A power cross arm key node connection configuration topology and an optimization design method thereof

Abstract

The application provides a power cross arm key node connection configuration topology and an optimization design method thereof. The method comprises the following steps: obtaining key node position information such as a cross arm initial design domain, a load application point and a structure support point, and obtaining a finite element unit set through sectioning; performing initial static force analysis based on a full entity model, calculating an initial strain energy density of the unit and establishing an initial pseudo-density variable field; in iterative optimization, dividing key function subdomains and transition connection subdomains according to the key node positions, performing finite element analysis in combination with the current pseudo-density variable field, determining an evaluation neighborhood and calculating a local density influence factor; identifying a main load-bearing structure connected domain through topology connectivity analysis, setting an isolation penalty term for island unit outside the domain; calculating and correcting a pseudo-density sensitivity, updating the pseudo-density variable under the global volume constraint and the minimum material consumption constraint of the key subdomain, and generating the power cross arm connection configuration after convergence.

Description

Technical Field

[0001] This application belongs to the field of power crossarms, and in particular relates to a topology of connection configuration of key nodes of power crossarms and its optimization design method. Background Technology

[0002] Transmission towers are crucial supporting structures in power systems. Electric crossarms, as an important component of transmission towers, are primarily used to suspend insulator strings, support conductors, and transfer conductor loads to the tower body. The rationality of their structural design directly affects the operational safety and construction costs of transmission lines. In recent years, with the development of computational mechanics and structural optimization techniques, continuum topology optimization methods have been gradually applied to the lightweight design of electric crossarms. This method typically uses mathematical optimization algorithms to find material distribution forms that meet preset mechanical performance requirements, given a design space, boundary conditions, and load conditions. In conventional continuum topology optimization, the design domain is usually discretized into a finite element mesh, and the element pseudo-density is used as the design variable. Static analysis and iterative updates are then performed using a material interpolation model to achieve structural weight reduction.

[0003] However, in the actual service environment of power crossarms, the crossarm structure not only needs to withstand overall bending, torsion, and conductor loads, but also experiences strong local stress influences in key node areas such as load application points and support connection points. The connection reliability at key nodes plays a crucial role in the overall structural stability. Under a single global volume constraint, existing optimization methods typically employ a uniform sensitivity analysis and density update strategy for the entire design domain, making it difficult to distinguish the different functional requirements of key node areas and ordinary transition areas. This can easily lead to excessive material reduction near key nodes in the later stages of optimization, causing local stress concentration or insufficient connection strength, making it difficult for the optimized theoretical configuration to directly meet engineering application requirements. At the same time, conventional numerical iteration processes do not adequately identify and constrain the material connectivity state, easily resulting in isolated material blocks or discontinuous force transmission paths. This leads to insufficient connection, uneven transition, or unclear force transmission paths between the topological configuration and the main structure. Therefore, a new power crossarm structure optimization design method is needed to reasonably retain the material distribution in the key node area while meeting the overall lightweight goal, and guide the main load-bearing path to remain continuous, so as to obtain a power crossarm connection configuration with reasonable key node connection, clear force transmission path and more suitable for engineering application. Summary of the Invention

[0004] To address the problem in existing power crossarm topology optimization techniques that struggle to balance critical node material retention with the continuity of the main load-bearing path, leading to critical node hollowing and material islands, this invention proposes, in a first aspect, a power crossarm critical node connection configuration topology and its optimization design method, comprising the following steps: The initial design domain and preset key node location information of the power crossarm are obtained. The key nodes include load application points and structural support points. Finite element mesh is generated based on the initial design domain to obtain a set of finite element elements. Initial static analysis is performed based on the full solid model of the initial design domain to obtain the initial strain energy density of each element and the initial pseudo density variable field is set according to the initial strain energy density. Entering iterative optimization calculation, in each iteration, the initial design domain is divided into key functional subdomains and transition connection subdomains based on the key node location information. Finite element analysis is performed on the current configuration based on the current pseudo density variable field to obtain the response of each element. An evaluation neighborhood is set based on the subdomain type to which the element belongs, and the local density influence factor is calculated according to the evaluation neighborhood. Topological connectivity analysis is performed on the elements to obtain the main load-bearing structure connectivity domain, and an isolation penalty term is set for elements that do not belong to the main load-bearing structure connectivity domain. The sensitivity of each unit's pseudo-density variable is calculated, and the sensitivity is corrected according to the local density influence factor and the isolation penalty term to obtain the corrected sensitivity. Based on the corrected sensitivity, the pseudo-density variable values ​​of all units are updated under the constraints of global volume and minimum material usage of the key functional subdomain. When the set iterative convergence conditions are met, the final pseudo-density variable field is output, and the connection configuration of the power crossarm is generated based on the final pseudo-density variable field.

