A high-efficiency fluid-structure coupling calculation method for membrane structure considering initial slack

Abstract

The application discloses a kind of membrane structure high-efficiency fluid-structure coupling calculation methods considering initial relaxation, belong to membrane structure fluid-structure coupling field;Specifically: the wing under supersonic speed is simplified as rectangular model with initial relaxation, and structural grid is divided;Read current grid node coordinates and speed, aerodynamic grid uses structural grid, the pressure corresponding to each face element is calculated by piston theory, open geometric nonlinear setting, calculate structural deformation, obtain the new position of each node, speed and the stress value of structure are exported to.dat file, read the new displacement and speed of generated node;Then, the pressure corresponding to grid face element is solved using piston theory, ABAQUS restart function is called, and iteration is continuously carried out until all time step calculation is completed.Last, the structure time-domain deformation response is obtained by summarizing, and the calculation results of flutter speed, maximum deformation and the like are summarized and analyzed;The application avoids interpolation process, and aerodynamic force also uses piston theory, which greatly improves calculation efficiency.

Description

Technical Field

[0001] This invention belongs to the field of fluid-structure interaction calculation for membrane structures, specifically a highly efficient fluid-structure interaction calculation method for membrane structures that considers initial relaxation. Background Technology

[0002] In recent years, supersonic aircraft have been favored by major aerospace powers due to their high speed and high penetration capability, and have become a hot research topic. In order to reduce weight and achieve better flight performance, high-speed aircraft have increasingly lightweight and flexible structural designs. Their structural dynamics exhibit strong geometric and material nonlinear characteristics, while the flow field around them is more complex, and aeroelasticity problems are becoming more prominent.

[0003] Membrane structures are a special type of material, characterized by their lightweight, flexibility, and ability to withstand significant pressure; therefore, they are increasingly being used in aircraft design. However, membrane materials differ considerably from traditional materials, and they also exhibit a certain initial relaxation in practical applications, rendering traditional calculation methods inapplicable. To accurately calculate the aeroelastic response of aircraft during the design process, fluid-structure interaction (FSI) calculations are the most effective approach.

[0004] Fluid-structure interaction (FSI) computational methods employ independent software or methods for each discipline, achieving interdisciplinary coupling through data transmission and iterative iteration. This process typically involves using fluid dynamics to calculate aerodynamic forces, then interpolating these forces onto the structure using interpolation algorithms for deformation calculations. This process is repeated iteratively to obtain the computational results.

[0005] However, while this calculation method yields high-precision results, it also places high demands on computing power. Both CFD calculation and interpolation calculation require a large number of matrix solutions, and it usually takes a long time to calculate a single working condition, often several weeks. Obviously, this cannot meet the needs of rapid iterative calculation in the design phase.

[0006] While traditional flutter calculation methods, such as the Vg method and PK method, are efficient, they can only solve the structural dynamics equations in the frequency domain to obtain the flutter divergence velocity and flutter frequency of the aircraft. They cannot accurately obtain the time-domain response of the aircraft's elastic deformation, resulting in lower accuracy compared to fluid-structure interaction methods. Furthermore, these methods have poor applicability to objects with special configurations and complex nonlinear factors, leading to larger calculation errors.

[0007] Therefore, there is an urgent need for a fluid-structure interaction calculation method that balances efficiency and computational accuracy for aeroelastic calculations of aircraft during the design phase. Summary of the Invention

[0008] To address the simulation requirements of aircraft design, and to solve the problems of traditional fluid-structure interaction (FSI) algorithms being unable to effectively simulate the large deformations of relaxed thin-film structures under stress, being computationally expensive and unable to perform large-scale calculations, and traditional flutter algorithms being limited to the frequency domain, this invention proposes a FSI calculation method for membrane structures that considers initial relaxation. This method can efficiently calculate the time-domain response of aircraft, quickly solve for the flutter velocity and aeroelastic response, and can be widely applied in the aircraft design phase.

[0009] The specific steps of the fluid-structure interaction calculation method for membrane structures considering initial relaxation are as follows:

[0010] Step 1: For the wings and missile wings under supersonic speeds, simplify them into rectangular models with initial relaxation, and divide the structural mesh and set the calculation parameters;

[0011] The specific process is as follows:

[0012] First, considering the initial relaxation, we replace the traditional flat rectangle model with a curved rectangle model.

