loads of a stiffened cylindrical shell in an embodiment of the present invention.

[0018] Figure 4 This is a schematic diagram showing different positions where the probe is applied in an embodiment of the present invention;

[0019] Figure 5 This is a three-dimensional curve showing the relationship between probe displacement and pressure under different axial compressions in an unreinforced cylindrical shell model according to an embodiment of the present invention.

[0020] Figure 6 The above are the quadratic fitting curves of the maximum probe pressure and axial load in the embodiments of the present invention, as well as the error graph of the prediction results.

[0021] Figure 7 This is a schematic diagram of the axial compression test equipment in an embodiment of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0023] In one embodiment, such as Figures 1 to 7 As shown, a method for predicting the ultimate bearing capacity of a stiffened cylindrical shell structure is provided, including the following steps:

[0024] Step S101: Establish a three-dimensional model of a reinforced cylindrical shell with different rib thicknesses.

[0025] Specifically, a three-dimensional model of the stiffened cylindrical shell is created using three-dimensional modeling software (e.g., finite element simulation software), and the relevant parameters of the stiffened cylindrical shell three-dimensional model are set according to requirements.

[0026] The design of the cylindrical shell model structure includes parameters such as the thickness of the reinforcing ribs, the inner and outer diameters of the cylindrical shell, the wall thickness of the cylindrical shell, the height of the cylindrical shell, and the material of the cylindrical shell.

[0027] Specifically, to reduce errors, the shell and stiffeners are modeled separately. The cylindrical shell is modeled using the finite element simulation software Abaqus, while the stiffeners are modeled using the 3D modeling software SolidWorks. The surfaces of the shell and stiffeners are connected to assemble them together. The stiffened cylindrical shell can be made of metal, and the stiffener thickness is set to 1, 2, 3, and 4 times the shell thickness, respectively. Figure 2 As shown.

[0028] Step S102: Apply axial load and radial disturbance at different locations to models with different stiffener thicknesses based on numerical simulation.

[0029] Specifically, the finite element simulation was performed in Abaqus software. The stiffened cylindrical shell was discretized using the S4R four-node shell element of the structural mesh. The indenter used in the finite element model was replaced by a rigid sphere with a diameter of 2 mm, and the indentation was discretized using R3D4 rigid elements. The gaps between the stiffeners were much larger than the size of the indenter. The mesh size in the area in contact with the indenter was 0.1 mm, and the mesh size in other areas was 1.0 mm. In addition, mesh convergence was studied to ensure that the results were independent of the mesh size.

[0030] Specifically, a given axial load is applied to the model and the axial load is continuously increased. For each different axial load, a radial perturbation is simultaneously applied to the model using a fixed displacement method, such as... Figure 3As shown, a three-dimensional model of a stiffened cylindrical shell is simulated using a general static method. A concentrated force representing axial compression is applied to the upper surface of the stiffened cylindrical shell model. During the axial compression simulation, an increasing axial load is applied to the stiffened cylindrical shell model, for example, from 0 to the buckling load of the structure, while a radial perturbation is applied using a pressure head model. All six degrees of freedom of the model's bottom surface, including three translations and three rotations, are constrained. For the upper surface of the model, two radial and three circumferential translations and three rotations are constrained, while axial translation is free. All nodes on the upper surface are coupled to a central reference point. Applying a concentrated axial force generates axial compression, and the motion of the upper surface is synchronized with the reference point. Specifically, a probe perpendicular to the shell surface moves radially and gradually contacts the shell, defining a surface-to-surface contact between the probe and the shell surface.

[0031] For ease of analysis, this patent focuses only on the elastic deformation stage of the structure, ignoring the plastic deformation. In the simulation, an increasing axial load is applied to the three-dimensional model of the stiffened cylindrical shell, and the frequency of the axial load increase gradually decreases with the increase of axial pressure. Specifically, the stiffener density studied in the model is relatively sparse, and the gaps between the stiffeners are much larger than the diameter of the probe. The different positions of the radial perturbation applied by the probe affect the research results.

[0032] Specifically, the probe was applied at different locations: the midpoint of the transverse rib (P1), the midpoint of the diagonal rib (P2), the centroid of the triangle (P3), and the intersection of the ribs (P4). Schematic diagrams of these different locations are shown below. Figure 4 As shown.

[0033] Step S103: Perform a second fitting on the data composed of the maximum value of the radial disturbance reaction force and the axial load obtained from the numerical simulation, and obtain the predicted value of the buckling load of the designed structure from the fitting curve.

[0034] Specifically, as the probe moves forward, the displacement and reaction force of the probe are recorded, and the corresponding force-displacement curve is plotted until the cylindrical shell buckles and the simulation can no longer continue.

