Elastic frame optimization design method and system based on finite element theory

Abstract

The invention relates to the technical field of data processing, in particular to an elastic frame optimization design method and system based on the finite element theory, and the method comprises the steps: constructing a nonlinear finite element model of an elastic frame, and for each node, determining the sealing reliability of the node based on the normal contact stress value, fluid pressure value and displacement vector of the node; for each unit, determining a fluid permeation trend factor of the unit based on the sealing reliability of the nodes in the unit, remodeling a material relative density iterative updating formula of the optimization criterion method by using the fluid permeation trend factor, updating the material relative density of each unit, generating an optimal topological configuration, and carrying out the optimal topological configuration; therefore, the optimal design of the elastic frame is completed. According to the method, the problem of high-pressure leakage caused by neglecting microscopic sealing in traditional topological optimization is solved, and synchronous optimization of the structural rigidity and the sealing performance under the ultrahigh-pressure working condition is achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of data processing. Specifically, it relates to an elastic frame optimization design method and system based on finite element theory. BACKGROUND

[0002] In the field of environmental protection solid waste treatment and chemical separation, the super-high pressure filter press is the key equipment to realize deep dewatering of materials and reduce volume. In the filter press, the elastic frame plays a crucial role in preventing high-pressure slurry leakage. The design quality of the elastic frame directly determines the safety and environmental performance of the equipment.

[0003] Currently, for the structural design of such elastic elements, the industry usually relies on the variable density topology optimization method based on the finite element theory, such as the SIMP (Solid Isotropic Material with Penalization) method. The typical process is: dividing the design domain into countless small finite element units, and iteratively updating the relative density of each unit by traditional optimization criterion method (OC method) or moving asymptote method.

[0004] The traditional optimization criterion method follows the minimum compliance criterion. Its core numerical mechanism is to calculate the strain energy density of each unit in the design domain to construct the objective function, which represents the contribution rate of the unit to the overall structural stiffness. In the iteration process, if the strain energy density of a unit is high, it means that it contributes a lot to resisting deformation and has high stiffness, and the relative density tends to 1. Conversely, the relative density tends to 0, and the algorithm will identify the unit with high strain energy density as a high-efficiency bearing material and retain it, and identify the unit with low strain energy density as a low-efficiency material and reduce its relative density until it is removed. This method has advantages in achieving lightweight and maximizing the bearing stiffness of the structure.

[0005] However, when the traditional optimization criterion method is applied to super-high pressure sealing design, under the super-high pressure sealing working condition, the key to blocking fluid leakage lies in the fluid pressure penetration resistance ability of the micro area of the contact interface. This ability often depends on small local bosses or lip structures to achieve. Physically, these micro sealing features at the front of the fluid pressure penetration have low deformation energy and correspondingly low strain energy density. Therefore, the traditional optimization criterion method is prone to identify these key anti-fluid penetration structures as low-efficiency bearing units and remove them in the iteration and updating process. This functional structure removal caused by the lack of physical dimensions of the optimization criterion makes the optimized frame meet the overall stiffness requirement, but lacks anti-penetration structures at the sealing interface, forming a leakage channel, leading to unreliable sealing, easy high-pressure leakage, and affecting safety.

[0006] Therefore, there is an urgent need for an optimization design method that can quantify the fluid pressure penetration risk and correct the material relative density iterative update model, thereby ensuring the convergence of the objective function while retaining low strain energy sensitivity but high sealing value units. SUMMARY

[0007] To solve the problem that the traditional optimization criterion method is easy to delete key sealing features in sealing structure design, leading to leakage, the application provides an elastic frame optimization design method and system based on finite element theory.

[0008] In a first aspect, the elastic frame optimization design method based on finite element theory comprises: A nonlinear finite element model of the elastic frame is constructed, the elastic frame is discretized into a plurality of units composed of a plurality of nodes, and the displacement vector, normal contact stress value and fluid pressure value of each node are obtained; For each node, the effective sealing stress ratio of the node is calculated based on the normal contact stress value and the fluid pressure value, the tangential slip stability coefficient of the node is determined based on the normal contact stress value and the displacement vector of the node, and the sealing reliability of the node is determined by correcting the effective sealing stress ratio using the tangential slip stability coefficient; For each unit, the fluid pressure gradient of the unit is calculated based on the fluid pressure values of the nodes in the unit, the volume strain of the unit is calculated based on the displacement vectors of the nodes in the unit, and the fluid permeation trend factor of the unit is determined in combination with the fluid pressure gradient and the volume strain and the sealing reliability of the nodes in the unit. The material relative density iterative update formula of the optimization criterion method is reshaped based on the fluid permeation trend factor of each unit, the material relative density of each unit is updated based on the reshaped material relative density iterative update formula, and the optimization design of the elastic frame is completed until the optimal topology configuration is generated.

