A method for reconstructing floating raft displacement under elastic boundary conditions

Abstract

The present invention relates to a method for reconstructing the displacement of a floating raft under elastic boundary conditions. The present invention constructs an error function between discrete strain, finite displacement measurement values ​​and theoretical values ​​represented by modal coordinates, and calculates the modal coordinates of the error function taking the minimum value as output by minimizing the error function. Combined with the full-field displacement mode, the full-field displacement reconstruction under elastic boundary conditions can be achieved according to the traditional modal superposition method. Compared with the prior art, the present invention integrates strain data and displacement data, effectively solves the problem of displacement reconstruction of floating raft structures under elastic boundary constraints, and can be widely promoted in the field of ships and other fields where large raft frame structures need to be deformed and reconstruction needs to be carried out.

Description

Technical Field

[0001] The invention relates to the field of displacement reconstruction after deformation of a ship floating raft structure, and in particular to a method for displacement reconstruction of a floating raft under elastic boundary conditions. Background Art

[0002] In recent years, with the continuous upgrading of ship equipment, the rafts of ship propulsion systems have also developed towards large-scale, integrated and lightweight. The increase in the span of the raft frame is inevitably accompanied by a decrease in stiffness, which is prone to large elastic deformation, thus having an adverse effect on the centering state of the generator set equipment on the raft and the attitude control of the raft. Therefore, it is necessary to grasp the full-field structural displacement information of the large raft of the propulsion system in real time. Unlike aerospace structures and bridge structures under fixed constraints, the large raft structure of the ship propulsion system under elastic boundary conditions has a structural displacement that includes not only elastic deformation but also rigid body displacement. For the displacement reconstruction of structural deformation, the currently known inverse finite element deformation reconstruction technology (patent numbers 202311535664.3, 202310494306.6, 202211128284.3, 202210312365.2, 202210019848.3, 202110806838.X, 202011615128.0) solves the structural deformation by fusing the surface strain information. However, the current method requires fixing one end of the structure, and the solved structural deformation is equivalent to the displacement, or performing displacement reconstruction under the free boundary. It cannot solve how to achieve full-field displacement reconstruction when the displacement under elastic constraints is a combination of rigid body displacement and structural deformation. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a method for reconstructing the displacement of a floating raft under elastic boundary conditions in view of the above shortcomings.

[0004] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0005] A method for reconstructing displacement of a floating raft under elastic boundary conditions comprises the following steps:

[0006] Step 1, using finite element software to model the floating raft, and the floating raft is connected to the hull through elastic elements, determining the specifications, quantity and position of the elastic elements, determining the location of each node in the model and numbering the nodes, determining the strain measurement points and displacement measurement points on the floating raft surface, and obtaining and extracting the displacement mode and strain mode of the floating raft under elastic boundary conditions through simulation;

[0007] Step 2: for the physical floating raft, measuring points with the same distribution as the finite element model are selected, strain sensors and displacement sensors are arranged respectively, the same elastic element specifications, quantity and position are adopted, and loads are applied to the designated nodes of the physical floating raft to measure the strain and displacement of the physical floating raft, so as to obtain discrete strain measurement data and finite displacement measurement data of the physical floating raft;

[0008] Step 3, combining displacement measurement data, strain measurement data, displacement mode and strain mode, taking modal coordinates as independent variables, taking the second norm after subtracting the reconstructed displacement and displacement measurement value, and performing dimensionless processing on the strain measurement data and displacement measurement data respectively to obtain strain error weight and displacement error weight, introducing the strain error weight and displacement error weight to obtain the error function expression, and taking the derivative of the error function with respect to the modal coordinates, and obtaining the modal coordinates with the minimum comprehensive error when the derivative is 0.

[0009] Step 4: Substitute the modal coordinates obtained in the previous step into the displacement modal expression obtained by the modal conversion method in step 1 to obtain the full-field reconstructed displacement.

