A data processing method for ice and elastic plate extrusion test and storage medium
By using elastic plate compression tests and data processing methods, the problem of neglecting structural deformation feedback in existing technologies has been solved, enabling more accurate prediction of ice loads and forming a universal ice load prediction method.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- DALIAN UNIV OF TECH
- Filing Date
- 2026-05-06
- Publication Date
- 2026-07-14
AI Technical Summary
Existing ice and structure simulation tests simplify structures as rigid bodies and ignore the feedback effect of structural deformation on the action process, resulting in inaccurate prediction of ice force loads.
The test strain and test pressure values of the strain gauges were obtained through elastic plate compression tests. The deflection function was fitted using the modal superposition method and the least squares method to calculate the compression energy of the elastic plate and the ice block, taking into account the feedback effect of structural deformation on the interaction between the ice and the structure.
More accurate prediction of ice loads has been achieved, a universal method for predicting ice loads has been developed, and the feedback effect of structural deformation on the action process has been taken into account.
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Figure CN122133266B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of ship structural mechanics technology, specifically to a data processing method and storage medium for ice and elastic plate compression tests. Background Technology
[0002] When ships enter polar ice zones, the ice loads exerted by the sea ice are extremely destructive, posing significant risks and challenges to the vessels in the polar environment. Therefore, it is essential to conduct collision simulation experiments between polar sea ice and ships to study the physical characteristics of polar sea ice. Based on these physical characteristics, corresponding strategies can be adopted to address the problem of the extremely destructive ice loads exerted by polar sea ice on ships.
[0003] Polar vessels navigating in ice-covered areas are subjected to ice loads, which severely impacts their structural safety. The ice fracturing process is highly complex, involving microcrack propagation, crushing, and spalling. Furthermore, influenced by factors such as porosity, the constitutive relationship of ice is complex and difficult to characterize effectively. Therefore, model testing remains an effective means of studying ice-structure interactions. Previous ice-structure interaction model tests often simplified the structure as a rigid body, aiming to simplify the complex problem and focus on studying the highly uncertain mechanical behavior and failure modes of the ice itself. However, this rigidity assumption has significant limitations; it completely ignores the feedback effect of structural deformation on the interaction process. Summary of the Invention
[0004] In view of the above problems, this application provides a data processing method and storage medium for ice and elastic plate compression tests, which solves the problem that existing ice and structure simulation tests simplify the structure as a rigid body and ignore the feedback effect of structural deformation on the action process.
[0005] To achieve the above objectives, a data processing method for ice-elastic plate compression tests is provided, comprising the following steps:
[0006] A compression test was conducted by pressing an ice block sample against an elastic plate, wherein strain gauges were provided at several test points on the elastic plate.
[0007] After the compression test is completed, the test pressure value and the test strain value of the strain gauge are obtained when the elastic plate compresses the ice sample.
[0008] The fitted deflection function is obtained by selecting a preset order of vibration modes and summing them using the modal superposition method.
[0009] The fitted strain value corresponding to each test point of the elastic plate is determined based on the fitted deflection function.
[0010] The time coefficient is calculated from the test strain value and the fitted strain value of the strain gauge using the least squares method, and the fitted deflection distribution function of the elastic plate is obtained.
[0011] The compressive energy of the elastic plate and ice block samples was calculated based on the fitted deflection distribution function and the test pressure value.
[0012] In some embodiments, the step of selecting a preset order of vibration modes and summing them to obtain the fitted deflection function by means of the modal superposition method specifically includes the following steps:
[0013] By selecting hyperbolic trigonometric functions as mode shape functions, the mode shape functions of the beams fixed at both ends of the elastic plate are obtained by solving the problem using the span of the beams fixed at both ends of the elastic plate.
[0014] The vibration mode functions of the rigidly fixed plates around the elastic plate are obtained by multiplying the vibration mode functions of the beams fixed at both ends of the elastic plate.
[0015] By using the modal superposition method, the modal functions of the four rigid fixed plates of the elastic plate of a preset order are selected and summed to obtain the fitted deflection function with respect to the time coefficient.
[0016] In some embodiments, the step of calculating the time coefficient from the test strain value and the fitted strain value of the strain gauge using the least squares method to obtain the fitted deflection distribution function of the elastic plate specifically includes the following steps:
[0017] According to the least squares principle, the summation function is obtained by summing the squared differences between the test strain values and the fitted strain values at each test point in two directions at a given time.
[0018] By taking the partial derivatives of the sum function with respect to the time coefficients ai of the i-modes, and setting the equation to 0, we obtain the i-variable equation with respect to the time coefficients a1 to ai.
[0019] Solve the system of i equations simultaneously to obtain a homogeneous system of equations.
[0020] If there is a unique solution, then the i time coefficients at that moment are obtained, and the fitted deflection function is brought back to obtain the fitted deflection function at the current moment.
[0021] If the system of equations has no solution or has infinite solutions, then the mode shape is reselected until the fitted deflection function at the current moment is obtained.