[0009] The technical scheme constructs a set of physical evaluation and intervention mechanism specially for sealing performance. Firstly, by constructing a nonlinear finite element model and obtaining displacement, contact stress and fluid pressure, the digital mapping of the physical state of the elastic frame under real high pressure working conditions is realized. Then, the sealing reliability of the micro node index is introduced. It not only looks at whether the contact pressure is greater than the fluid pressure, but also further introduces the tangential slip stability coefficient for correction. This is based on the deep insight into the physical scene: even if the contact pressure is large enough, if the contact point has a large tangential slip, the sealing interface will become unstable and cause leakage. Then, the scheme rises from the micro node to the mesoscopic unit, calculates the fluid penetration tendency factor, which combines the pressure gradient (reflecting the strength of the fluid driving force) and the volume strain (reflecting whether the material is loose and swollen), and combines the sealing reliability of the node to accurately identify those units which are in the key path of fluid breakthrough although the stiffness contribution is small. Finally, by remodeling the relative density iterative update formula, the fluid penetration tendency factor is directly intervened in the optimization process to force to retain those material units that are crucial to sealing. This design increases the sealing reliability of the elastic frame.

[0010] Preferably, the effective sealing stress ratio of the node is determined based on the following way: calculating the square difference and the square sum of the normal contact stress value and the fluid pressure value of each node, non-negative truncating the ratio of the square difference and the square sum and square root to obtain a value between 0 and 1 as the effective sealing stress ratio of the node.

[0011] The technical scheme defines the effective sealing stress ratio by constructing the ratio model of the square difference and the square sum. Physically, the normal contact stress must be greater than the fluid pressure to form a seal. This calculation method amplifies the sensitivity of the difference between the two by squaring operation, and through non-negative truncation processing, it clearly defines the boundary between effective sealing and failure. The square root operation normalizes the value to the linear perception interval. This processing method can sensitively capture the nodes on the contact interface that are in a critical sealing state, providing accurate benchmark data for subsequent stability correction.

[0012] Preferably, the tangential slip stability coefficient of the node is determined based on the following way: calculating the tangential slip distance according to the displacement vector of each node, calculating the product of the normal contact stress value and the tangential slip distance of the node as the slip energy dissipation; dimensionless processing the slip energy dissipation, and using the hyperbolic tangent function to map it into an attenuation coefficient, and subtracting the attenuation coefficient from 1 to obtain the tangential slip stability coefficient of the node.

[0013] The technical solution evaluates tangential instability by calculating slip energy dissipation. High-pressure seals often fail due to fretting wear or large deformation slip. The product of the normal contact stress and the tangential slip distance essentially represents the size of the interface friction work, i.e. the energy size of the seal adhesion state destruction. The hyperbolic tangent function is introduced as a mapping tool, which utilizes its S-shaped curve characteristics to smoothly map the energy dissipation value to When the slip energy dissipation is large, the attenuation coefficient approaches 1, resulting in a stability coefficient approaching 0, and vice versa. This nonlinear mapping mechanism conforms to the threshold effect in physics, i.e. small slip can be tolerated, but once a certain energy threshold is exceeded, the seal stability will decrease sharply.

[0014] Preferably, the tangential slip stability coefficient is used to correct the effective seal stress ratio to determine the seal reliability of the node, which is carried out by the following relationship: the tangential slip stability coefficient of each node and the effective seal stress ratio of the node are multiplied to correct the multiplication value as the seal reliability of the node.

[0015] This technical solution adopts a multiplication correction strategy, which embodies the bucket effect in the sealing system. The seal reliability, as the final evaluation index, must meet both the conditions of tight normal pressure (high effective seal stress ratio) and stable tangential direction (high tangential slip stability coefficient), avoiding the one-sidedness of a single dimension, thereby ensuring the accuracy of the evaluation results.

[0016] Preferably, the fluid permeation trend factor of the unit is determined based on the following relationship:

[0017] wherein, is the fluid permeation trend factor of the i th unit, is the average value of the seal reliability of all nodes in the i th unit, is the fluid pressure gradient of the i th unit, is the modulus length symbol, is the average value of the modulus length of the fluid pressure gradient of all units, is a preset parameter to prevent the denominator from being 0, is the volumetric strain of the i th unit, is a preset volumetric strain threshold value for dimensionless normalization of the volumetric strain, representing the volumetric expansion limit leading to seal failure, is a natural exponential function, is a natural exponential function, is a natural exponential function, is a natural exponential function, is a natural exponential function, Macaulay's bracket, taking the value inside the bracket when it is greater than 0, and 0 otherwise.

[0018] The technical solution constructs a risk and demand evaluation model of multi-physical field coupling. The first term represents the sealing defect degree. The more unreliable the current sealing is, the larger the term is, and the higher the optimization urgency is. In the second term, the natural exponential function internally fuses the pressure gradient term and the volume strain term. The larger the pressure gradient is, the more intense the fluid pressure change of the unit is. The larger the volume strain is, the more likely the unit is to expand and produce microscopic gaps. The attenuation characteristics of the exponential function are used to convert these risk factors into a weight approaching 1. By multiplying the sealing defect degree and the environmental risk degree, those units in the high-risk area and with substandard sealing performance are accurately locked, and accurate navigation is provided for subsequent forced increase of material density.