[0005] On the other hand, the present invention also proposes a topology for the connection configuration of key nodes of power crossarms and its optimization design system, including the following modules: The acquisition module is used to acquire the initial design domain of the power crossarm and the preset key node location information. The key nodes include load application points and structural support points. Based on the initial design domain, finite element mesh is performed to obtain a set of finite element elements. Based on the full solid model of the initial design domain, initial static analysis is performed to obtain the initial strain energy density of each element and the initial pseudo density variable field is set according to the initial strain energy density. The calculation module is used to enter the iterative optimization calculation. In each iteration, the initial design domain is divided into key functional subdomains and transition connection subdomains based on the key node location information. Finite element analysis is performed on the current configuration based on the current pseudo density variable field to obtain the response of each element. An evaluation neighborhood is set based on the subdomain type to which the element belongs and the local density influence factor is calculated according to the evaluation neighborhood. Topological connectivity analysis is performed on the elements to obtain the main load-bearing structure connectivity domain and an isolation penalty term is set for elements that do not belong to the main load-bearing structure connectivity domain. The output module is used to calculate the sensitivity of each unit's pseudo-density variable and correct the sensitivity according to the local density influence factor and the isolation penalty term to obtain the corrected sensitivity. Based on the corrected sensitivity, the pseudo-density variable values ​​of all units are updated under the constraints of global volume and minimum material usage of the key functional subdomain. When the set iterative convergence conditions are met, the final pseudo-density variable field is output, and the connection configuration of the power crossarm is generated based on the final pseudo-density variable field.

[0006] This invention divides the design domain into key functional subdomains and transitional connection subdomains, and calculates local density influence factors based on different subdomain types to provide differentiated guidance for material evolution in key node regions and transitional connection regions. It identifies the main load-bearing structural connectivity domains through topological connectivity analysis and sets isolation penalty terms for isolated elements outside these domains to reduce material islands and discontinuous force transmission paths. Furthermore, it uses local density influence factors and isolation penalty terms to correct sensitivity, and updates pseudo-density variables under global volume constraints and minimum material usage constraints in key subdomains. This achieves lightweighting of the power crossarm while ensuring sufficient material is retained in key areas such as load application points and structural support points, resulting in a power crossarm connection configuration with clear force transmission paths and good connectivity. Attached Figure Description

[0007] Figure 1 A flowchart of the first embodiment; Figure 2 A schematic diagram of the initial pseudo-density variable field distribution of the power crossarm; Figure 3 A schematic diagram showing the partitioning results of the key functional subdomains and transitional connection subdomains of the design domain; Figure 4 This is a schematic diagram of the results of iterative topological connectivity analysis and island unit identification. Detailed Implementation

[0008] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0009] Before providing a further detailed description of the embodiments of this application, the nouns and terms involved in the embodiments of this application will be explained, and the nouns and terms involved in the embodiments of this application shall be interpreted as follows.

[0010] 1. Constitutive matrix: The constitutive matrix is ​​a matrix used to describe the relationship between stress and strain in a material. In finite element analysis, it is usually used to calculate the corresponding stress based on the strain of the element.

[0011] 2. Boolean matrix: The Boolean matrix is ​​a matrix consisting only of 0 and 1, used in finite element assembly to represent the correspondence between the local degrees of freedom of an element and the global degrees of freedom of the overall structure.

