Optimization design method and system of elastic frame based on finite element theory

Abstract

The application relates to the technical field of data processing, in particular to an elastic frame optimization design method and system based on a finite element theory, which comprises the following steps: constructing a nonlinear finite element model of an elastic frame; determining the sealing reliability of each node based on the normal contact stress value, the fluid pressure value and the displacement vector of the node; determining the fluid permeation trend factor of each unit based on the sealing reliability of the nodes in the unit; remodeling the material relative density iterative update formula of the optimization criterion method by using the fluid permeation trend factor, updating the material relative density of each unit, and generating an optimal topology configuration, so as to complete the optimization design of the elastic frame. The method solves the high-pressure leakage problem caused by the ignorance of micro-sealing in traditional topology optimization, and realizes the synchronous optimization of the structural stiffness and the sealing performance under the super-high pressure working condition.

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:

[0009] 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;

[0010] 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;

[0011] 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.

[0012] 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.

[0013] 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.

[0014] Preferably, the effective sealing stress ratio of the node is determined based on the following manner: calculating the square difference and the square sum of the normal contact stress value and the fluid pressure value of each node, performing non-negative truncation processing on the ratio of the square difference to the square sum, and taking the square root to obtain a value between 0 and 1 as the effective sealing stress ratio of the node.

[0015] 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 a 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.

[0016] Preferably, the tangential slip stability coefficient of the node is determined based on the following manner: 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, performing dimensionless processing on the slip energy dissipation, and using the hyperbolic tangent function to map it to a decay coefficient. The tangential slip stability coefficient of the node is obtained by subtracting the decay coefficient from 1.

[0017] This technical solution evaluates tangential instability by calculating slip energy dissipation. High-pressure seals often fail due to fretting wear or large deformation slippage. The product of normal contact stress and tangential slippage distance essentially characterizes the magnitude of interfacial friction work, i.e., the energy required to disrupt the seal adhesion state. Introducing the hyperbolic tangent function as a mapping tool, utilizing its S-curve characteristics, allows for a smooth mapping of energy dissipation values ​​to... The range serves as the attenuation coefficient. When the slip energy consumption is large, the attenuation coefficient approaches 1, causing the stability coefficient to approach 0, and vice versa. This nonlinear mapping mechanism conforms to the physical threshold effect, that is, small slip can be tolerated, but once a certain energy threshold is exceeded, the sealing stability will drop sharply.

[0018] Preferably, the sealing reliability of a node is determined by correcting the effective sealing stress ratio using the tangential slip stability coefficient, and the correction is performed by multiplying the tangential slip stability coefficient of each node with the effective sealing stress ratio of that node, and the result of the multiplication is taken as the sealing reliability of that node.

[0019] This technical solution adopts a multiplicative correction strategy, which reflects the barrel effect in the sealing system. As the final evaluation index, the sealing reliability must simultaneously meet two conditions: normal compression (high effective sealing stress ratio) and tangential stability (high tangential slip stability coefficient). This avoids the one-sidedness of a single dimension and thus ensures the accuracy of the evaluation results.

[0020] Preferably, the fluid permeation tendency factor of the unit is determined based on the following relationship:

[0021]

[0022] in, It is the first Fluid permeation tendency factor of each unit, For the first The average sealing reliability of all nodes within a unit. For the first Fluid pressure gradient of each unit, To determine the sign of the modulus, 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. For the first Volumetric strain of each element A preset volumetric strain threshold is used to perform dimensionless normalization on the volumetric strain, characterizing the volumetric expansion limit that leads to seal failure. It is a natural exponential function. The value inside the brackets is Macaulay brackets. If the value inside the brackets is greater than 0, the value is taken; if the value inside the brackets is not greater than 0, the value is taken as 0.

[0023] This technical solution constructs a multi-physics coupled risk and demand evaluation model. The first term represents the sealing defect degree; the more unreliable the current seal, the larger this term, and the higher the urgency of optimization. In the second term, the natural exponential function integrates the pressure gradient term and the volumetric strain term. The larger the pressure gradient, the more drastic the fluid pressure change of the unit; the larger the volumetric strain, the more the unit is expanding and prone to microscopic gaps. Utilizing the decay characteristics of the exponential function, these risk factors are transformed into a weight approaching 1. By multiplying the sealing defect degree with the environmental risk degree, units in high-risk areas that have not yet met the sealing performance standards are accurately identified, providing precise guidance for the subsequent forced increase of material density.