[0022] In some embodiments, after obtaining the fitted deflection function at the current moment, the method further includes the following steps:
[0023] Determine whether the fitted deflection function at the current moment conforms to physical laws;
[0024] If the conditions are met, the three-dimensional fitting deflection function of the elastic plate at the next moment can be calculated.
[0025] If it does not meet the requirements, then the mode shape is reselected until a fitting deflection function that conforms to the physical laws at the current moment is obtained.
[0026] In some embodiments, the elastic plate has seven strain gauges.
[0027] Another technical solution is also provided: a storage medium storing a computer program, which, when executed by a processor, performs the following steps:
[0028] A compression test was conducted by pressing an ice block sample against an elastic plate, wherein strain gauges were provided at several test points on the elastic plate.
[0029] After the compression test is completed, the test pressure value and the test strain value of the strain gauge are obtained when the elastic plate compresses the ice sample.
[0030] The fitted deflection function is obtained by selecting a preset order of vibration modes and summing them using the modal superposition method.
[0031] The fitted strain value corresponding to each test point of the elastic plate is determined based on the fitted deflection function.
[0032] The time coefficient is calculated from the test strain value and the fitted strain value of the strain gauge using the least squares method, and the fitted deflection distribution function of the elastic plate is obtained.
[0033] The compressive energy of the elastic plate and ice block samples was calculated based on the fitted deflection distribution function and the test pressure value.
[0034] In some embodiments, the step of selecting a preset order of vibration modes and summing them to obtain the fitted deflection function by means of the modal superposition method specifically includes the following steps:
[0035] By selecting hyperbolic trigonometric functions as mode shape functions, the mode shape functions of the beams fixed at both ends of the elastic plate are obtained by solving the problem using the span of the beams fixed at both ends of the elastic plate.
[0036] The vibration mode functions of the rigidly fixed plates around the elastic plate are obtained by multiplying the vibration mode functions of the beams fixed at both ends of the elastic plate.
[0037] By using the modal superposition method, the modal functions of the four rigid fixed plates of the elastic plate of a preset order are selected and summed to obtain the fitted deflection function with respect to the time coefficient.
[0038] In some embodiments, the step of calculating the time coefficient from the test strain value and the fitted strain value of the strain gauge using the least squares method to obtain the fitted deflection distribution function of the elastic plate specifically includes the following steps:
[0039] According to the least squares principle, the summation function is obtained by summing the squared differences between the test strain values and the fitted strain values at each test point in two directions at a given time.
[0040] By taking the partial derivatives of the sum function with respect to the time coefficients ai of the i-modes, and setting the equation to 0, we obtain the i-variable equation with respect to the time coefficients a1 to ai.
[0041] Solve the system of i equations simultaneously to obtain a homogeneous system of equations.
[0042] If there is a unique solution, then the i time coefficients at that moment are obtained, and the fitted deflection function is brought back to obtain the fitted deflection function at the current moment.
[0043] If the system of equations has no solution or has infinite solutions, then the mode shape is reselected until the fitted deflection function at the current moment is obtained.
[0044] In some embodiments, after obtaining the fitted deflection function at the current moment, the method further includes the following steps:
[0045] Determine whether the fitted deflection function at the current moment conforms to physical laws;
[0046] If the conditions are met, the three-dimensional fitting deflection function of the elastic plate at the next moment can be calculated.
[0047] If it does not meet the requirements, then the mode shape is reselected until a fitting deflection function that conforms to the physical laws at the current moment is obtained.
[0048] In some embodiments, the elastic plate has seven strain gauges.
[0049] Unlike existing technologies, the above-mentioned technical solution involves conducting a compression test by pressing an ice sample against an elastic plate. After the compression test, the strain values of the strain gauges at the test points of the elastic plate and the test pressure values of the elastic plate pressing the ice sample are obtained. Different modes are selected by the modal superposition method and multiplied by a time coefficient to fit the deflection surface. Then, the fitted values of the corresponding test points are calculated. The time coefficient is calculated using the least squares method with the strain values of the strain gauges and the corresponding fitted values, thereby obtaining the fitted deflection distribution function of the elastic plate. Then, the compression energy between the elastic plate and the ice sample is calculated based on the fitted deflection distribution function and the test pressure value. By conducting an ice compression test using an elastic plate and focusing on the deformation of the elastic plate, this method explores the interaction between ice and structure from an energy perspective, considers the feedback influence of structural deformation on the action process, and forms a universal method for predicting ice loads.
[0050] The above description of the invention is merely an overview of the technical solution of this application. In order to enable those skilled in the art to better understand the technical solution of this application and to implement it based on the description and drawings, and to make the above-mentioned objectives and other objectives, features and advantages of this application easier to understand, the following description is provided in conjunction with the specific embodiments and drawings of this application. Attached Figure Description
[0051] The accompanying drawings are only used to illustrate the principles, implementation methods, applications, features, and effects of specific embodiments of this application and other related content, and should not be considered as limitations on this application.
[0052] In the accompanying drawings of the instruction manual:
[0053] Figure 1 This is a schematic flowchart of a data processing method for an ice-elastic plate compression test as described in a specific implementation.