[0012] In the first embodiment, the present invention proposes a topology for the connection configuration of key nodes of a power crossarm and its optimization design method, such as... Figure 1 As shown, it includes the following steps: S1. Obtain the initial design domain of the power crossarm and the preset key node location information. The key nodes include load application points and structural support points. Based on the initial design domain, perform finite element meshing to obtain a set of finite element elements. Based on the full solid model of the initial design domain, perform initial static analysis to obtain the initial strain energy density of each element and set the initial pseudo density variable field according to the initial strain energy density.

[0013] A three-dimensional geometric model of the power crossarm is established using three-dimensional computer-aided design software as the initial design domain. Based on the actual working conditions, the spatial coordinates of the load application points of the power crossarm under the tension of the transmission line and the structural support points connected to the transmission tower are determined as key node location information. The power crossarm is a transverse support component installed on a pole or tower, mainly used to suspend insulators, support conductors, and transfer conductor loads to the main body of the tower.

[0014] The initial design domain is meshed using eight-node hexahedral elements to generate a set of finite element elements containing node coordinates and node connection relationships.

[0015] The initial material elastic modulus and Poisson's ratio are assigned to the full solid model. Fixed displacement constraints are applied to the structural support points, and a three-dimensional static load vector is applied at the load application points. The finite element solver is invoked to assemble the global stiffness matrix and load vector, and the linear equations are solved to obtain the displacement vectors of all nodes. The initial strain energy density of each element in the finite element set is calculated using the nodal displacement vectors, element stiffness matrices, and element volumes. The maximum and minimum values ​​of the initial strain energy density of all elements are extracted, and the initial strain energy density of each element is linearly normalized. The normalized strain energy density values ​​are then mapped to the initial pseudo-density variable values ​​of the corresponding elements, establishing a global initial pseudo-density variable field.

[0016] In an optional embodiment, the step of performing initial static analysis based on the full solid model of the initial design domain to obtain the initial strain energy density of each element and setting the initial pseudo-density variable field according to the initial strain energy density includes: A fixed displacement boundary condition is applied based on the structural support point, and a load vector under rated working conditions is applied based on the load application point; Construct the overall stiffness matrix of the full solid model and assemble the load vector, solve the finite element equilibrium equations to obtain the global nodal displacement vector, and extract the local nodal displacement corresponding to each element; The strain tensor and stress tensor of each element are calculated based on the nodal displacements, and the initial strain energy density of each element is obtained. The initial strain energy density of each element is normalized, and the normalized values ​​are mapped to initial pseudo-density variables in the interval greater than 0 and less than or equal to 1, thus obtaining the initial pseudo-density variable field.

[0017] In the static analysis phase of the full solid model, structural support points were identified, such as the locations of the four bolt holes connecting the power crossarm to the tower. Fixed displacement boundary conditions were applied to the corresponding nodes, and the three translational degrees of freedom of the nodes were set. = = =0. At the point of load application, such as the insulator suspension point, apply the load vector under rated conditions, for example, along the direction of gravity, i.e., the negative Z-axis direction. A concentrated force of -15000N is applied along the wind load direction, i.e., the Y-axis direction. A concentrated force of 3000N is taken as the value when no additional concentrated force is applied along the X-axis. =0. Based on material properties, such as elastic modulus E = 2.1 × 10⁻⁶. 11 Given Pa, Poisson's ratio ν = 0.3, calculate the stiffness matrix of a single hexahedral finite element. And construct the global stiffness matrix K with a global dimension of 3N×3N through the standard Boolean matrix assembly process, where N is the total number of nodes, for example N=50000.