[0024] Preferably, the fluid pressure gradient of the element is determined as follows: a continuous pressure field inside the element is constructed based on the fluid pressure values ​​of each node in the element using finite element shape functions; the continuous pressure field is spatially differentiated to obtain a pressure gradient vector characterizing the rate of pressure change; and the magnitude of the pressure gradient vector is calculated as the fluid pressure gradient of the element.

[0025] Preferably, the volumetric strain of the element is determined by: spatially differentiating the displacement vectors of all nodes within each element using finite element shape functions to obtain the strain tensor, and calculating the trace of the strain tensor as the volumetric strain of the element.

[0026] Preferably, the material relative density iterative update formula of the optimization criterion method is reshaped based on the fluid permeation tendency factor of each unit, including:

[0027]

[0028] in, and The first The relative density of materials in each unit after and before the update This is the objective term for the mechanical optimization of this unit. It is determined based on the optimization criterion method and is used to characterize the contribution efficiency of this element to the overall stiffness of the structure. The preset damping coefficient, For the first The fluid permeability tendency factor for each unit is used to adjust the weight of the influence of the fluid permeability tendency factor on the relative density of the material.

[0029] The technical scheme introduces a multiplication factor, when the fluid permeation tendency factor is large, that is, the unit has a leakage risk and is in a critical position, the factor is significantly greater than 1, thereby producing a forced gain effect on the material density, which means that even if the stiffness contribution of the unit is small and is originally deleted by the algorithm, as long as it is important to sealing, the algorithm will be forced to retain or even increase the density of the unit, and accurate retention of the small unit important to sealing is achieved.

[0030] Preferably, the material relative density of each unit is updated based on the updated material relative density iterative updating formula until the optimal topology configuration is generated, including: in each iteration, the updated material relative density of each unit is calculated by using the updated material relative density iterative updating formula until the change amount of the updated material relative density of all units between adjacent two iterations is less than a preset convergence tolerance, and the iteration is ended; and the material relative density of all units at the end of the iteration is taken as the optimal topology configuration of the elastic frame.

[0031] In the second aspect, the elastic frame optimization design system based on the finite element theory 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 the aspects.

[0032] The present application has the following effects:

[0033] The present application quantifies the sealing reliability from the node micro level by constructing a nonlinear finite element model containing displacement, contact stress and fluid pressure, generates a fluid permeation tendency factor by combining the pressure gradient and volume strain of the unit mesoscopic level, and finally remodels the iterative updating formula of the optimization criterion method. The method breaks the limitation of traditional topology optimization which only takes stiffness as a single target, can accurately identify and forcibly retain the microstructure with low strain energy but important to leakage resistance while ensuring the overall bearing capacity of the elastic frame, which makes the designed elastic frame not only have sufficient structural strength but also form a stable and reliable self-adaptive sealing interface under superhigh pressure working conditions, effectively solves the common frame leakage problem in high-pressure filter presses and other equipment, and improves the safety of the equipment. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 is a method flowchart of the present application;

[0035] Figure 2a is a strain energy density distribution diagram of the micro sealing unit of the elastic frame of the present application;

[0036] Figure 2b is a fluid permeation tendency factor distribution diagram of the micro sealing unit of the elastic frame of the present application;

[0037] Figure 3a is a schematic diagram of the macroscopic topological configuration and inner edge sealing integrity of the prior art elastic frame as a whole;

[0038] Figure 3b is a schematic diagram of the macroscopic topological configuration and inner edge sealing integrity of the elastic frame as a whole according to the present application. DETAILED DESCRIPTION

[0039] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application.

[0040] Reference Figure 1 The present application provides an elastic frame optimization design method based on finite element theory, comprising:

[0041] S1: Constructing a nonlinear finite element model of the elastic frame, obtaining the displacement vector of each node, the normal contact stress value and the fluid pressure value.