[0019] Preferably, the fluid pressure gradient of the unit is determined based on the following manner: a continuous pressure field inside the unit is constructed based on the fluid pressure values of the nodes in the unit by using the finite element shape function, the continuous pressure field is spatially differentiated to obtain a pressure gradient vector representing the rate of pressure change, and the module length of the pressure gradient vector is calculated as the fluid pressure gradient of the unit.

[0020] Preferably, the volume strain of the unit is determined based on the following manner: the displacement vectors of all nodes in each unit are spatially differentiated by using the finite element shape function to obtain a strain tensor, and the trace of the strain tensor is calculated as the volume strain of the unit.

[0021] Preferably, the material relative density iterative update formula of the optimization criterion method is reshaped based on the fluid permeation trend factor of each unit, including:

[0022] wherein, and are the material relative densities of the i-th unit after updating and before updating, respectively, is the mechanical optimization objective term of the unit, is determined based on the optimization criterion method and is used to represent the contribution efficiency of the unit to the overall stiffness of the structure, is a preset damping coefficient, is the fluid permeation trend factor of the i-th unit, used to adjust the influence weight of the fluid permeation trend factor on the material relative density.

[0023] ​​This technical solution introduces a multiplication factor. When the fluid permeation tendency factor is large, that is, when the unit has a leakage risk and is in a critical position, the factor will be significantly greater than 1, thereby producing a forced gain effect on the material density. This means that even if the stiffness contribution of the unit is very small and would originally be deleted by the algorithm, as long as it is important to the seal, the algorithm will be forced to retain or even increase the density of the unit, thus achieving accurate retention of small units that are important to the seal.

[0024] Preferably, the material relative density of each unit is updated based on the iterative update formula of the reshaped material relative density until the optimal topology is generated. This includes: in each iteration, the updated material relative density of each unit is calculated using the iterative update formula of the reshaped material relative density until the change in the updated material relative density of all units between two adjacent iterations is less than the preset convergence tolerance, the iteration ends, and the material relative density of all units at the end of the iteration is taken as the optimal topology of the elastic bounding box.

[0025] Secondly, a flexible border optimization design system based on finite element theory, the flexible border optimization design system including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the flexible border optimization design method as described in any one of the claims.

[0026] The present invention has the following effects: This invention quantifies sealing reliability at the node microscopic level by constructing a nonlinear finite element model incorporating displacement, contact stress, and fluid pressure. It then combines the pressure gradient and volumetric strain at the element mesoscopic level to generate a fluid permeation tendency factor, ultimately reshaping the iterative update formula of the optimization criterion method. This method breaks through the limitations of traditional topology optimization, which focuses solely on stiffness. It accurately identifies and forcibly retains microstructures with low strain energy but crucial for preventing leakage, while ensuring the overall load-bearing capacity of the elastic frame. This results in an elastic frame that possesses sufficient structural strength and forms a stable and reliable adaptive sealing interface under ultra-high pressure conditions, effectively solving the common frame leakage problem in high-pressure filter presses and other equipment, and improving equipment safety. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the method flow of the present invention; Figure 2a This is a schematic diagram of the strain energy density distribution of the elastic frame micro-sealing unit of the present invention; Figure 2b This is a schematic diagram of the fluid permeation tendency factor distribution of the elastic frame micro-sealing unit of the present invention; Figure 3a This is a schematic diagram of the overall macroscopic topological configuration and inner edge sealing integrity of the existing flexible frame; Figure 3b This is a schematic diagram of the overall macroscopic topological configuration of the elastic frame and the inner edge sealing integrity of the present invention. Detailed Implementation

[0028] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0029] refer to Figure 1 This invention provides an optimization design method for elastic borders based on finite element theory, including: S1: Construct a nonlinear finite element model of the elastic frame to obtain the displacement vector, normal contact stress value and fluid pressure value of each node.

[0030] High-pressure filter presses typically operate at pressures as high as 8 MPa or even higher. In practical applications, the elastic frame involves large deformations of hyperelastic materials like rubber, nonlinear contact with rigid filter plates and diaphragms, and fluid-structure interaction with the high-pressure slurry. Simple linear analysis cannot accurately reflect its physical response. This step aims to precisely capture the microscopic behavior of the structure under load through nonlinear finite element analysis. The purpose is to provide accurate raw data for subsequent sealing performance evaluation, including the spatial position changes of each node, the stress state at the contact interface, and the distribution of fluid pressure.

[0031] Specifically, the initial geometric model of the elastic frame is first constructed using CAD software and then imported into finite element analysis software (such as ABAQUS or ANSYS). Since the elastic frame is usually made of rubber, the material properties of the elastic frame are defined using a hyperelastic constitutive model (such as the Mooney-Rivlin model or Yeoh model) to accurately characterize its nonlinear stress-strain relationship under compression.