[0054] Figure 2 A schematic diagram of one structure of the elastic plate described in a specific embodiment;
[0055] Figure 3 This is another flowchart illustrating the data processing method for the ice and elastic plate compression test described in the specific implementation method.
[0056] Figure 4 This is a schematic diagram of the structure of the fitted deflection function expression at the current moment in MATLAB software, as described in the specific implementation method.
[0057] Figure 5 A structural schematic diagram showing the comparison between the fitted strain values and the experimental strain values at the extended side directions of the 7 strain measurement points described in the specific implementation method;
[0058] Figure 6 A structural schematic diagram showing the comparison between the fitted strain values and the experimental strain values at the 7 strain measurement points along the short side direction as described in the specific implementation method;
[0059] Figure 7 This is a schematic diagram of the structure of the storage medium described in a specific embodiment.
[0060] The reference numerals used in the above figures are explained as follows:
[0061] 710. Storage medium,
[0062] 720. Processor. Detailed Implementation
[0063] To illustrate the possible application scenarios, technical principles, implementable specific solutions, and achievable objectives and effects of this application in detail, the following description, in conjunction with the listed specific embodiments and accompanying drawings, provides a detailed explanation. The embodiments described herein are merely illustrative of the technical solutions of this application and are therefore intended to limit the scope of protection of this application.
[0064] In this document, the term "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The term "embodiment" appearing in various places throughout the specification does not necessarily refer to the same embodiment, nor does it specifically limit its independence or connection with other embodiments. In principle, in this application, as long as there are no technical contradictions or conflicts, the technical features mentioned in each embodiment can be combined in any way to form corresponding implementable technical solutions.
[0065] Unless otherwise defined, the technical terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains; the use of related terms herein is merely for the purpose of describing particular embodiments and is not intended to limit this application.
[0066] In the description of this application, the term "and / or" is used to describe the logical relationship between objects, indicating that three relationships can exist. For example, A and / or B means: A exists, B exists, and A and B exist simultaneously. Additionally, the character " / " in this document generally indicates that the preceding and following objects have an "or" logical relationship.
[0067] In this application, terms such as “first” and “second” are used only to distinguish one entity or operation from another, and do not necessarily require or imply any actual quantity, hierarchy or order relationship between these entities or operations.
[0068] Unless otherwise specified, the use of terms such as “comprising,” “including,” “having,” or other similar expressions in this application is intended to cover non-exclusive inclusion, which does not exclude the presence of additional elements in a process, method, or product that includes the stated elements, such that a process, method, or product that includes a list of elements may include not only those defined elements but also other elements not expressly listed, or elements inherent to such a process, method, or product.
[0069] In this application, expressions such as "greater than", "less than", and "exceeding" are understood to exclude the stated number; expressions such as "above", "below", and "within" are understood to include the stated number. Furthermore, in the description of the embodiments of this application, "multiple" means two or more (including two), and similar expressions related to "multiple" are also understood in this way, such as "multiple groups" and "multiple times", unless otherwise explicitly specified.
[0070] In the description of the embodiments of this application, the space-related expressions used, such as "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "vertical," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential," indicate the orientation or positional relationship based on the orientation or positional relationship shown in the specific embodiments or drawings. They are only for the purpose of describing the specific embodiments of this application or for the reader's understanding, and do not indicate or imply that the device or component referred to must have a specific position, a specific orientation, or be constructed or operated in a specific orientation. Therefore, they should not be construed as limitations on the embodiments of this application.
[0071] Unless otherwise expressly specified or limited, the terms "installation," "connection," "linking," "fixing," and "setting," as used in the description of the embodiments of this application, should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral setting; it can be a mechanical connection, an electrical connection, or a communication connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be the internal connection of two components or the interaction between two components. For those skilled in the art to which this application pertains, the specific meaning of the above terms in the embodiments of this application can be understood according to the specific circumstances.
[0072] Please see Figure 1 This embodiment provides a data processing method for ice-elastic plate compression tests, including the following steps:
[0073] A compression test was conducted by pressing an ice block sample against an elastic plate, wherein strain gauges were provided at several test points on the elastic plate.
[0074] After the compression test is completed, the test pressure value and the test strain value of the strain gauge are obtained when the elastic plate compresses the ice sample.
[0075] The fitted deflection function is obtained by selecting a preset order of vibration modes and summing them using the modal superposition method.
[0076] The fitted strain value corresponding to each test point of the elastic plate is determined based on the fitted deflection function.
[0077] The time coefficient is calculated from the test strain value and the fitted strain value of the strain gauge using the least squares method, and the fitted deflection distribution function of the elastic plate is obtained.
[0078] The compressive energy of the elastic plate and ice block samples was calculated based on the fitted deflection distribution function and the test pressure value.