[0018] Specifically, based on the elastic modulus E and Poisson's ratio ν in the material properties, the constitutive matrix D is determined according to the three-dimensional isotropic linear elastic relationship. For each eight-node hexahedral finite element, the standard isoparametric shape function corresponding to the element type is used as the displacement interpolation function, and the partial derivatives of the shape function with respect to the global spatial coordinates are calculated based on the global coordinates of the eight nodes of the element. The element strain-displacement matrix B is composed of the partial derivatives. Then, the relationship is calculated according to the element stiffness matrix. The stiffness matrix of the element is obtained by numerically integrating over its volume. Based on the global node numbers of the eight local nodes of this element in the finite element mesh, the global degree of freedom numbers corresponding to each local degree of freedom are determined, and a Boolean matrix is ​​established to characterize the correspondence between local and global degrees of freedom. and through stiffness matrix of each element The accumulated components are incorporated into the overall stiffness matrix K, resulting in an overall stiffness matrix K with a global dimension of 3N×3N.

[0019] The large linear algebraic equation system KU=F is solved by using the preprocessing conjugate gradient method, where K is the global stiffness matrix, U is the global displacement vector, and F is the global load vector assembled from the rated load at the load application point, thus obtaining the global displacement vector U containing the three translational degrees of freedom of all nodes.

[0020] Based on the obtained global nodal displacement vector U, the local nodal displacement vector corresponding to each element e is extracted. The element strain vector is calculated by combining the element strain-displacement matrix constructed based on the partial derivatives of the shape functions of the hexahedral element. Then the strain vector Substituting the three-dimensional isotropic linear elastic constitutive relation, according to Calculate the stress vector of this element. Where D is the constitutive matrix determined by the elastic modulus E and Poisson's ratio ν; then according to the stress vector The normal stress component and shear stress component are used to construct the corresponding three-dimensional stress tensor.

[0021] The initial strain energy density of each element is expressed as: ,in Let e ​​be the volume of element e, and assume the strain energy density of a certain element is obtained. =4.5×10 -3 J / m 3 .

[0022] To establish the initial pseudo-density field and identify the maximum and minimum strain energy densities across the entire domain, the strain energy density of each element is linearly normalized using the maximum-minimum normalization formula, yielding the normalized strain energy density value. The normalized strain energy density is mapped to a defined density range. Internally, a mapping formula is used. The initial pseudo-density variables of the corresponding units are obtained, including the lower limit value of the void phase. To reduce the risk of singularity in the stiffness matrix, a value of 0.001 was used to construct an initial pseudo-density variable field representing the initial force flow distribution. The initial pseudo-density variable field of the power crossarm is shown below. Figure 2 As shown.

[0023] S2, enter iterative optimization calculation. In each iteration, the initial design domain is divided into key functional subdomains and transition connection subdomains based on the key node location information. Finite element analysis is performed on the current configuration based on the current pseudo density variable field to obtain the response of each element. An evaluation neighborhood is set based on the subdomain type to which the element belongs, and the local density influence factor is calculated according to the evaluation neighborhood. Topological connectivity analysis is performed on the elements to obtain the main load-bearing structure connectivity domain, and an isolation penalty term is set for elements that do not belong to the main load-bearing structure connectivity domain.

[0024] An iteration counter is set, and a preset subdomain partitioning radius is used as the partitioning radius for critical functional subdomains. Based on the Euclidean distance from the center of each element to the nearest critical node, finite element elements with an Euclidean distance less than or equal to the partitioning radius are partitioned into critical functional subdomains and assigned to the nearest critical node, thus obtaining the local critical functional subdomains corresponding to each critical node. All remaining elements in the finite element set are partitioned into transition connection subdomains. A lower limit for material usage is set for each local critical functional subdomain corresponding to each critical node, constructing corresponding minimum material usage constraints.

[0025] A solid isotropic material penalty model is used as the material interpolation function to calculate the equivalent elastic modulus of the corresponding element based on the pseudo-density variable values ​​of each element in the current iteration step. Specifically, the current pseudo-density variable value of element i is used as the interpolation function. Substitute material interpolation relationship The equivalent elastic modulus of element i is obtained. ;in, The elastic modulus of solid materials, denoted as the lower limit of the elastic modulus of the void phase, and p as the penalty factor.

[0026] The stiffness matrix of each element is recalculated based on the updated element elastic modulus, and the global stiffness matrix of the current iteration step is reassembled according to the finite element assembly relationship. While keeping the displacement constraints at the structural support points and the load conditions at the load application points unchanged, the nodal displacement vector of the current iteration step is solved, and the strain, stress and strain energy density of each element are calculated based on the nodal displacement vector as the response of each element under the current configuration.