[0032] Next, the contact surface between the rigid filter plate and the elastic frame is defined, and boundary conditions and fluid pressure loads under actual working conditions are applied to simulate the real fluid wedging process. The elastic frame is discretized into multiple elements composed of multiple nodes. Quadrilateral or hexahedral hybrid elements suitable for large deformation analysis are preferably used. The solution is submitted to the solver for nonlinear solution, and the displacement vector, normal contact stress value, and fluid pressure value of each node are calculated and obtained. Among them, the displacement vector of each node is obtained based on the finite element equilibrium equation, representing the change of spatial coordinates of the node relative to the initial position after deformation. The normal contact stress value of each node is extracted based on the contact algorithm (such as the penalty function method or the Lagrange multiplier method), characterizing the compressive stress on the node in the normal direction of the contact interface. The fluid pressure value of each node is determined based on the application of fluid load boundary conditions and the fluid penetration algorithm, characterizing the static pressure of the fluid acting on the node.

[0033] S2: Calculate the effective sealing stress ratio and tangential slip stability coefficient for each node, and use the tangential slip stability coefficient to correct the effective sealing stress ratio to obtain the sealing reliability of the node.

[0034] After obtaining the basic physical data for each node, considering that for the elastic frame of the filter press, simply having a contact pressure greater than the fluid pressure is insufficient to guarantee a long-term seal, and that severe tangential slippage at the contact surface can lead to wear or dynamic peeling of the sealing lip, resulting in leakage, this step analyzes the normal compression degree and tangential stability to accurately assess the sealing status of individual nodes.

[0035] Specifically, the process includes the following: S21: Calculate the effective sealing stress ratio based on the normal contact stress value and the fluid pressure value.

[0036] For the elastic frame of the filter press, it mainly resists the pressure of the slurry by the rebound force generated by the compression of the filter plate. Considering that the essence of sealing is that the reaction force on the contact interface must be able to resist the intrusion pressure of the fluid, simply comparing the numerical values ​​cannot provide a normalized evaluation standard, and it is difficult to measure the risk of critical failure due to pressure fluctuations.

[0037] Therefore, this step aims to construct a dimensionless effective sealing stress ratio. Through the mathematical construction of the difference of squares and the sum of squares, it precisely quantifies the safety margin of the current contact state relative to the fluid pressure. Specifically, for the first... The effective sealing stress ratio for each node is determined based on the following relationship:

[0038] In this relation, For the first The effective sealing stress ratio of each node It is the first The normal contact stress value of each node describes the stress value generated by the contact between the elastic frame and the external mating components (i.e., the rigid boundary where the elastic frame is installed, such as the housing, slot, flange face, or sealing cover) on the elastic frame. The rebound force generated when the rubber is squeezed is responsible for sealing the gap. This is the fluid pressure value at that node, representing the magnitude of the fluid pressure that the elastic frame must be able to withstand. To find the maximum value function, This is a preset parameter used to prevent the denominator from being zero, and is usually set to a very small positive number. .

[0039] This relationship conforms to the fluid pressure permeation criterion in physics, and the basic principle of sealing is contact stress. It must be greater than the fluid pressure ,when The rubber is compressed tightly enough to prevent fluid from entering, thus ensuring an effective seal; when The fluid pressure was too high, which caused the contact surface to break open, resulting in a leak.

[0040] It is evident that the effective sealing stress ratio utilizes the square operation to amplify the nonlinear characteristics of the difference between the two, thus amplifying the difference in critical states. Slightly larger At this point, the ratio will rise rapidly, which aligns with engineering intuition: near the critical point, even a small increase in safety margin can lead to a significant qualitative change in reliability.

[0041] when When this occurs, it indicates that the node is located in the sealed core area of ​​the elastic border. At this point, the numerator approaches the denominator, the ratio approaches 1, and the square root is then calculated. This indicates that the sealing effect of the node is excellent; when When this occurs, it indicates that the node is in the critical sealing zone of the elastic frame or at the edge where pressure penetration is about to occur. At this time, the molecules approach 0, and the ratio drops sharply. This indicates that the node has an extremely high risk of leakage. This design makes the effective sealing stress ratio highly sensitive at the leakage critical point, enabling precise detection of even minor sealing hazards. The denominator uses a sum of squares, strictly limiting the entire fraction's range to [0, 1). Regardless of whether the pressure is 1 MPa or 100 MPa, the evaluation standard is consistent, solving the problem of dimensional uniformity under multiple operating conditions. The max function implements a non-negative truncation operation, mathematically forcing the leakage state to zero. Since failure is equivalent to zero for sealing reliability, negative values ​​are not needed to represent the degree of failure.

[0042] S22: Determine the tangential slip stability coefficient of the node based on the normal contact stress value and the displacement vector of the node.

[0043] After determining the normal clamping degree of the elastic frame, it is considered that high-pressure sealing depends not only on tightness but also on stability. If drastic relative slippage occurs at the contact point in the tangential direction, it can lead to wear, tearing, or the formation of dynamic leakage channels on the sealing surface. Therefore, this step aims to introduce a tangential slippage stability coefficient. By analyzing the energy dissipated during slippage, the anchoring capability of the node in the tangential direction can be assessed. This allows for the elimination of pseudo-safe nodes that, despite having high clamping force, are unstable in position, ensuring that the optimization direction is towards generating a sealing structure that is both tight and robust.