[0079] An ice compression test was conducted by pressing an ice sample against an elastic plate. After the test, the strain values of the strain gauges at the test points of the elastic plate and the pressure values of the elastic plate pressing the ice sample were obtained. Different modes of vibration were selected by the modal superposition method and multiplied by a time coefficient to fit the deflection surface. Then, the fitted values of the corresponding test points were calculated. The time coefficient was calculated by the least squares method using the strain values of the strain gauges and the corresponding fitted values, thus obtaining the fitted deflection distribution function of the elastic plate. Then, the compression energy between the elastic plate and the ice sample was calculated based on the fitted deflection distribution function and the test pressure value. By conducting an ice compression test using an elastic plate and focusing on the deformation of the elastic plate, this method explores the interaction between ice and structure from an energy perspective, considering the feedback influence of structural deformation on the action process, and forming a universal method for predicting ice loads.
[0080] In some embodiments, the step of selecting a preset order of vibration modes and summing them to obtain the fitted deflection function by means of the modal superposition method specifically includes the following steps:
[0081] By selecting hyperbolic trigonometric functions as mode shape functions, the mode shape functions of the beams fixed at both ends of the elastic plate are obtained by solving the problem using the span of the beams fixed at both ends of the elastic plate.
[0082] The vibration mode functions of the rigidly fixed plates around the elastic plate are obtained by multiplying the vibration mode functions of the beams fixed at both ends of the elastic plate.
[0083] By using the modal superposition method, the modal functions of the four rigid fixed plates of the elastic plate of a preset order are selected and summed to obtain the fitted deflection function with respect to the time coefficient.
[0084] Based on the modal superposition method, the vibration of an elastic plate can be decomposed into a superposition of multiple modes, as shown in the formula:
[0085] ;
[0086] Based on elasticity theory, the mode shapes of a rigidly fixed plate can be considered as the product of the mode shapes of a beam under the same boundary conditions in two perpendicular directions, as shown in the formula:
[0087] .
[0088] in, It is a time-varying deflection distribution function. These are the time coefficients for different vibration modes. It is the mode shape function of a rigidly fixed plate on all four sides. and It is the mode shape function of a beam fixed at both ends.
[0089] Based on the above description of a beam fixed at both ends, the mode shape function of the elastic plate is chosen to be in the form of a hyperbolic trigonometric function sum, as shown in the formula:
[0090] ;
[0091] .
[0092] Where a and b are the spans of the beam, which are the long side length and short side length of the elastic plate, respectively. All of these are parameters that can be calculated.
[0093] By selecting mode shapes of a certain order for summation based on the principle of modal superposition, a fitted deflection function with respect to the time coefficient can be obtained. .
[0094] The mode shape function of the plate is decomposed into the product of the mode shape functions of beams in different directions under the same boundary conditions, and the beam mode shape function in hyperbolic trigonometric form is adopted. This type of function has strong orthogonality and good fitting effect.
[0095] In some embodiments, the step of calculating the time coefficient from the test strain value and the fitted strain value of the strain gauge using the least squares method to obtain the fitted deflection distribution function of the elastic plate specifically includes the following steps:
[0096] According to the least squares principle, the summation function is obtained by summing the squared differences between the test strain values and the fitted strain values at each test point in two directions at a given time.
[0097] By taking the partial derivatives of the sum function with respect to the time coefficients ai of the i-modes, and setting the equation to 0, we obtain the i-variable equation with respect to the time coefficients a1 to ai.
[0098] Solve the system of i equations simultaneously to obtain a homogeneous system of equations.
[0099] If there is a unique solution, then the i time coefficients at that moment are obtained, and the fitted deflection function is brought back to obtain the fitted deflection function at the current moment.
[0100] If the system of equations has no solution or has infinite solutions, then the mode shape is reselected until the fitted deflection function at the current moment is obtained.
[0101] By fitting the deflection function The fitted strain values along the long side and along the short side of the corresponding measuring point on the elastic plate are calculated respectively. Using the least squares principle, the summation function is obtained by summing the squared differences between the measured strain value and the fitted strain value of each measuring point in the two directions at a given time. The formula is as follows:
[0102] .
[0103] Will Taking the partial derivatives of the time coefficients ai for each i-mode, and setting the equations to 0, we obtain the time coefficients from a1 to ai. i An i-variable equation.
[0104] Solve the i equations simultaneously to obtain a homogeneous system of equations. If the system of equations has no solution or has infinitely many solutions, then choose a new mode shape until the fitted deflection function at the current moment is obtained.
[0105] If we obtain the i-th time coefficient at that moment and substitute it back into the fitted deflection function... .
[0106] Because the least squares method is used to optimize the squared loss, outliers that are far from the population will have their impact amplified by being squared, making it easier to detect measurement errors in the experiment.
[0107] In some embodiments, after obtaining the fitted deflection function at the current moment, the method further includes the following steps:
[0108] Determine whether the fitted deflection function at the current moment conforms to physical laws;
[0109] If the conditions are met, the three-dimensional fitting deflection function of the elastic plate at the next moment can be calculated.
[0110] If it does not meet the requirements, then a new mode shape is selected until a fitting deflection function that conforms to the physical laws at the current moment is obtained.