[0010] Furthermore, the step 1 specifically includes the following steps:

[0011] Step 1.1, the floating raft model structure is a complex geometric model composed of plates and shells. According to the expansion theorem, the displacement and strain are described as the linear combination of displacement mode and strain mode respectively. The displacement data and strain data expressions of the floating raft model are determined as follows:

[0012] D N×1 =Φ N×n q n×1

[0013] S M×1 =Ψ M×n q n×1

[0014] Where D N×1 Represents the displacement vector, i.e., displacement data, S M×1 represents the strain vector, i.e., the strain data, Φ N×n represents the displacement mode matrix, Ψ M×n represents the strain modal matrix, q n×1 represents the modal coordinates, N is the number of displacement sensors, M is the number of strain sensors, and n is the modal order.

[0015] Step 1.2: Under elastic boundary conditions, the modal matrix is ​​linearly composed of rigid body modes and elastic modes, and the displacement vector and strain vector are expressed in terms of modal coordinates, that is, the displacement mode and strain mode are as follows:

[0016]

[0017]

[0018] In the formula is the displacement rigid body mode, is the displacement elastic mode, is the strain rigid body mode, is the strain elastic mode, represents the rigid body modal coordinates, represents the elastic modal coordinates.

[0019] Furthermore, in step 2, the displacement measurement data and strain measurement data of the floating raft entity are expressed as:

[0020]

[0021]

[0022] Where D i represents the displacement data measured by the i-th displacement sensor, S j Represents the strain data measured by the jth strain sensor.

[0023] Furthermore, step 3 specifically includes the following steps:

[0024] Step 3.1: Determine the final error function expression:

[0025]

[0026] Where w ε 、w d are the strain error weight and displacement error weight respectively, where K is the number of displacement measurement points, which can be taken as represents the square of the two-norm;

[0027] Step 3.2, Minimize have to:

[0028]

[0029] After simplification, we get:

[0030]

[0031] Step 3.3: Solve to obtain the modal coordinate q with the minimum comprehensive error n×1 :

[0032]

[0033] Furthermore, step 4 specifically includes the following steps:

[0034] The modal coordinates q n×1 Substituting into the displacement modal expression, the full-field displacement reconstruction D′ can be obtainedN×1

[0035]

[0036] After adopting the above technical solution, the present invention has the following advantages compared with the prior art:

[0037] The present invention proposes a method for reconstructing the displacement of a floating raft under elastic boundary conditions. By constructing an error function between discrete strain and finite displacement measurement values ​​and theoretical values ​​represented by modal coordinates, the error function is minimized, and the modal coordinates at which the error function takes the minimum value are calculated as output. Combined with the full-field displacement mode, the full-field displacement reconstruction under elastic boundary conditions can be achieved according to the traditional modal superposition method. Compared with the prior art, the present invention integrates strain data and displacement data, effectively solves the problem of displacement reconstruction of floating raft structures under elastic boundary constraints, and can be widely promoted in the field of ships and other fields where large raft frame structures need to be deformed and reconstruction needs to be carried out.

[0038] The present invention is described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flow chart of the method of the present invention;

[0040] Figure 2 A schematic diagram of grid division and sensor arrangement of a raft structure provided by an embodiment of the present invention;

[0041] Figure 3 The cloud map of the full-field displacement and displacement reference quantity reconstructed by the present invention;

[0042] Figure 4 This is a comparison diagram of the full-field displacement reconstructed by the present invention and the displacement reference.

[0043] The components represented by the reference numerals in the accompanying drawings are as follows:

[0044] Among them, D1, D3, D6, D9, D13, and D18 are displacement measurement points, D2, D4, D5, D7, D8, D10, D11, D12, D14, D15, D16, and D17 are displacement reconstruction points, S1 to S10 are strain measurement points, F1 and F2 are weight application points, and SP1 to SP6 are elastic support points. DETAILED DESCRIPTION

[0045] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0046] The floating raft in the present invention is used to be installed on a ship to place various equipment. The elastic boundary condition means that the floating raft and the ship (equivalent to the ground) are connected by elastic elements to achieve shock absorption.