[0044] Specifically, for the first Each node, based on its displacement vector. Calculate the tangential slip distance of this node. And calculate the tangential slip stability coefficient according to the following relationship:

[0045] In this relation, It is the first The tangential slip stability coefficient of each node, This is a preset benchmark energy threshold used for dimensionless transformation. The specific setting is usually obtained based on tribological property tests of the material. It characterizes the critical energy density required for wear or adhesion failure per unit area. The elastic frame of the filter press is typically made of EPDM rubber with a Shore hardness of 65-75. Based on the frictional slip work characteristics of the rubber-metal interface, the energy required for macroscopic slip failure per unit area is obtained, based on experimental results. For 500 .

[0046] In this relation, This represents the dissipation of sliding energy, calculated by multiplying stress by the sliding distance. Physically, it represents work done or energy density. A large sliding distance alone does not necessarily lead to wear; it could be slight contact. Similarly, high pressure alone does not necessarily cause wear; it could be a static state. Only when sliding occurs under high pressure, generating strong frictional work, will it lead to heating, wear, or tearing of the sealing surface. Therefore, sliding energy dissipation is chosen as the indicator. Due to the properties of the function, when the slip energy dissipation is large, the node undergoes significant slippage under high pressure. If it approaches 1, then A value approaching 0 indicates extreme instability and a high likelihood of wear and leakage; when the sliding energy dissipation is extremely small, the node is within the range of static friction or fretting. Approaching 0, A value approaching 1 indicates high stability. This mapping aligns with the physical definition of stability, which states there exists a permissible range of small fluctuations; once this range is exceeded, stability rapidly declines. By introducing... This reflects the baseline energy threshold, which aligns with common sense in materials science: rubber materials have a destructive energy threshold; below this value, it is elastic micromotion, a safe state; above this value, it is macroscopic slip failure, a dangerous state.

[0047] S23: Determine the reliability of the seal.

[0048] After obtaining the evaluation metrics for the normal and tangential directions of a node, given that sealing failure follows the barrel effect (i.e., insufficient compression will lead to leakage, and excessive slippage will also cause failure), this step adopts a multiplicative coupling approach to fuse the two-dimensional metrics into a unique sealing reliability. This step essentially executes a rigorous AND gate logic, and a node is only judged as a reliable node when it simultaneously satisfies both the normal compression and tangential stability conditions.

[0049] Specifically, the following relationship is satisfied:

[0050] In this relation, It is the first The sealing reliability of each node, It is the first The effective sealing stress ratio of each node It is the first The tangential slip stability coefficient of each node. The larger the value, the tighter the normal force of the node. This indicates that the tangential direction of the node is very stable, only when both are close to 1. Only then will it approach 1. Through this operation, the nodes that truly contribute to the sealing are selected, providing accurate input for subsequent assessment of fluid permeation risk at the unit level.

[0051] S3: Calculate the fluid pressure gradient and volumetric strain of each element, and determine the fluid permeation tendency factor of the element by combining the sealing reliability of the nodes within the element.

[0052] After evaluating the micro-nodes, and considering that the optimized operation is an element, the fluid permeation behavior within or at the material boundary is influenced by both the fluid driving force (pressure gradient) and the pore channels (volume strain). Therefore, this step aims to construct a comprehensive fluid permeation tendency factor to identify key elements located in high pressure differential regions that are expanding and may lead to micro-gaps.

[0053] Specifically, the process includes the following: S31: Calculate the fluid pressure gradient of the cell based on the fluid pressure values ​​of the nodes within the cell.

[0054] For the A continuous pressure field is constructed within each element using finite element shape functions based on the fluid pressure values ​​at each node. Spatial differentiation of this continuous pressure field yields a pressure gradient vector characterizing the rate of pressure change. The magnitude of this pressure gradient vector is then calculated as the fluid pressure gradient of the element. , This reflects the strength of the driving force for the fluid to penetrate the sealing structure at this unit location. For elastic frames, high pressure gradients usually occur at the contact edge between the sealing lip and the rigid filter plate, where the fluid pressure drops sharply from 8 MPa to 0 MPa. The large gradient means that the fluid has a very strong extrusion effect and can easily break through the elastomer.

[0055] S32: Calculate the volumetric strain of the element based on the displacement vectors of the nodes within the element.

[0056] For the For each element, the displacement vectors of all nodes within that element are spatially differentiated using finite element shape functions to obtain the strain tensor. The trace of this strain tensor is then calculated as the volumetric strain of that element. This reflects the volume expansion or compression state of the elastic frame material. For nearly incompressible rubber materials, Poisson's ratio is close to 0.5. Positive volume strain means that the unit is in a triaxial tensile state, the molecular chain spacing increases, and microscopically, micropores that allow fluid to permeate or cavitation phenomena are easily formed, leading to sealing failure.

[0057] S33: Determine the fluid permeation tendency factor by combining the fluid pressure gradient, volumetric strain, and sealing reliability of the nodes within the unit.