[0042] The working pressure of the high-pressure filter press is usually as high as 8 MPa or even higher. The elastic frame involves large deformation of super-elastic materials such as rubber in actual work, nonlinear contact between rigid filter plates and diaphragm plates, and fluid-structure coupling effect of high-pressure slurry fluid. Simple linear analysis cannot truly reflect the physical response. This step aims to accurately capture the micro behavior of the structure under load through nonlinear finite element analysis, and the purpose is to provide accurate raw data for subsequent sealing performance evaluation, including the spatial position change of each node, the stress state on the contact interface and the distribution of fluid pressure.

[0043] Specifically, first, an initial geometric model of the elastic frame is constructed using CAD software, and is imported into a finite element analysis software (such as ABAQUS or ANSYS). Since the elastic frame is usually made of rubber material, the material properties of the elastic frame are defined using a hyperelastic constitutive model (such as Mooney-Rivlin model or Yeoh model) to accurately represent the nonlinear stress-strain relationship under pressure.

[0044] Then, the contact surface between the rigid filter plate and the elastic frame is set, and the boundary conditions and fluid pressure load under actual working conditions are applied to simulate the real fluid wedge process. The elastic frame is discretized into multiple units composed of multiple nodes, preferably using quadrilateral or hexahedral hybrid elements suitable for large deformation analysis, and submitted to the solver for nonlinear solving to calculate and obtain the displacement vector, normal contact stress value and fluid pressure value of each node. The displacement vector of each node is obtained based on the finite element balance equation, which represents the spatial coordinate change 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), which represents the extrusion stress of 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 fluid permeation algorithm, which represents the static pressure of the fluid acting on the node position.

[0045] S2: Calculate the effective sealing stress ratio and tangential slip stability coefficient of each node, and use the tangential slip stability coefficient to correct the effective sealing stress ratio to obtain the sealing reliability of the node.

[0046] After obtaining the basic physical data of each node, considering that for the elastic frame of the filter press, simply comparing the contact pressure to the fluid pressure is not enough to ensure long-term sealing. If the contact surface slips severely in the tangential direction, it will cause the sealing lip to wear or dynamically peel off, thereby causing leakage. Therefore, this step accurately evaluates the sealing state of a single node by analyzing the normal compression degree and tangential stability.

[0047] Specifically, the process includes the following steps:

[0048] S21: Calculate the effective sealing stress ratio based on the normal contact stress value and the fluid pressure value.

[0049] For the elastic frame of the filter press, it mainly resists the pressure of the slurry through the rebound force generated by the filter plate. Considering that the essence of sealing is that the counterforce on the contact interface must be able to resist the invasion pressure of the fluid, however, simply comparing the numerical values cannot provide a normalized evaluation standard, and it is difficult to measure the critical failure risk caused by pressure fluctuations.

[0050] Therefore, this step aims to construct a dimensionless effective sealing stress ratio, which sensitively quantifies the safety margin of the current contact state relative to the fluid pressure through the mathematical construction of the square difference and the square sum. Specifically, for the th node, the effective sealing stress ratio is determined based on the following relationship:

[0051]

[0052] In this relationship, 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. .

[0053] 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.

[0054] 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.

[0055] 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.

[0056] S22: Determine the tangential slip stability coefficient of the node based on the normal contact stress value and the displacement vector of the node.

[0057] 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.

[0058] 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:

[0059]

[0060] 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 .

[0061] 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, Approaching 1, indicating very stable, this mapping relationship conforms to the physical definition of stability, that is, there is a allowed micro-motion range, once out of the range, the stability decreases rapidly. By introducing Reflects the benchmark energy threshold, which conforms to the common sense of materials: there is a damage energy threshold for rubber materials, below this value is elastic micro-motion, safe state, above this value is macroscopic slip damage, in a dangerous state.

[0062] S23: Determine the sealing reliability.

[0063] After obtaining the normal and tangential evaluation indicators of a node respectively, in view of the fact that sealing failure follows the barrel effect, that is, if it is not pressed tightly, it will leak, and large slip will also lead to failure, therefore, this step adopts the coupling mode of multiplication to fuse the indicators of the two dimensions into a unique sealing reliability. This step is essentially performing an AND gate logic, only when a node meets both the conditions of normal tightness and tangential stability, it will be determined as a reliable node.