[0013] Then, initial relaxation is applied to the film in a semi-sine or sinusoidal shape, i.e., in the form of a curve z = m*sin(nπx). The relaxation degree is defined as:

[0014]

[0015] Among them, l s It is the curve length of the model with the relaxation film on the XZ plane; l ori It is the curve length of the model with a flat film on the XZ plane.

[0016] After establishing the thin film structure model, a quadrilateral structure mesh was divided according to a fixed size, and the mesh element type was selected as S4R.

[0017] The calculation parameters include: Mach number Ma, dynamic pressure q, air density ρ, and angle of attack α, etc.

[0018] Step 2: Read the current grid node coordinates and grid node velocities. The aerodynamic grid adopts a structured grid, and the pressure corresponding to each surface element is calculated through piston theory.

[0019] The formula for calculating pressure is as follows:

[0020]

[0021] 'a' represents the speed of sound. γ is the specific heat ratio; H(x,y) is the thickness function measured from the centerline of the airfoil, with the direction of the upper (lower) wash taken as the direction away from the airfoil; V is the flight speed, and z(x,y,t) is the vibration displacement at the current position.

[0022] Step 3: Apply the pressure value to the corresponding structural surface element mesh, write the nodal aerodynamic forces into the Abaqus .inp file, enable geometric nonlinearity settings, call the structural solver to calculate the structural deformation, and obtain the new position, velocity and force value of each node.

[0023] Solving the structural dynamics equations using Newton's iterative algorithm:

[0024]

[0025] M is the mass matrix, C is the damping matrix, K is the current stiffness matrix of the model, and F is the normal force of the mesh, which is obtained by multiplying the pressure of each mesh element by its area.

[0026] Step 4: Output the new position, velocity, and structural force values ​​of each node to a .dat file, and read the generated new displacement and velocity files of the nodes.

[0027] Step 5: Return the new node displacements and nodal velocities to Step 2 and use piston theory again to solve for the pressure corresponding to the mesh elements. Write the results into a new .inp file, call the ABAQUS restart function, continue the calculation, and output the node calculation results to the .dat file. Iterate until all time steps are completed.

[0028] Step 6: Summarize the results of each time step to obtain the structural time-domain deformation response, and summarize and analyze the calculation results such as flutter velocity and maximum deformation to ensure that the design specifications are met.

[0029] After the calculation is completed, the calculation results of each time step are summarized according to the requirements, and the curves of deformation, velocity and other parameters of monitoring points at different locations as a function of time, flutter velocity and internal stress of the thin film structure at each moment can be obtained.

[0030] The advantages of this invention are:

[0031] This invention provides a fluid-structure interaction calculation method for membrane structures that takes initial relaxation into account. The entire calculation process is constructed for membrane structures with relaxation, and the aerodynamic calculation and structural calculation use the same mesh, avoiding the interpolation process. The aerodynamic force also adopts piston theory, which greatly improves the calculation efficiency. Attached Figure Description

[0032] Figure 1 This is a flowchart of a fluid-structure interaction calculation method for membrane structures considering initial relaxation, according to the present invention.

[0033] Figure 2Comparison of thin film modeling using different methods in this invention: (a) Traditional flat thin film modeling; (b) Half-sine relaxed thin film modeling; (c) Sine relaxed thin film modeling;

[0034] Figure 3 This is a schematic diagram illustrating the principle of fluid-structure interaction simulation calculation based on piston theory with an initially relaxed thin film, according to the present invention.

[0035] Figure 4 This invention provides a comparison of XZ plane deformation results under different modeling methods.

[0036] Figure 5 This invention provides a comparison of XZ plane deformation results under different relaxation degrees. Detailed Implementation

[0037] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail and in depth below with reference to the accompanying drawings.