[0058] Specifically, the fluid permeation tendency factor of the unit is determined by the following relationship:

[0059] In this relation: It is the first The fluid permeability tendency factor for each unit; the higher the value, the stronger the tendency for the unit to leak, and the more material is needed for filling. It is the average value of the sealing reliability of all nodes within this unit. This reflects the current sealing defect level of the unit. The higher the value, the lower the sealing reliability of the node to which the unit belongs, that is, the more likely it is to have inadequate normal compression or tangential slippage, and the more significant the internal cause of leakage. The lower the value, the better the sealing condition of the unit, and no excessive intervention is required. For the first The fluid pressure gradient of each unit means that a large fluid pressure gradient means strong fluid scouring force. Seal failure often occurs at the lip edge where the pressure difference changes drastically. Introducing the fluid pressure gradient accurately locates these high-risk areas. To determine the sign of the modulus, It is the first The modulus of the fluid pressure gradient in each unit. It is the average value of the modulus of the fluid pressure gradient across all units. This is a preset parameter to prevent the denominator from being zero; it is usually set to a very small positive number. , The larger the value, the more drastic the change in fluid pressure differential and the stronger the driving force for permeation. It is the first Volumetric strain of each element Macaulay brackets, only when This resulted in volumetric strain, and the value of this element was taken when gap extrusion and cavitation failure occurred under high pressure. When no volumetric strain occurs, the value is 0 and is not considered as a risk. The Macaulay brackets are introduced to calculate only volumetric expansion and ignore compression. This is because rubber seals under pressure are normal, but if there is volume expansion, it means that microscopic cavities have been created or the rubber has been stretched and torn, which is a precursor to leakage. This is the volumetric strain threshold, set as the critical volumetric strain value at which microcracks or cavities occur in the material. It is used to perform dimensionless normalization on the volumetric strain. The volume expansion limit that leads to seal failure is characterized by a triaxial tensile test on rubber material. Rubber is a hyperelastic material. When the volume strain reaches 5%, it means that microscopic voids or physical damage are likely to occur inside the material, reflecting the limit of seal failure. Therefore, it is set to 0.05.

[0060] In this relation, the first term This reflects the degree of internal sealing defects in the unit, which is an internal factor. If the sealing performance of a unit is already excellent, Then the first term approaches 0. A value close to 0 indicates that no additional intervention is needed. (Second item) An environmental risk assessment model was constructed to characterize the driving force of fluid penetration into the unit under the combined effects of fluid pressure and structural deformation, which is an external factor. This represents the dimensionless relative pressure gradient, reflecting the multiple of the fluid driving force relative to the overall average level. This represents the driving force for fluid to penetrate the sealed interface. Dividing by the average value is for normalization, while squaring is to amplify the weight of the high pressure gradient region. The larger this value is, the stronger the fluid scouring and extrusion effect at that unit. The dimensionless risk term representing structural volume expansion only applies when Risk is only considered when volume expansion occurs. Dividing this value by the limit threshold reflects the ratio of the current degree of material expansion to the failure limit. The larger this value is, the greater the possibility of the micropores inside the material opening up, and the easier it is to form a leakage channel. It is the environmental risk intensity synthesized by the superposition of pressure gradient and volume expansion, which is expressed by exp. These two combined environmental risk values ​​are mapped to the (0,1] interval. By subtracting 1, high-risk areas are transformed into high-weight coefficients close to 1, thereby achieving precise identification of high-risk units. The larger the value, the greater the fluid pressure experienced at that unit. The larger the value, the more likely the unit is to experience volume expansion, posing a risk of gap formation. or When it is very large, The exponent of the function will become a negative number with a very large absolute value. The overall value approaches 0, thus A value close to 1 indicates an extremely high environmental risk, meaning that the unit is under severe fluid impact (high pressure gradient) and its structure is loosened (volume expansion).

[0061] At the initial stage of feeding into the filter press, the high-pressure slurry will violently impact the inner corner of the elastic frame and the contact front of the sealing lip. If the unit here expands in volume, the fluid will quickly wedge into the contact surface, causing a wedge effect that leads to overall seal failure. These structural areas are high-risk areas that are prone to sealing defects.

[0062] The fluid permeation trend factor achieves the coupled determination of internal and external factors by multiplying the first and second terms. When a unit is in a high-risk area and its sealing capacity is insufficient, the fluid permeation trend factor will increase sharply, thereby triggering the subsequent material filling correction, providing guidance for subsequent optimization, and accurately pointing out the weak units that the optimization algorithm needs to focus on repairing.

[0063] like Figure 2a As shown, the distribution of strain energy density of the elastic frame is illustrated. The lower left corner is the microscopic sealing lip inside the elastic frame. Since it mainly undergoes kinematic deformation, its strain energy value is extremely low and it is easily regarded as useless material by traditional algorithms. Figure 2b This shows the distribution of the fluid permeation tendency factor of the elastic border. Since the sealing lip directly blocks the high-pressure slurry, its surface is subjected to a huge pressure gradient, resulting in an extremely high value of the fluid permeation tendency factor.

[0064] S4: The material relative density iterative update formula of the optimization criterion method is reshaped based on the fluid permeation trend factor of each unit.