[0064] Specifically, the following relationship is satisfied:

[0065]

[0066] In this relationship, is the sealing reliability of the th node, is the effective sealing stress ratio of the th node, is the tangential slip stability coefficient of the th node. The larger the value is, the tighter the node is pressed in the normal direction, The larger the value is, the more stable the node is in the tangential direction, only when both are close to 1, It will be close to 1. Through this operation, the nodes that really contribute to sealing are screened out, providing accurate input for subsequent evaluation of fluid permeation risk at the unit level.

[0067] S3: Calculate the fluid pressure gradient and volume strain of each unit, and determine the fluid permeation trend factor of the unit in combination with the sealing reliability of the nodes in the unit.

[0068] After the evaluation of the micro nodes is completed, considering that the object of optimization is the unit, the permeation behavior of the fluid in the material or at the boundary is jointly affected by the fluid driving force (pressure gradient) and the pore channel (volume strain). Therefore, this step aims to build a comprehensive fluid permeation trend factor, the purpose of which is to identify those key units that are in a high pressure difference area and are themselves expanding, which may lead to micro gaps.

[0069] Specifically, the following processes are included:

[0070] S31: Calculate the fluid pressure gradient of the cell based on the fluid pressure values ​​of the nodes within the cell.

[0071] 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.

[0072] S32: Calculate the volumetric strain of the element based on the displacement vectors of the nodes within the element.

[0073] 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.

[0074] S33: Determine the fluid permeation tendency factor by combining the fluid pressure gradient, volumetric strain, and sealing reliability of the nodes within the unit.

[0075] Specifically, the fluid permeation tendency factor of the unit is determined by the following relationship:

[0076]

[0077] 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.

[0078] 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 non-dimensionalized risk term representing the volume expansion of the structure, only when , the volume expansion is taken into account, and it is divided by the limit threshold, which reflects the proportion of the current expansion of the material relative to the failure limit. The larger this value is, the greater the possibility of the opening of micro-pores in the material, and the easier the formation of leakage channels. is the environmental risk intensity synthesized by the superposition of the pressure gradient and the volume expansion. The two synthesized environmental risk values are mapped to the interval (0, 1] by the 1 minus operation, which converts the high-risk area into a high-weight coefficient close to 1, thereby achieving precise locking of high-risk units, The larger the value is, the greater the fluid pressure at the unit, The larger the value is, the more likely the unit is to produce volume expansion and exist gap risk, or is large, The exponential part of the function will become a large negative number, The overall tends to 0, so tends to 1, indicating that the environmental risk is extremely high, which means that the unit is in a state of severe fluid impact (high pressure gradient) and structure loosening (volume expansion).

[0079] The inner corner of the elastic frame and the contact front of the sealing lip are impacted by the high-pressure slurry at the initial stage of the filter press feeding. If the unit at this position expands in volume, the fluid will quickly wedge into the contact surface, causing the overall sealing failure due to the wedge effect. These structural areas belong to high-risk areas that are prone to sealing defects.

[0080] The fluid penetration tendency factor realizes the coupling 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 ability is insufficient, the fluid penetration tendency factor will increase sharply, thereby triggering the subsequent material filling correction and providing navigation for subsequent optimization, accurately pointing out the weak units that need to be repaired by the optimization algorithm.

[0081] As shown in Figure 2a , the distribution of the strain energy density of the elastic frame is shown. The lower left corner is the micro-sealing lip inside the elastic frame, which mainly undergoes follow-up deformation, so its strain energy value is very low and is easily considered as useless material by traditional algorithms. Figure 2b The distribution of the fluid penetration tendency factor of the elastic frame is shown. The sealing lip directly blocks the high-pressure slurry, and its surface bears a large pressure gradient, resulting in a very high value of the fluid penetration tendency factor.

[0082] S4: Based on the fluid penetration tendency factor of each unit, the material relative density iterative update formula of the optimization criterion method is reshaped.

[0083] 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.

[0084] 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:

[0085]

[0086] 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.

[0087] 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.

[0088] 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 , which realizes the inheritance of the traditional optimization criterion method, that is, optimization is performed in full compliance with the traditional optimization criterion method, thereby forcibly retaining the material relative density of the unit. If the unit is in a small lip structure of the sealed edge, the strain energy thereof is often very low, very small (the traditional optimization criterion method usually deletes it), the present application considers that although the strain energy is very low, the unit is in a high-pressure boundary and is prone to leakage, will be large, will be greater than 1, not only has to bear the structural load, but also has to cope with the risk of fluid penetration, and therefore realizes the amplification operation of by a value greater than 1, thereby forcibly increasing the material relative density of the unit.