[0038] To address the limitations of commonly used engineering algorithms for membrane structures, which suffer from limited accuracy and time-consuming fluid-structure interaction (FSI) calculations, this invention proposes a FSI calculation method for membrane structures considering initial relaxation. First, a simplified structural model with initial relaxation is drawn based on the actual situation, and the structural mesh is generated and calculation parameters are set. Then, an external program reads the coordinates and velocities of the current mesh nodes. The aerodynamic mesh adopts the structural mesh, and efficient FSI calculations for supersonic membrane structures are based on piston theory, enabling rapid calculation of the aeroelastic response of the aircraft at different velocities. Aerodynamic forces are solved using piston theory, avoiding the step of aerodynamic force and displacement interpolation. Finally, the nodal aerodynamic forces are written into an Abaqus .inp calculation file, geometric nonlinearity is enabled, and the solver is called for calculation. The nodal positions and velocities are read from the results, and the structural deformation is obtained by summing the results from different time steps. FSI calculations are achieved through loosely coupled iteration.

[0039] like Figure 1 As shown, the specific steps are as follows:

[0040] Step 1: For the wings and missile wings under supersonic speeds, simplify them into rectangular models with initial relaxation, and divide the structural mesh and set the calculation parameters;

[0041] In real life, due to factors such as gravity and processing and assembly precision, the film cannot be taut at all times and has a certain degree of slack. This results in the film deforming under stress much more than under ideal taut conditions, leading to distorted simulation results.

[0042] Since the shapes of wings and missile wings under supersonic conditions are relatively fixed, they can generally be simplified to rectangular or triangular models. Here, we take a rectangular model as an example, establishing a rectangular film with a length of 0.4m in the X direction (incoming flow direction) and a length of 0.6m in the Y direction.

[0043] Due to the inherent inability of the thin film to resist bending, it will bend and deform downwards under gravity after being laid out, resulting in initial relaxation. This relaxation will lead to greater deformation of the structure under stress. The impact of this phenomenon on flight is difficult to consider in traditional engineering algorithms, so it is necessary to establish the initial relaxation of the thin film structure during modeling.

[0044] This invention, considering initial relaxation, replaces the traditional flat rectangular model with a curved rectangular model; that is, the XZ direction is no longer a straight line but a curve. To ensure the universality of applying relaxation amounts across different models, applying the relaxation amount in the form of a curve, z = m*sin(nπx), allows for better simulation of actual deformation in calculations. On this rectangular thin film, as... Figure 2 As shown, schematic diagrams of traditional flat thin film modeling, half-sine thin film modeling, and sinusoidal thin film modeling are presented. The same relaxation amount is applied in half-sine and sinusoidal forms respectively, and the calculation results are compared to prove that the relaxation application form has no effect on the calculation results.

[0045] for Figure 2 (b) Thin film model, XZ plane shape is

[0046] z = 0.04 sin(2.5πx) (1)

[0047] for Figure 2 (c) Thin film model, XZ plane shape is

[0048] z = -0.02*sin(5πx) (2)

[0049] Integral calculations show that both curves are 0.41m long and have the same 2.5% relaxation in the X direction.

[0050] Relaxation is defined as

[0051]

[0052] Among them, l s It is the curve length of the relaxed thin film model on the XZ plane; l ori It is the curve length of the flat thin film model on the XZ plane.

[0053] After establishing the thin film structure model, a quadrilateral mesh with dimensions of 0.02m x 0.02m was created, using S4R mesh elements. The material properties were set to 1mm thickness and 1300kg / m³ density.3 Young's modulus 2.4e 10 Pa.

[0054] The calculation parameters include: Mach number Ma, dynamic pressure q, air density ρ, and angle of attack α, etc.

[0055] Step 2: Use an external program to read the current grid node coordinates and grid node velocities. The aerodynamic grid adopts a structured grid, and the pressure corresponding to each surface element is calculated through piston theory.

[0056] First, based on the given operating parameters, the relevant atmospheric parameters, such as temperature, density, and speed of sound, are retrieved. In this embodiment, Ma = 5, the angle of attack α is 8°, and the air density ρ is 0.068 kg / m³.

[0057] The program then directly reads the coordinate and velocity information of the structural nodes from the finite element model. Since the aerodynamic mesh is also calculated using a structural mesh, the velocity and displacement information of the structural nodes can be used to calculate pressure in piston theory. Substituting this information into the piston theory calculation formula, as follows:

[0058]

[0059] 'a' represents the speed of sound. γ is the specific heat ratio; H(x,y) is the thickness function measured from the centerline of the airfoil, with the direction of the upper (lower) wash taken as the direction away from the airfoil; V is the flight speed, and z(x,y,t) is the vibration displacement at the current position.