[0047] like Figure 1 As shown, a method for reconstructing the displacement of a floating raft under elastic boundary conditions comprises the following steps:

[0048] (1) Finite element software is used to model the raft, such as Figure 2 As shown, the elastic boundary conditions, i.e., the specifications, quantity and position of the elastic elements, are determined; the locations of the nodes in the model are determined and the nodes are numbered; the strain measurement points and displacement measurement points on the surface of the raft are determined; the selection method is manual random selection, and the general principle is to distribute them as widely as possible to avoid being too dense. For the convenience of calculation, they are arranged on a straight path, and the size requirements of the sensor layout need to be considered for selection; the displacement mode and strain mode of the raft are obtained through simulation.

[0049] (2) Conduct experiments, using the same elastic boundary conditions as in the previous modeling step, select measurement points for the raft with the same distribution as the finite element model, arrange displacement sensors and strain sensors respectively, apply loads to the specified nodes of the physical raft, measure the displacement and strain of the physical raft, and obtain displacement measurement data and strain measurement data.

[0050] (3) Combining displacement measurement data, strain measurement data, displacement mode and strain mode, taking modal coordinates as independent variables, taking the second norm after subtracting the reconstructed displacement and displacement measurement value to construct the error function, and performing dimensionless processing on the strain measurement data and displacement measurement data respectively to obtain the strain error weight and displacement error weight, which are introduced into the error function to obtain the final error function expression. The error function is differentiated with respect to the modal coordinates, and the modal coordinates with the minimum comprehensive error are obtained when the derivative is 0.

[0051] (4) Combine the modal coordinates and displacement modes to obtain the full-field reconstructed displacement.

[0052] Furthermore, in step (1), the raft structure is a complex geometric model composed of plates and shells, and the raft structure is a plate of equal thickness. According to the expansion theorem, the displacement and strain are described as linear combinations of displacement modes and strain modes, respectively, and the displacement mode coordinates are equal to the strain mode coordinates.

[0053] In order to verify the effectiveness of the present invention in reconstructing the full-field displacement, a simulation experiment is carried out using a simple elastic support thin plate as an example. The specific details are as follows:

[0054] The z-axis of the elastically supported thin plate model is perpendicular to the xoy surface and faces outward. The plate structure is made of steel, with plate length, plate width, plate thickness, density, Poisson's ratio, and Young's modulus. The model is meshed using Quadratic Hexahedron, with a total of 1500 units and 10928 nodes, and the unit type is C3D20.

[0055] Conditions for displacement reconstruction of thin plates:

[0056] like Figure 2 As shown in the figure, this example is a four-point elastic support of SP1~SP4, the stiffness is set to 272N / mm, and the first-order frequency is 11.11Hz. First, the 12th-order z-direction displacement mode of the whole field and the 12th-order x-direction strain mode of S1~S10 are obtained by ANSYS calculation. When different z-direction loads are applied at F1, F2, and F3, Figure 4 The x-strain data of S1 to S10 are substituted into the existing modal conversion method to predict the vertical displacement. At the same time, the x-strain data of S1 to S10 and the vertical displacement data of D1, D3, D6, D9, D13, and D18 are substituted into the improved modal conversion method to predict the vertical displacement. Subsequently, the reconstructed displacement is compared with the vertical displacement of the finite element analysis. Figure 3 The full-field displacement cloud map and ANSYS displacement cloud map when a -490N load is applied alone at F1.

[0057] Calculation process description:

[0058] In the first step, ANASYS software is used to calculate the nodal displacements of the plate under the elastic boundary conditions of four-point support and subjected to load F1. The nodal displacements of the simulation results are used as reference quantities, and the displacement modal matrix and strain modal matrix are calculated.

[0059] The second step is to carry out experiments. Displacement sensors and strain sensors are arranged at various measuring points of the elastically supported thin plate, and loads are applied at designated nodes to measure the displacement and strain of the thin plate to obtain displacement and strain measurement values.