[0065] After obtaining the fluid permeation tendency factor for each unit, in order to solve the problem that the optimization criterion method may mistakenly delete it due to the low strain energy of the sealing structure, this step aims to reshape the core iterative update formula. By introducing the fluid permeation tendency factor as a gain term, the material distribution logic is forcibly changed. The purpose is to give the algorithm the ability to automatically repair leakage points while retaining the traditional algorithm's pursuit of stiffness, so as to ensure that the elastic frame of the final generated topology design has reliable sealing performance.

[0066] Specifically, the material relative density iterative update formula of the optimization criterion method is reshaped based on the fluid permeation tendency factor of each unit, as follows:

[0067] in, and These are the relative densities of the material before and after the update. It is a mechanical optimization objective term based on strain energy calculation, characterizing its contribution to the overall stiffness. This is the damping coefficient, a standard value in traditional optimization criterion methods, used to smooth the iterative process and prevent the material density from oscillating drastically between 0 and 1. It is typically taken as 0.5. For the first Fluid permeation trend factor for each unit.

[0068] in, Based on the finite element theory, the strain energy of each element is obtained, and the strain energy of all elements is summed to obtain the overall structural flexibility C. This overall structural flexibility C is then used to... Take the derivative, using the result as the numerator and the Lagrange multipliers as the denominator; the ratio formed is used as... The derivative represents the sensitivity of the element, reflecting how much adding material to the element contributes to reducing structural deformation. The Lagrange multiplier reflects the average cost per unit of material under the current volume constraints. If A value greater than 1 indicates that the contribution outweighs the cost, and the relative material density of this unit should be increased; conversely, a value less than 1 indicates that the contribution is less than the cost, and the relative material density of this unit should be decreased.

[0069] This relationship expresses the stiffness requirement through multiplication. and sealing requirements Since fusion has been achieved and the fluid pressure gradient is small, it means that the unit is located in a solid region or a non-sealed contact region within the material. Fluid permeation does not need to be considered here; it only needs to bear the structural load. At this point, the formula degenerates into This achieves the inheritance of traditional optimization criteria, that is, it completely follows traditional optimization criteria for optimization, thereby forcibly preserving the relative density of the material in the element. However, if the element is located in a micro-lip structure at the sealed edge, its strain energy is often very low. The strain energy is very small (traditional optimization criteria would typically eliminate it), but this invention takes into account that although the strain energy is very low, it is located at a high-pressure boundary and is prone to leakage. It will be very big. A value greater than 1 is needed not only to bear structural loads but also to address the risk of fluid seepage. Therefore, a value greater than 1 is used to achieve [the desired effect]. The amplification operation forces an increase in the relative density of the material in that unit.

[0070] It should be noted that during the first iteration, the relative density of the material in all cells is usually initialized to a uniform value according to the preset volume constraint. For example, if the volume constraint is to retain 30% of the material, the relative density of the material in all cells is initialized to 0.3.

[0071] This step achieves simultaneous optimization of rigidity within the structure and sealing at the boundaries through this mechanism, ultimately resulting in an elastic frame that can adapt to ultra-high pressure conditions and improves sealing reliability.

[0072] S5: Update the relative density of each unit's material based on the iterative update formula of the reshaped material relative density until the optimal topology is generated, so as to complete the optimization design of the flexible border.

[0073] After establishing new update rules, it is necessary to iterate repeatedly to reach equilibrium in the material distribution. This step aims to control the optimization process and ensure that the design results are mathematically convergent and physically feasible.

[0074] The convergence tolerance is set to 0.01. This tiny difference usually means that the error is almost negligible. In each iteration, the new density of each unit is calculated using the iterative update formula based on the relative density of the reshaped material. The average value of the density change of all units between two adjacent iterations is calculated. When the change is less than 0.01, the optimization is considered to have ended.

[0075] Finally, elements with a relative material density greater than 0.5 in the design domain are identified as solid materials, and their boundary contours are extracted using isosurface extraction technology to obtain the final elastic frame geometry. This geometry is the optimal solution that integrates mechanical stiffness and fluid sealing performance.

[0076] like Figure 3a As shown, the overall shape of the elastic frame optimized using existing technology is displayed. At the key part of the frame that contacts the high-pressure fluid, the flexible sealing lip that should exist is removed, resulting in the inner edge exhibiting a simple structural support form, or even discontinuous broken edges. This deficiency means that the frame cannot form an effective interference fit with the filter plate on a macroscopic level, and the high-pressure slurry will leak directly along the contact gap. Figure 3b This demonstrates the overall morphology of the elastic frame obtained by applying the method of the present invention. The inner side of the generated frame retains and reconstructs the sealing lip, which not only ensures the structural strength of the frame, but also achieves excellent self-sealing performance by utilizing the flexible deformation of the lip. This achieves the effect of simultaneous optimization of stiffness and sealing from a macroscopic configuration perspective.