[0060] Step 3: Apply the pressure value to the corresponding structural surface element mesh, write the nodal aerodynamic forces into the Abaqus .inp file, enable geometric nonlinearity settings, call the structural solver to calculate the structural deformation, and obtain the new position, velocity and force value of each node.

[0061] First, the solved pressure value is applied to the corresponding structural surface element mesh through the main program;

[0062] Then, depending on the solution requirements, select either an implicit dynamics solver or a general statics solver, and integrate the model's boundary conditions, geometric nonlinearities, etc., into the Abaqus input file.

[0063] Finally, the structural dynamics solution was solved by calling Abaqus restart using a Windows batch processing method;

[0064] The solver first multiplies the pressure corresponding to each mesh element by its area to obtain the normal force F of the mesh. Then, it obtains the current stiffness matrix K, damping matrix C, and mass matrix M of the model, and solves the structural dynamics equations using the Newton-Raphson iterative algorithm.

[0065]

[0066] Step 4: Output the new position, velocity, and structural force values ​​of each node to a .dat file, and read the generated new displacement and velocity files of the nodes for use in the next interpolation call;

[0067] Step 5: Return the new node displacements and nodal velocities to Step 2 and use piston theory again to solve for the pressure corresponding to the mesh elements. Write the results into a new .inp file, call the ABAQUS restart function to perform a loop calculation, continue the calculation, and output the node calculation results to the .dat file. Iterate until all time steps are completed.

[0068] Step 6: Summarize the results of each time step to obtain the structural time-domain deformation response, and summarize and analyze the calculation results such as flutter velocity and maximum deformation to ensure that the design specifications are met.

[0069] After the calculation is completed, the calculation results of each time step are summarized according to the requirements, and the curves of deformation, velocity and other parameters of monitoring points at different locations as a function of time, flutter velocity and internal stress of the thin film structure at each moment can be obtained.

[0070] Traditional fluid-structure interaction (FSI) calculations are time-consuming, hindering large-scale engineering applications. Furthermore, given the supersonic flight conditions, this method aims to improve FSI efficiency by first employing piston theory to calculate the aerodynamic forces acting on the aircraft. This method requires significantly less computation compared to CFD and other similar methods. Secondly, it ignores the aerodynamic and structural interpolation processes, using a single mesh for both fluid and solid components to avoid data transmission delays, thus greatly reducing computation time. The entire calculation process begins by solving for the aerodynamic forces using piston theory, applying this solution to the structural solver, and then using the structural solver to solve the structural dynamics equations, completing one time step of the FSI calculation. The calculation is then iteratively completed to obtain the aeroelastic dynamic response of the aircraft during flight.

[0071] The procedure is as follows: Figure 3 As shown, after establishing the structural mesh, the aerodynamic calculation mesh also adopts the structural mesh to avoid the interpolation process and improve computational efficiency. Then, through secondary development of Abaqus, the displacement and velocity of each node on the structure are read, converted into coordinates and velocities at the control points, and substituted into piston theory to solve for aerodynamic forces. The pressure at each mesh can then be obtained and applied to the structure for dynamic solution, thus performing structural dynamics solution.

[0072] This invention uses the same mesh for both aerodynamic and structural calculations, avoiding interpolation processes. Aerodynamic forces also employ piston theory, significantly improving computational efficiency. Because the computational model's characteristics resemble a thin-film structure, structural modeling needs to reflect the properties of the thin-film material. However, using membrane materials in finite element calculations presents challenges such as convergence difficulties and inconvenient setup. Therefore, common plate and shell materials are considered as alternatives to membrane materials, although their properties differ. Membrane elements lack bending stiffness under no external force or deformation and cannot withstand bending deformation. According to the bending theory of rectangular thin plates, the bending stiffness of a thin plate is cubically related to its thickness. Therefore, by reducing the thickness and increasing the Young's modulus, plate and shell elements can maintain constant tensile and compressive stiffness while significantly reducing bending stiffness, effectively simulating the properties of a thin film. Simultaneously, the density increases accordingly, ensuring consistent structural mass.

[0073] Piston theory is a reasonably simplified method for solving supersonic aerodynamic forces. When the Ryle Mach number is much greater than 1, the disturbance generated by the airfoil can be assumed to propagate along the normal direction of the object, neglecting the mutual influence between points. Piston theory is computationally simple, and compared with most fluid-structure interaction methods that use CFD to calculate aerodynamic forces, it can reduce the calculation time by more than an order of magnitude while maintaining a certain level of calculation accuracy.