[0035] The simulation of the unreinforced cylindrical shell yielded a three-dimensional relationship between the axial load, probe displacement, and probe reaction force, as shown in the figure below. Figure 5 As shown, the curve trends obtained for cylindrical shell structures with different stiffener thicknesses are different; the relationship between different structures under different axial loads and corresponding peak indentation pressures is plotted using second-order polynomial fitting to obtain a quantitative relationship between the maximum indentation pressure and the corresponding axial load; the data are one-to-one correspondence, and the ultimate bearing pressure of the model is obtained from the intercept of the quadratic fitting curve, which is the predicted ultimate load; the actual critical buckling load of the cylindrical shell is obtained through nonlinear buckling analysis; the error between the predicted value and the actual value is compared to determine the accuracy of the prediction, and the ultimate bearing capacity is predicted without damaging the specimen.

[0036] Step S104: Print reinforced cylindrical shell samples with different rib thicknesses.

[0037] Specifically, 3D printing is used to print the specimens, with high-performance nylon as the material. The material of the specimens differs from that of the simulation model. The specimen parameters include the inner and outer diameters of the cylindrical shell structure, the shell thickness, the thickness of the reinforcing ribs, and the height of the cylindrical shell. The test specimens use triangular reinforcing ribs, and the gap formed by the intersection of the reinforcing ribs should be much larger than the diameter of the indenter used in the experiment. The thickness of the reinforcing ribs in the printed specimens must be controlled within a certain range; insufficient thickness will affect the roundness of the structure, causing initial defects and preventing the acquisition of accurate experimental results.

[0038] Step S105: Apply an axial load to the stiffened cylindrical shell sample, and apply radial disturbance to the stiffened cylindrical shell sample at different positions using a probe as the axial load changes.

[0039] Specifically, experimental equipment such as Figure 7 As shown. A cylindrical shell is placed on a testing machine, and a constant axial pressure is applied. Pressure is applied to each cylindrical shell with a different stiffener thickness using a pressure gauge perpendicular to the stiffened cylindrical shell. The probe is gradually increased in displacement along the radial direction. The maximum displacement is controlled within 1.5 mm to prevent plastic deformation of the cylindrical shell. The pressure of the indenter under different axial pressures is recorded as a function of the indenter displacement. The axial pressure is gradually increased until the structure buckles under radial disturbance, and the probe reaction force drops sharply to 0.

[0040] In each data set, the axial load value increases at a certain frequency, while the radial displacement of the probe remains unchanged. The experimental procedure is repeated for cylindrical shell models with different stiffener thicknesses, with the probe applied at two locations: the centroid of the triangular face formed by the intersection of the stiffeners and the intersection point of the stiffeners.

[0041] Step S106: Perform a second-order fitting on the data composed of the maximum pressure value of the probe and the axial load to predict the ultimate bearing pressure of the stiffened cylindrical shell specimen.

[0042] Specifically, the maximum pressure value of the probe under each axial load is extracted. The data consisting of the maximum pressure values ​​corresponding to each axial load in the experiment is then subjected to a second-order fitting. Based on the result of the second-order fitting, the axial load value corresponding to when the probe pressure is 0 is predicted, which is the ultimate bearing pressure of the specimen. Figure 6 As shown.

[0043] Step S107: Unload the radial disturbance on the stiffened cylindrical shell specimen, apply an axial load to the stiffened cylindrical shell specimen until the specimen collapses, and obtain the axial load value at the moment of crushing; compare the ultimate bearing pressure and the axial load value at the moment of crushing; and determine the accuracy of the prediction under different stiffener thicknesses and different radial disturbance positions.

[0044] Specifically, the specimen is subjected to axial pressure without disturbance, and the axial load value of the specimen at the moment of crushing is obtained. The predicted ultimate bearing pressure and the axial load value at the moment of crushing are compared. The accuracy of the prediction under different reinforcement and different radial disturbance positions is obtained. The experimental results are compared with the simulation results to verify the accuracy of the method.

[0045] In this embodiment, stiffened cylindrical shell models with different stiffener thicknesses are designed to simulate the axial load on these shells. Different radial disturbance positions are selected, and the ultimate bearing capacity of the structure under different conditions is predicted through quadratic data fitting. The actual ultimate load of the structure is obtained through nonlinear buckling, and compared with the predicted results to analyze the influence of different stiffener thicknesses and radial disturbance positions on the prediction accuracy. Cylindrical shell samples with different stiffener thicknesses are printed using 3D printing technology for experimental verification. The gap formed by the intersection of the stiffeners should be much larger than the diameter of the indenter used in the experiment. Axial load and radial disturbance are applied to the samples on the experimental equipment, and the above steps are repeated to obtain data at different positions of the stiffener structure. Quadratic fitting is used to predict the ultimate bearing capacity of the structure under different conditions. The specimens are then subjected to axial pressure without disturbance, and the axial load value at the moment of crushing is obtained. The predicted ultimate bearing pressure and the axial load value at the moment of crushing are compared to verify the agreement between the experimental and simulation results, demonstrating the feasibility of nondestructive testing.