[0060] The third step is to obtain the error weights of displacement and strain based on the displacement data and strain data measured in the second step. Taking the modal coordinates as the independent variables, combined with the displacement modal matrix and the strain modal matrix, the second norms are obtained after subtracting the displacement measurement data and the strain measurement data, respectively, and the error function is constructed by combining the error weights.

[0061] The fourth step is to find the derivative of the error function and obtain the modal coordinates with the minimum error when the derivative is 0.

[0062] The fifth step is to combine the modal coordinates obtained at this time with the modal transfer algorithm to obtain the full-field reconstruction displacement, which is compared with the displacement reference cloud diagram as shown in Figure 3As shown in the figure, the comparison results between the displacement reconstructed by the improved mode transfer method and the displacement reference are shown in Figure 4 The results show that the displacement reconstructed by the improved modal conversion method is very consistent with the displacement measurement value. Compared with the existing modal conversion method, the trend is more consistent and the calculation accuracy is higher.

[0063] The above is an example of the best implementation of the present invention, and the parts not described in detail are common knowledge of ordinary technicians in the field. The protection scope of the present invention shall be based on the content of the claims, and any equivalent transformation based on the technical enlightenment of the present invention is also within the protection scope of the present invention.

Claims

1. A method for reconstructing the displacement of a floating raft under elastic boundary conditions, characterized in that: The following steps are involved: Step 1, using finite element software to model the floating raft, and the floating raft is connected to the hull through elastic elements, determining the specifications, quantity and position of the elastic elements, determining the location of each node in the model and numbering the nodes, determining the strain measurement points and displacement measurement points on the floating raft surface, and obtaining and extracting the displacement mode and strain mode of the floating raft under elastic boundary conditions through simulation; The step 1 comprises the following steps: Step 1.1, the floating raft model structure is a geometric model composed of plates and shells. According to the modal expansion theorem, the displacement and strain are described as linear combinations of displacement modes and strain modes respectively. The displacement modal expression and strain modal expression of the floating raft model are determined as follows: D N×1 =Φ N×n q n×1 S M×1 =Ψ M×n q n×1 Where D N×1 represents the displacement vector, S M×1 represents the strain vector, Φ N×n represents the displacement mode matrix, Ψ M×n represents the strain modal matrix, q n×1 represents the modal coordinates, N is the number of displacement nodes, M is the number of strain nodes, and n represents the modal order used; Step 1.2: Under elastic boundary conditions, the modal matrix is ​​composed of rigid body modes and elastic modes linearly, and the representation of displacement vectors and strain vectors with respect to modal coordinates is obtained as follows: ; In the formula is the displacement rigid body mode, is the displacement elastic mode, is the strain rigid body mode, is the strain elastic mode, represents the rigid body modal coordinates, represents elastic modal coordinates; Step 2: for the physical floating raft, measuring points with the same distribution as the finite element model are selected, strain sensors and displacement sensors are arranged respectively, the same elastic element specifications, quantity and position are adopted, and loads are applied to the designated nodes of the physical floating raft to measure the strain and displacement of the physical floating raft, so as to obtain discrete strain measurement data and finite displacement measurement data of the physical floating raft; Step 3, combining discrete strain measurement data, finite displacement measurement data, displacement mode and strain mode, taking modal coordinates as independent variables, taking the square of the norm of the difference between the strain theoretical value calculated by multiplying the strain mode of the corresponding measuring point with the modal coordinates and the strain measurement value to form a strain error function, taking the square of the norm of the difference between the displacement theoretical value calculated by multiplying the displacement mode of the corresponding measuring point with the modal coordinates and the displacement measurement value to form a displacement error function, performing dimensionless processing on the strain error function and the displacement error function respectively and superimposing them to form a final error function expression, taking the derivative of the final error function with respect to the modal coordinates, and obtaining the modal coordinates with the minimum final error function when the derivative is 0; Step 4: Substitute the modal coordinates obtained in the previous step into the displacement modal expression of step 1 to obtain the full-field reconstructed displacement.

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