[0027] For each central element within the critical functional subdomain, an isotropic evaluation neighborhood is constructed with the centroid of that central element as the center and an isotropic filtering radius is set. For each central element within the transition connection subdomain, a directional evaluation neighborhood is constructed with the current principal stress direction of that central element as the major axis direction. The distance weights between each adjacent element and the central element within the evaluation neighborhood are calculated. The pseudo-density variable values ​​of each adjacent element within the evaluation neighborhood are normalized and weighted using the distance weights to obtain the local density influence factor of that central element.

[0028] Set a connectivity threshold, extract units whose current pseudo-density variable value is greater than the connectivity threshold as entity units, and form a set of entity units; and in the local key functional subdomain corresponding to each key node, select the entity unit with the largest pseudo-density value as the representative entity unit of the corresponding key node, which is used to determine the association relationship between the key node and the continuous entity connected domain.

[0029] Based on the adjacency relationship of shared complete unit surfaces among entity units, a depth-first search algorithm or a breadth-first search algorithm is used to perform connectivity traversal on the entity unit set, resulting in several continuous entity connected regions. For each continuous entity connected region, it is determined whether the continuous entity connected region contains a representative entity unit corresponding to the load application point, and whether it contains a representative entity unit corresponding to at least one structural support point. If the same continuous entity connected region contains both a representative entity unit corresponding to the load application point and a representative entity unit corresponding to at least one structural support point, then the continuous entity connected region is marked as a primary load-bearing candidate connected region. When there are multiple load application points, the above connectivity determination is performed for each load application point, and the union of all primary load-bearing candidate connected regions is set as the primary load-bearing structural connected region. An isolation penalty term equal to 1 is set for entity units belonging to the primary load-bearing structural connected region, and an attenuation coefficient less than 1 and greater than 0 is set as an isolation penalty term for other entity units not belonging to the primary load-bearing structural connected region.

[0030] In an optional embodiment, dividing the initial design domain into a key functional subdomain and a transitional connection subdomain based on the key node location information in each iteration includes: Calculate the Euclidean distance from the center of each element to the nearest critical node within the initial design domain; When the Euclidean distance is less than or equal to the preset subdomain division radius, the corresponding unit is assigned to the key functional subdomain and the corresponding unit is assigned to the local key functional subdomain corresponding to the nearest key node. When the Euclidean distance is greater than the preset subdomain division radius, the corresponding unit is assigned to the transition connection subdomain. A lower volume limit threshold is set for each local key functional subdomain corresponding to each key node, and a local volume constraint equation is constructed for each local key functional subdomain as the minimum material usage constraint.

[0031] During the subdomain partitioning process, the center coordinates of each element i in the finite element mesh are extracted. And a pre-defined set of M key nodes, including the coordinates of load application points and structural support points. .

[0032] For each cell i, calculate the shortest Euclidean distance from the cell center to all critical nodes. A subdomain partitioning radius is predefined. For example, the radius can be set according to the engineering safety margin requirements of bolt holes and connectors. =30mm.

[0033] Iterate through all units and check if the calculated value is... If the value is ≤30mm, it indicates that the element is located in the tightly affected area of ​​a critical stress or connection point. Therefore, the element is marked and classified into the critical functional subdomain. The unit is then assigned to its corresponding local critical functional subdomain according to the principle of the nearest critical node. When the influence areas of multiple key nodes overlap, the unique affiliation of the unit is determined according to the principle of closest distance; conversely, if... If the distance is greater than 30mm, it indicates that the element is far from the connection point, and therefore the element is classified into the transition connection subdomain used for load conduction. The results of dividing the design domain into key functional subdomains and transition connection subdomains are as follows: Figure 3 As shown.

[0034] To ensure the local strength and connection reliability of the power crossarm at critical nodes and to prevent excessive material hollowing out of key stress-bearing areas during optimization, minimum material usage constraints are applied to the defined key functional subdomains. Specifically, based on the coordinate assignment of the key nodes, the key functional subdomains are divided into... Divided into local key functional subdomains corresponding to each key node. And for each local key functional subdomain Set a lower limit for material usage.