[0077] The present invention also provides a flexible border optimization design system based on finite element theory. The design system includes a processor and a memory. The memory stores computer program instructions, which, when executed by the processor, implement all or part of the steps of the flexible border optimization design method. The processor may be a central processing unit (CPU), a graphics processing unit (GPU), an application-specific integrated circuit (ASIC), or a field-programmable gate array (FPGA). The processor is preferably a GPU to achieve parallel acceleration. The memory may include volatile memory (such as RAM) and non-volatile memory (such as ROM or flash memory).

[0078] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An elastic frame optimization design method based on finite element theory, characterized in that, The method comprises the following steps: a nonlinear finite element model of the elastic frame is constructed, the elastic frame is discretized into a plurality of units composed of a plurality of nodes, and a displacement vector, a normal contact stress value and a fluid pressure value of each node are obtained; for each node, an effective sealing stress ratio of the node is calculated based on the normal contact stress value and the fluid pressure value, a tangential slip stability coefficient of the node is determined based on the normal contact stress value and the displacement vector of the node, and the effective sealing stress ratio is corrected by using the tangential slip stability coefficient to determine the sealing reliability of the node; for each unit, a fluid pressure gradient of the unit is calculated based on the fluid pressure values of the nodes in the unit, a volume strain of the unit is calculated based on the displacement vectors of the nodes in the unit, and a fluid permeation tendency factor of the unit is determined by combining the fluid pressure gradient and the volume strain and the sealing reliability of the nodes in the unit; based on the fluid permeation tendency factor of each unit, a material relative density iterative update formula of an optimization criterion method is reshaped, the material relative density of each unit is updated based on the reshaped material relative density iterative update formula, and the optimization design of the elastic frame is completed until an optimal topology configuration is generated.

2. The elastic edge optimization design method of claim 1, wherein, The effective sealing stress ratio of the node is determined based on the following manner: the square difference and the square sum of the normal contact stress value and the fluid pressure value of each node are calculated, the ratio of the square difference to the square sum is non-negative truncated and square rooted to obtain a value between 0 and 1, which is used as the effective sealing stress ratio of the node.

3. The elasticated frame optimization design method of claim 1, wherein, The tangential slip stability coefficient of the node is determined based on the following manner: the tangential slip distance is calculated according to the displacement vector of each node, and the product of the normal contact stress value and the tangential slip distance of the node is calculated as slip energy dissipation; the slip energy dissipation is dimensionless processed, and the hyperbolic tangent function is used to map it into an attenuation coefficient, and the tangential slip stability coefficient of the node is obtained by subtracting the attenuation coefficient from 1.

4. The elasticated frame optimization design method of claim 1, wherein, The sealing reliability of the node is determined by correcting the effective sealing stress ratio by using the tangential slip stability coefficient, which is realized by multiplying the tangential slip stability coefficient of each node and the effective sealing stress ratio of the node, and the multiplied value is used as the sealing reliability of the node.

5. The elasticated frame optimization design method of claim 1, wherein, The fluid permeation tendency factor of the unit is determined based on the following relationship: ； wherein, is a fluid permeation tendency factor of the th element, is an average value of sealing reliability of all nodes within the th element, is a fluid pressure gradient of the th element, is a modulus length sign, is an average value of modulus lengths of fluid pressure gradients of all elements, is a preset parameter for preventing a denominator from being 0, is a volumetric strain of the th element, is a preset volumetric strain threshold value, is a natural exponential function, is a Macaulay bracket, which takes a value within the bracket when the value is greater than 0, and takes 0 when the value is not greater than 0.

6. The elasticated frame optimization design method of claim 5, wherein, The fluid pressure gradient of the unit is determined based on the following manner: a continuous pressure field inside the unit is constructed based on the fluid pressure values of the nodes in the unit by using the finite element shape function, the continuous pressure field is spatially differentiated to obtain a pressure gradient vector representing the rate of pressure change, and the module length of the pressure gradient vector is calculated as the fluid pressure gradient of the unit.

7. The elasticated frame optimization design method of claim 5, wherein, The volume strain of the unit is determined based on the following manner: the displacement vectors of all the nodes in each unit are spatially differentiated by using the finite element shape function to obtain a strain tensor, and the trace of the strain tensor is calculated as the volume strain of the unit.

8. The elasticated frame optimization design method of claim 1, wherein, The material relative density iterative update formula of the optimization criterion method is reshaped based on the fluid permeation tendency factor of each unit, which comprises: ； wherein, and are the relative densities of the material after and before the update of the th element, respectively, is the mechanical optimization objective of the element, is determined based on the optimization criteria method, and is used to represent the contribution efficiency of the element to the overall stiffness of the structure, is a preset damping coefficient, is the fluid permeation trend factor of the th element.

9. The elasticated frame optimization design method of claim 1, wherein, The material relative density of each unit is updated based on the remolded material relative density iterative updating formula until an optimal topological configuration is generated, including: In each iteration, the updated material relative density of each unit is calculated using the remolded material relative density iterative updating formula until the change of the updated material relative density of all units between two adjacent iterations is less than a preset convergence tolerance, and the iteration ends.

10. An elastic frame optimization design system based on finite element theory, characterized by, The elastic frame optimization design system comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to realize the steps of the elastic frame optimization design method according to any one of claims 1-9.

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