[0111] Once the fitted deflection function for the current moment is obtained, it is determined whether the fitted deflection function for the current moment conforms to physical laws. If it does, the three-dimensional fitted deflection function of the elastic plate for the next moment is calculated, i.e., the fitted deflection distribution function of the elastic plate is obtained. If it does not conform, the mode shape is reselected until a fitted deflection function for the current moment that conforms to physical laws is obtained.
[0112] The effects of different experimental technical parameters, such as plate thickness and loading speed, were considered. For different working conditions, different combinations of vibration modes were selected for fitting.
[0113] In some embodiments, the elastic plate has seven strain gauges.
[0114] like Figure 2 As shown, strain gauges are placed at seven locations on the elastic plate. By selecting seven mode functions of different orders, the fitted deflection function with respect to the unknown time coefficient is obtained. Then, based on the fitted deflection function, the fitted strain values in the extended side direction and along the short side direction of the corresponding test point in the experiment are calculated. Using the least squares principle, the sum function of the test strain value and the fitted strain value with respect to the test point is obtained. The partial derivative of the sum function with respect to the seven time coefficients is taken, and the equation is set to 0 to obtain the homogeneous linear equation system of the time coefficients.
[0115] In some embodiments, to study and develop a universal method for predicting ice loads, focusing on exploring the interaction between ice and structures from an energy perspective, an ice-elastic plate compression test was designed to investigate the energy exchange and conversion relationship between ice and structures. This test involves a compressor connected to a clamping structure, which uses the clamping structure to fix an elastic plate against an ice specimen fixed to the bottom of the compressor for compression. In this test, a force sensor built into the universal compressor measures the pressure between the ice and the elastic plate, and strain gauges arranged on the elastic plate measure the plate's deformation. Strain values are measured at seven points to fit the plate's deformation deflection surface. Before each ice-elastic plate compression test, the center of the upper surface of the ice specimen is aligned with the center of the elastic plate to ensure maximum deflection at the plate's center. After the test, different modes are selected using the modal superposition method and multiplied by the time coefficient to fit the deflection surface. The fitted values at the corresponding measuring points are calculated. The time coefficient is calculated using the least squares method with the measured strain values and the fitted values to obtain the fitted deflection distribution of the plate. The fitted strain values at the corresponding measuring points are then compared with the experimental strain values to verify the accuracy of the fitting. Finally, the energy of the plate and ice is calculated based on the deflection distribution function and the measured pressure value to achieve the test objective. Figure 3 As shown, the data processing method for the ice-elastic plate compression test specifically includes the following steps:
[0116] 1. Select seven strain measurement points on the elastic plate and arrange strain gauges.
[0117] 2. Conduct an ice-elastic plate compression test and record the test data, including pressure data and strain data;
[0118] 3. Based on the modal superposition method, the vibration of an elastic plate can be decomposed into the superposition of multiple modes, as shown in formula (1). Based on elasticity theory, the mode shape of a rigidly fixed plate can be regarded as the product of the mode shapes of a beam under the same boundary conditions in two perpendicular directions, as shown in formula (2).
[0119] (1);
[0120] (2).
[0121] in: It is a time-varying deflection distribution function. These are the time coefficients for different vibration modes. It is the mode shape function of a rigidly fixed plate on all four sides. and It is the mode shape function of a beam fixed at both ends.
[0122] 4. Based on the description of the two-end fixed beam in step 3, select its mode function as a hyperbolic trigonometric function and form, such as formula (3) and formula (4).
[0123] (3);
[0124] (4).
[0125] Where: a and b are the spans of the beam, which are the long side length and short side length of the elastic plate, respectively. All of these are parameters that can be calculated.
[0126] 5. Based on the principle of modal superposition described in step 3, select a certain order of mode shape and sum them to obtain the fitted deflection function with respect to the time coefficient. .
[0127] 6. Based on the fitted deflection function Calculate the fitted strain values along the long side and along the short side of the corresponding measuring point.
[0128] 7. According to the least squares principle, the sum function is obtained by squaring the difference between the experimental measurement value and the theoretical fitted value of each measuring point in two directions at a certain time, as shown in formula (5).
[0129] (5)
[0130] 8. By taking the partial derivatives with respect to the time coefficients ai of each i-mode and setting the equations to 0, we obtain the i-variable equations for a1 to ai.
[0131] 9. Solve the system of i equations simultaneously to obtain a homogeneous system of equations, and obtain the i time coefficients at that moment. Substitute these coefficients back into the fitted deflection function. .
[0132] 10. If the system of equations has no solution, has infinitely many solutions, or has a displacement solution but the fitted deflection function does not conform to physical laws, then reselect the mode shape and repeat steps 5 to 9.
[0133] 11. Repeat steps 5-10 at the next time step.
[0134] 12. Fitting the deflection function It was obtained.
[0135] This scheme provides a relatively accurate fit for the small deflection bending deformation of elastic plates.
[0136] This solution considers different working conditions (different plate thicknesses and different loading speeds) and the fitting effect is good.