[0046] Obviously, those skilled in the art will understand that the various steps of the present invention described above can be performed in a manner different from that described above, and the simulation methods and experimental equipment include, but are not limited to, the above description. The steps of the present invention described above can be performed in a different order in certain circumstances, and the steps shown or described above can be performed separately. Therefore, the present invention is not limited to any particular combination of hardware and software.

[0047] The above description, in conjunction with specific embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the inventive concept, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for predicting the ultimate bearing capacity of a reinforced cylindrical shell structure, characterized in that, Includes the following steps: Establish three-dimensional models of reinforced cylindrical shells with different rib thicknesses; Numerical simulation was used to apply axial loads and radial disturbances at different locations to models with different stiffener thicknesses. Specifically, axial loads were applied to the three-dimensional model of the stiffened cylindrical shell, and the axial load was continuously increased. For each different axial load, a probe was used to apply radial disturbances to the side of the three-dimensional model of the stiffened cylindrical shell. The probe was controlled by a fixed displacement. The different locations where the probe was applied were the midpoint of the transverse stiffener, the midpoint of the oblique stiffener, the centroid of the triangle, and the intersection of the stiffeners. The maximum value of the radial disturbance reaction force and the axial load obtained from the numerical simulation are subjected to a second fitting, and the buckling load prediction value of the designed structure is obtained from the fitting curve. Specifically, this includes: performing a second fitting between different axial compressions and corresponding reaction force data of the same stiffened cylindrical shell specimen, and the axial compression data and the corresponding reaction force data are in one-to-one correspondence. The ultimate bearing pressure of the three-dimensional model of the stiffened cylindrical shell is obtained from the intercept of the second fitting curve. Print reinforced cylindrical shell samples with different rib thicknesses; An axial load is applied to a stiffened cylindrical shell specimen, and as the axial load changes, a probe is used to apply radial disturbance to the stiffened cylindrical shell specimen at different positions. The maximum pressure value of the probe and the axial load are subjected to a second-order fitting to predict the ultimate bearing pressure of the stiffened cylindrical shell specimen.

2. The method for predicting the ultimate bearing capacity of a reinforced cylindrical shell structure according to claim 1, characterized in that, The establishment of three-dimensional models of reinforced cylindrical shells with different rib thicknesses specifically includes: Based on preset cylindrical shell parameters, a three-dimensional model of a reinforced cylindrical shell with different rib thicknesses is established. The cylindrical shell parameters include the rib thickness, inner diameter, wall thickness, height, and material of the cylindrical shell.

3. The method for predicting the ultimate bearing capacity of a reinforced cylindrical shell structure according to claim 1, characterized in that, The axial compression is applied using a concentrated force method, with the concentrated force acting on a reference point, which is formed by coupling the upper surface of the stiffened cylindrical shell 3D model.

4. The method for predicting the ultimate bearing capacity of a reinforced cylindrical shell structure according to claim 1, characterized in that, The printing of reinforced cylindrical shell samples with different rib thicknesses specifically includes: The stiffened cylindrical shell specimen is made of natural nylon and is manufactured using 3D printing. The parameters of the stiffened cylindrical shell specimen required for the experiment are designed, including the inner and outer diameters of the cylindrical shell structure, the shell thickness, the thickness of the stiffeners, and the height of the cylindrical shell.

5. The method for predicting the ultimate bearing capacity of a reinforced cylindrical shell structure according to claim 1, characterized in that, The process of applying an axial load to the stiffened cylindrical shell specimen, and applying radial disturbance to the stiffened cylindrical shell specimen at different positions using a probe as the axial load changes, specifically includes: An increasing axial load is applied to the stiffened cylindrical shell specimen, while radial pressure is applied from the side of a probe controlled by a fixed displacement.

6. The method for predicting the ultimate bearing capacity of a reinforced cylindrical shell structure according to claim 1, characterized in that, The method of performing a secondary fitting of the data composed of the maximum pressure value of the probe and the axial load to predict the ultimate bearing pressure of the stiffened cylindrical shell specimen specifically includes: Extract the maximum pressure value of the probe under each axial load; The data composed of each axial load and the maximum pressure of the corresponding probe are subjected to a second-order fitting. Based on the results of the quadratic fitting, the magnitude of the axial load corresponding to the probe pressure being 0 is predicted, and the ultimate bearing pressure of the stiffened cylindrical shell specimen is obtained.

7. The method for predicting the ultimate bearing capacity of a reinforced cylindrical shell structure according to claim 1, characterized in that, After performing a second-order fitting on the data composed of the maximum pressure value of the probe and the axial load to predict the ultimate bearing pressure of the stiffened cylindrical shell specimen, the method further includes: The radial disturbance on the stiffened cylindrical shell specimen was unloaded, and an axial load was applied to the stiffened cylindrical shell specimen until the specimen collapsed, and the axial load value at the moment of crushing was obtained. Compare the ultimate bearing pressure with the axial load value at the moment of crushing; To determine the accuracy of predictions under different stiffener thicknesses and different radial disturbance locations.

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