[0074] Example:

[0075] by Figure 2 The rectangular thin film shown is the subject of this study. Figure 3 The fluid-structure interaction (FSI) analysis calculation flow is shown. This example verifies the effectiveness of the method. Based on piston theory, this invention constructs a FSI calculation framework with Abaqus, enabling rapid calculation of aeroelastic static / dynamic responses as needed. For example... Figure 4 As shown, a comparison of calculation results for a flat thin film and a model with 2.5% relaxation is presented, demonstrating that the relaxed model exhibits greater Z-axis deformation and a significant rightward shift in the deformation peak, better reflecting actual conditions. Furthermore, a comparison of results from two relaxation application methods—a sinusoidal thin film model and a half-sinusoidal model—shows that the relaxation application method has almost no impact on the calculation results. Figure 5 As shown, the calculation results are given under different relaxation degrees. It can be seen that the greater the relaxation degree, the greater the deformation amplitude, and the deformation peak gradually shifts to the right.

[0076] This invention uses a plate shell to effectively simulate the thin film structure, and adds initial relaxation to make the calculation results more consistent with the actual situation. It solves the problem that engineering algorithms cannot effectively solve thin film objects, and balances the solution efficiency and solution accuracy, which has certain practical engineering significance.

Claims

1. A computational method for fluid-structure interaction of membrane structures considering initial relaxation, characterized in that, The specific steps are as follows: Step 1: For the wings and missile wings under supersonic speeds, simplify them into rectangular models with initial relaxation, and divide the structural mesh and set the calculation parameters; The specific process is as follows: First, considering the initial relaxation, we replace the traditional flat rectangle model with a curved rectangle model. Then, initial relaxation is applied to the film in a half-sine or sinusoidal shape, i.e., with... The curve form, relaxation is defined as: in, It is the curve length of the model with the relaxation film on the XZ plane; It is the curve length of the model with a flat film on the XZ plane; Step 2: Read the current grid node coordinates and grid node velocities. The aerodynamic grid adopts a structured grid, and the pressure corresponding to each surface element is calculated through piston theory. The formula for calculating pressure is as follows: air density, For the speed of sound, , For specific heat ratio, It is the Mach number; It is a thickness function measured from the centerline of the airfoil; For flight speed, This represents the vibration displacement at the current position. Step 3: Apply the pressure value to the corresponding structural surface element mesh, write the nodal aerodynamic forces into the Abaqus .inp file, enable geometric nonlinearity settings, call the structural solver to calculate the structural deformation, and obtain the new position, velocity and force value of each node. Step 4: Output the new position, velocity, and structural force values ​​of each node to a .dat file, and read the generated new displacement and velocity files of the nodes. Step 5: Return the new displacement and velocity of the nodes to Step 2 and use the piston theory to solve for the pressure corresponding to the mesh elements again. Write the solution into a new .inp file, call the ABAQUS restart function, continue the calculation, and output the node calculation results to the .dat file. Iterate until all time steps are completed. Step 6: Summarize the results of each time step to obtain the structural time-domain deformation response, summarize and analyze the flutter velocity and the maximum deformation calculation results to ensure that the design specifications are met.

2. The fluid-structure interaction calculation method for membrane structures considering initial relaxation as described in claim 1, characterized in that, In step one, after establishing the thin film structure model, a quadrilateral structure mesh is divided according to a fixed size, and the mesh cell type is S4R. The calculation parameters include: dynamic pressure and angle of attack .

3. The fluid-structure interaction calculation method for membrane structures considering initial relaxation as described in claim 1, characterized in that, In step three, the structural dynamics equations are solved using the Newton-Raphson iterative algorithm: For the quality matrix, For damping array, The current stiffness matrix of the model, The force is normal to the grid and is obtained by multiplying the pressure of each grid element by its area.

4. The fluid-structure interaction calculation method for membrane structures considering initial relaxation as described in claim 1, characterized in that, In step six, after the calculation is completed, the calculation results of each time step are summarized according to the requirements to obtain the deformation and velocity parameters of monitoring points at different locations as a function of time, the flutter velocity, and the internal stress of the thin film structure at each moment.

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