[0089] It should be noted that in the first iteration, the material relative density of all units is usually initialized to a uniform value according to a preset volume constraint, for example, if the volume constraint is to retain 30% of the material, the material relative density of all units is initialized to 0.3.

[0090] This step realizes the simultaneous optimization of pursuing stiffness inside the structure and pursuing sealing at the boundary through this mechanism, and the final generated elastic edge frame can adapt to super-high pressure working conditions and improve the sealing reliability.

[0091] S5: Update the material relative density of each unit based on the remodeled material relative density iterative update formula until the optimal topological configuration is generated to complete the optimization design of the elastic edge frame.

[0092] After the new update rule is established, the material distribution needs to be balanced through repeated iterations, and this step aims to control the progress of optimization to ensure that the design result is mathematically convergent and physically feasible.

[0093] The convergence tolerance is set to 0.01, which usually means that the error can be almost negligible. In each iteration, the new density of each unit is calculated using the remodeled material relative density iterative update formula, and the average of the density change of all units between the adjacent two iterations is calculated. When the change is less than 0.01, it is determined that the optimization is completed.

[0094] Finally, the units with a material relative density greater than 0.5 in the design domain are identified as solid materials, and the boundary contour thereof is extracted using the isosurface extraction technology, thereby obtaining the final elastic edge frame geometry, which is the optimal solution that integrates mechanical stiffness and fluid sealing performance.

[0095] As Figure 3aAs shown, the overall morphology of the elastic frame optimized by the prior art is shown, and at the key part of the inner side of the frame contacting the high-pressure fluid, the flexible sealing lip that should exist is removed, causing the inner edge to present a simple structural support form, and even a non-continuous broken edge. This lack cannot form an effective interference fit with the filter plate macroscopically, and the high-pressure slurry will directly leak along the contact gap. Figure 3b The overall morphology of the elastic frame obtained by applying the method of the present application is shown, and the generated inner side of the frame, the sealing lip is retained and reconstructed, which not only ensures the structural strength of the frame, but also realizes excellent self-sealing performance by the flexible deformation of the lip. This realizes the effect of synchronous optimization of stiffness and sealing from the macro configuration.

[0096] The present application also provides an elastic frame optimization design system based on the finite element theory, which comprises a processor and a memory, the memory stores computer program instructions, and the computer program instructions realize all steps or part of steps of the elastic frame optimization design method when executed by the processor; the processor can be a central processing unit (CPU), a graphics processing unit (GPU), an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA), and the processor can be preferably a GPU to realize parallel acceleration; the memory can include a volatile memory (such as RAM) and a non-volatile memory (such as ROM or flash memory).

[0097] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

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, and the following conditions are met: ； is the fluid permeation tendency factor of the i-th element, is the average value of the sealing reliability of all nodes within the i-th element, is the fluid pressure gradient of the i-th element, is the modulus length symbol, is the average value of the modulus length of the fluid pressure gradient of all elements, is the preset parameter for preventing the denominator from being 0, is the volumetric strain of the i-th element, is the preset volumetric strain threshold value, is the natural exponential function, is the Macaulay bracket, which takes the value within the bracket when the value is greater than 0, and takes 0 when the value is not greater than 0;​​​​ the material relative density iterative update formula of the optimization criterion method is reshaped based on the fluid permeation tendency factor of each unit, including: ； 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; the material relative density of each unit is updated based on the reshaped material relative density iterative update formula until an optimal topology configuration is generated, to complete the optimization design of the elastic frame.

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 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.

6. The elasticated frame optimization design method of claim 1, 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.

7. The elasticated frame optimization design method of claim 1, wherein, The material relative density of each unit is updated based on the reshaped material relative density iterative update formula until an optimal topology configuration is generated, including: In each iteration, the updated material relative density of each unit is calculated by using the remolded material relative density iteration update formula until the variation of the updated material relative density of all units between adjacent two iterations is less than a preset convergence tolerance, and the iteration ends. The material relative density of all units at the end of the iteration is taken as the optimal topological configuration of the elastic frame.

8. 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 in any one of claims 1-7.

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