[0137] This scheme decomposes the mode shape of the plate into the product of the mode shapes of the beam, and then fits the bending deformation of the plate by mode shape superposition method, thus decomposing the complex bending deformation into a superposition of a series of simple vibration modes.
[0138] Specifically, the elastic plate is made of elastic steel plate, and its dimensions are as shown. The actual length and width are 340mm × 120mm due to the boundary conditions. The thickness of the plate is 5mm, and the strain measurement points are 1~7.
[0139] Based on the beam's mode shape function, the different order mode shape functions of the plate are calculated.
[0140] 3. At a certain moment, select the mode functions of the seven orders and sum them to obtain the fitted deflection function with respect to the unknown time coefficient.
[0141] 4. Based on the fitted deflection function, calculate the fitted strain values along the long side and along the short side of the corresponding measuring point in the experiment.
[0142] 5. Using the least squares method, find the sum function of the experimental strain value and the fitted strain value at the measuring point.
[0143] 6. Take the partial derivatives of the sum function with respect to the 7 time coefficients, and set the expression equal to 0.
[0144] 7. Solve the homogeneous linear equations with respect to the time coefficient.
[0145] 8. The equation has a unique solution, yielding the fitted deflection function expression at the current time. Plot the expression in MATLAB software, as shown below. Figure 4 As shown, the physical laws governing the deformation of the plate are correct.
[0146] 9. At the next moment, repeat steps 3 to 8 to obtain the three-dimensional fitting deflection function of the plate.
[0147] 10. Calculate the fitted strain values in two directions at the seven strain measurement points based on the fitted deflection function, and compare them with the experimental strain values. The comparison graph of the fitted strain values and experimental strain values at the seven strain measurement points is shown below. Figure 5-6 As shown.
[0148] As can be seen from the figure above, the physical law of the bending deformation of the plate obtained by this method is correct and the fitted strain value is close to the experimental strain value, indicating a good fitting effect.
[0149] Please see Figure 7 A storage medium 710 stores a computer program, which, when executed by a processor 720, performs the following steps:
[0150] A compression test was conducted by pressing an ice block sample against an elastic plate, wherein strain gauges were provided at several test points on the elastic plate.
[0151] After the compression test is completed, the test pressure value and the test strain value of the strain gauge are obtained when the elastic plate compresses the ice sample.
[0152] The fitted deflection function is obtained by selecting a preset order of vibration modes and summing them using the modal superposition method.
[0153] The fitted strain value corresponding to each test point of the elastic plate is determined based on the fitted deflection function.
[0154] The time coefficient is calculated from the test strain value and the fitted strain value of the strain gauge using the least squares method, and the fitted deflection distribution function of the elastic plate is obtained.
[0155] The compressive energy of the elastic plate and ice block samples was calculated based on the fitted deflection distribution function and the test pressure value.
[0156] A compression test was conducted by pressing an ice sample against an elastic plate. After the test, the strain values of the strain gauges at the test points of the elastic plate and the pressure values of the elastic plate pressing the ice sample were obtained. Different modes were selected by the modal superposition method and multiplied by a time coefficient to fit the deflection surface. Then, the fitted values of the corresponding test points were calculated. The time coefficient was calculated by the least squares method using the strain values of the strain gauges and the corresponding fitted values, thus obtaining the fitted deflection distribution function of the elastic plate. Then, the compression energy between the elastic plate and the ice sample was calculated based on the fitted deflection distribution function and the test pressure value. This method focuses on exploring the interaction between ice and structure from the perspective of energy, forming a universal method for predicting ice loads.
[0157] In some embodiments, the step of selecting a preset order of vibration modes and summing them to obtain the fitted deflection function by means of the modal superposition method specifically includes the following steps:
[0158] By selecting hyperbolic trigonometric functions as mode shape functions, the mode shape functions of the beams fixed at both ends of the elastic plate are obtained by solving the problem using the span of the beams fixed at both ends of the elastic plate.
[0159] The vibration mode functions of the rigidly fixed plates around the elastic plate are obtained by multiplying the vibration mode functions of the beams fixed at both ends of the elastic plate.
[0160] By using the modal superposition method, the modal functions of the four rigid fixed plates of the elastic plate of a preset order are selected and summed to obtain the fitted deflection function with respect to the time coefficient.
[0161] Based on the modal superposition method, the vibration of an elastic plate can be decomposed into a superposition of multiple modes, as shown in the formula:
[0162] ;
[0163] Based on elasticity theory, the mode shapes of a rigidly fixed plate can be considered as the product of the mode shapes of a beam under the same boundary conditions in two perpendicular directions, as shown in the formula:
[0164] .
[0165] in, It is a time-varying deflection distribution function. These are the time coefficients for different vibration modes. It is the mode shape function of a rigidly fixed plate on all four sides. and It is the mode shape function of a beam fixed at both ends.
[0166] Based on the above description of a beam fixed at both ends, the mode shape function of the elastic plate is chosen to be in the form of a hyperbolic trigonometric function sum, as shown in the formula:
[0167] ;
[0168] .
[0169] Where a and b are the spans of the beam, which are the long side length and short side length of the elastic plate, respectively. All of these are parameters that can be calculated.
[0170] By selecting mode shapes of a certain order for summation based on the principle of modal superposition, a fitted deflection function with respect to the time coefficient can be obtained. .
[0171] The mode shape function of the plate is decomposed into the product of the mode shape functions of beams in different directions under the same boundary conditions, and the beam mode shape function in hyperbolic trigonometric form is adopted. This type of function has strong orthogonality and good fitting effect.
[0172] In some embodiments, the step of calculating the time coefficient from the test strain value and the fitted strain value of the strain gauge using the least squares method to obtain the fitted deflection distribution function of the elastic plate specifically includes the following steps:
[0173] According to the least squares principle, the summation function is obtained by summing the squared differences between the test strain values and the fitted strain values at each test point in two directions at a given time.
[0174] By taking the partial derivatives of the sum function with respect to the time coefficients ai of the i-modes, and setting the equation to 0, we obtain the i-variable equation with respect to the time coefficients a1 to ai.
[0175] Solve the system of i equations simultaneously to obtain a homogeneous system of equations.
[0176] If there is a unique solution, then the i time coefficients at that moment are obtained, and the fitted deflection function is brought back to obtain the fitted deflection function at the current moment.
[0177] If the system of equations has no solution or has infinite solutions, then the mode shape is reselected until the fitted deflection function at the current moment is obtained.
[0178] By fitting the deflection function The fitted strain values along the long side and along the short side of the corresponding measuring point on the elastic plate are calculated respectively. Using the least squares principle, the summation function is obtained by summing the squared differences between the measured strain value and the fitted strain value of each measuring point in the two directions at a given time. The formula is as follows:
[0179] .
[0180] Will Taking the partial derivatives of the time coefficients ai for each i-mode, and setting the equations to 0, we obtain the time coefficients from a1 to ai. i An i-variable equation.
[0181] Solve the i equations simultaneously to obtain a homogeneous system of equations. If the system of equations has no solution or has infinitely many solutions, then choose a new mode shape until the fitted deflection function at the current moment is obtained.
[0182] If we obtain the i-th time coefficient at that moment and substitute it back into the fitted deflection function... .
[0183] Because the least squares method is used to optimize the squared loss, outliers that are far from the population will have their impact amplified by being squared, making it easier to detect measurement errors in the experiment.
[0184] In some embodiments, after obtaining the fitted deflection function at the current moment, the method further includes the following steps:
[0185] Determine whether the fitted deflection function at the current moment conforms to physical laws;
[0186] If the conditions are met, the three-dimensional fitting deflection function of the elastic plate at the next moment can be calculated.
[0187] If it does not meet the requirements, then a new mode shape is selected until a fitting deflection function that conforms to the physical laws at the current moment is obtained.
[0188] Once the fitted deflection function for the current moment is obtained, it is determined whether the fitted deflection function for the current moment conforms to physical laws. If it does, the three-dimensional fitted deflection function of the elastic plate for the next moment is calculated, i.e., the fitted deflection distribution function of the elastic plate is obtained. If it does not conform, the mode shape is reselected until a fitted deflection function for the current moment that conforms to physical laws is obtained.
[0189] In some embodiments, the elastic plate has seven strain gauges.
[0190] like Figure 2As shown, strain gauges are placed at seven locations on the elastic plate. By selecting seven mode functions of different orders, the fitted deflection function with respect to the unknown time coefficient is obtained. Then, based on the fitted deflection function, the fitted strain values in the extended side direction and along the short side direction of the corresponding test point in the experiment are calculated. Using the least squares principle, the sum function of the test strain value and the fitted strain value with respect to the test point is obtained. The partial derivative of the sum function with respect to the seven time coefficients is taken, and the equation is set to 0 to obtain the homogeneous linear equation system of the time coefficients.
[0191] Finally, it should be noted that although the above embodiments have been described in the text and drawings of this application, this should not limit the scope of patent protection of this application. Any technical solutions that are based on the essential concept of this application and utilize the content described in the text and drawings of this application, resulting in equivalent structural or procedural substitutions or modifications, as well as the direct or indirect application of the technical solutions of the above embodiments to other related technical fields, are all included within the scope of patent protection of this application.
Claims
1. A data processing method for an ice-elastic plate compression test, characterized in that, Includes the following steps: A compression test was conducted by pressing an ice block sample against an elastic plate, wherein strain gauges were provided at several test points on the elastic plate. After the compression test is completed, the test pressure value and the test strain value of the strain gauge are obtained when the elastic plate compresses the ice sample. The fitted deflection function is obtained by selecting a preset order of vibration modes and summing them using the modal superposition method. The fitted strain value corresponding to each test point of the elastic plate is determined based on the fitted deflection function. The time coefficient is calculated from the test strain value and the fitted strain value of the strain gauge using the least squares method, and the fitted deflection distribution function of the elastic plate is obtained. The compressive energy of the elastic plate and ice block samples was calculated based on the fitted deflection distribution function and the test pressure value. The specific steps for obtaining the fitted deflection function by selecting a preset order of vibration modes using the modal superposition method include: By selecting hyperbolic trigonometric functions as mode shape functions, the mode shape functions of the beams fixed at both ends of the elastic plate are obtained by solving the problem using the span of the beams fixed at both ends of the elastic plate. The vibration mode functions of the rigidly fixed plates around the elastic plate are obtained by multiplying the vibration mode functions of the beams fixed at both ends of the elastic plate. By using the modal superposition method, the modal functions of the four rigid fixed plates of the elastic plate of a preset order are selected and summed to obtain the fitted deflection function with respect to the time coefficient.
2. The data processing method for the ice-elastic plate compression test according to claim 1, characterized in that, The step of calculating the time coefficient from the test strain value and the fitted strain value of the strain gauge using the least squares method to obtain the fitted deflection distribution function of the elastic plate specifically includes the following steps: According to the least squares principle, the summation function is obtained by summing the squared differences between the test strain values and the fitted strain values at each test point in two directions at a given time. By taking the partial derivatives of the sum function with respect to the time coefficients ai of the i-modes, and setting the equation to 0, we obtain the i-variable equation with respect to the time coefficients a1 to ai. Solve the system of i equations simultaneously to obtain a homogeneous system of equations. If there is a unique solution, then the i time coefficients at that moment are obtained, and the fitted deflection function is brought back to obtain the fitted deflection function at the current moment. If the system of equations has no solution or has infinite solutions, then the mode shape is reselected until the fitted deflection function at the current moment is obtained.
3. The data processing method for the ice-elastic plate compression test according to claim 2, characterized in that, After obtaining the fitted deflection function at the current moment, the following steps are also included: Determine whether the fitted deflection function at the current moment conforms to physical laws; If the conditions are met, the three-dimensional fitting deflection function of the elastic plate at the next moment can be calculated. If it does not meet the requirements, then a new mode shape is selected until a fitting deflection function that conforms to the physical laws at the current moment is obtained.
4. The data processing method for the ice-elastic plate compression test according to claim 1, characterized in that, The elastic plate has seven strain gauges.
5. A storage medium storing a computer program, characterized in that, The computer program, when executed by the processor, performs the following steps: A compression test was conducted by pressing an ice block sample against an elastic plate, wherein strain gauges were provided at several test points on the elastic plate. After the compression test is completed, the test pressure value and the test strain value of the strain gauge are obtained when the elastic plate compresses the ice sample. The fitted deflection function is obtained by selecting a preset order of vibration modes and summing them using the modal superposition method. The fitted strain value corresponding to each test point of the elastic plate is determined based on the fitted deflection function. The time coefficient is calculated from the test strain value and the fitted strain value of the strain gauge using the least squares method, and the fitted deflection distribution function of the elastic plate is obtained. The compressive energy of the elastic plate and ice block samples was calculated based on the fitted deflection distribution function and the test pressure value. The specific steps for obtaining the fitted deflection function by selecting a preset order of vibration modes using the modal superposition method include: By selecting hyperbolic trigonometric functions as mode shape functions, the mode shape functions of the beams fixed at both ends of the elastic plate are obtained by solving the problem using the span of the beams fixed at both ends of the elastic plate. The vibration mode functions of the rigidly fixed plates around the elastic plate are obtained by multiplying the vibration mode functions of the beams fixed at both ends of the elastic plate. By using the modal superposition method, the modal functions of the four rigid fixed plates of the elastic plate of a preset order are selected and summed to obtain the fitted deflection function with respect to the time coefficient.
6. The storage medium according to claim 5, characterized in that, The step of calculating the time coefficient from the test strain value and the fitted strain value of the strain gauge using the least squares method to obtain the fitted deflection distribution function of the elastic plate specifically includes the following steps: According to the least squares principle, the summation function is obtained by summing the squared differences between the test strain values and the fitted strain values at each test point in two directions at a given time. By taking the partial derivatives of the sum function with respect to the time coefficients ai of the i-modes, and setting the equation to 0, we obtain the i-variable equation with respect to the time coefficients a1 to ai. Solve the system of i equations simultaneously to obtain a homogeneous system of equations. If there is a unique solution, then the i time coefficients at that moment are obtained, and the fitted deflection function is brought back to obtain the fitted deflection function at the current moment. If the system of equations has no solution or has infinite solutions, then the mode shape is reselected until the fitted deflection function at the current moment is obtained.
7. The storage medium according to claim 6, characterized in that, After obtaining the fitted deflection function at the current moment, the following steps are also included: Determine whether the fitted deflection function at the current moment conforms to physical laws; If the conditions are met, the three-dimensional fitting deflection function of the elastic plate at the next moment can be calculated. If it does not meet the requirements, then a new mode shape is selected until a fitting deflection function that conforms to the physical laws at the current moment is obtained.
8. The storage medium according to claim 5, characterized in that, The elastic plate has seven strain gauges.