[0035] By statistically analyzing each local key functional subdomain The initial total volume of the subdomain is obtained by summing the volumes of all the cells within it. And set a lower limit threshold ratio for the total volume. For example, take =0.85, indicating that each local critical functional subdomain retains at least 85% of its initial total volume of solid material. Local volume constraint equations are constructed. ≤0, where For unit i, the pseudo-density variable, Let i be the intrinsic volume of element i, such as the volume of a single hexahedral element. =8mm 3When participating in the calculation of strain energy density and volume constraints, the element volume is uniformly converted to the same unit system. By applying the local volume constraints to the local key functional subdomains corresponding to each key node, the material retention constraints are distributed near each key node. This local constraint equation is embedded into the overall topology optimization model as a minimum material usage constraint, working in conjunction with the global volume constraints to ensure that the final configuration retains relatively sufficient material thickness near the key connection nodes.

[0036] In an optional embodiment, the step of setting an evaluation neighborhood based on the subdomain type to which the cell belongs and calculating a local density influence factor based on the evaluation neighborhood includes: When a unit belongs to a key functional subdomain, a circular or spherical region is constructed with the center of the unit as the center and a preset isotropic filtering radius as the radius, and all units within the region are regarded as geometrically neighboring units. When a unit belongs to a transitional connection subdomain, an elliptical or ellipsoidal region with a major-to-minor axis ratio greater than 1 is constructed, with the current principal stress direction of the unit as the major axis direction and the principal stress direction orthogonal to the current principal stress direction as the minor axis direction. All units within the region are considered as directional neighboring units. The weighting coefficients are calculated based on the distances between each neighboring cell and the central cell within the evaluation neighborhood. The pseudo-densities of the neighboring cells are then weighted and summed using these weighting coefficients to obtain the local density influence factor.

[0037] When unit i is determined to belong to a key functional subdomain, in order to maintain the three-dimensional isotropic characteristics of the structure of this region, a preset isotropic filtering radius is used with the center coordinates of unit i as the center of the sphere. For example, take 3 times the feature size of the unit. A spherical evaluation area with a radius of 15mm is constructed, and the distance to all centers within the sphere is determined by distance. Element j with a diameter ≤15mm is considered as the geometric neighbor set. .

[0038] When element i is determined to belong to the transitional connection subdomain, in order to promote continuous material growth along the principal force transmission path, the three-dimensional stress tensor of the element is decomposed into eigenvalues ​​to obtain the direction vector corresponding to the first principal stress with the largest absolute value. and the other two orthogonal principal stress directions , ;Build a For long axis, and For the ellipsoidal evaluation region with a minor axis, the ratio α of the major and minor axes is set, for example, α=2.0, the radius of the major axis a=20mm, and the radius of the minor axis b=c=10mm. Elements falling within this ellipsoid and satisfying the directional metric are considered as the set of directional neighboring elements. .

[0039] For the spherical evaluation neighborhood, first calculate the Euclidean distance between neighboring cell j and the central cell i. Divide the Euclidean distance between neighboring cell j and the central cell i by the isotropic filtering radius to obtain the normalized spherical distance. Subtract the normalized spherical distance from 1 to obtain the spherical distance difference. When the spherical distance difference is greater than 0, use the spherical distance difference as the weighting coefficient of neighboring cell j to the central cell i. When the difference in spherical distance is less than or equal to 0, Set to 0.

[0040] For the ellipsoidal evaluation neighborhood, the spatial coordinate difference between neighboring element j and central element i is first transformed into a local principal coordinate system based on the principal stress direction of central element i, obtaining the relative coordinate components of neighboring element j in the major axis direction, the first minor axis direction, and the second minor axis direction of the ellipsoid. The relative coordinate components in the major axis direction are divided by the ellipsoid's major axis radius, and the relative coordinate components in the two minor axis directions are divided by their corresponding ellipsoidal minor axis radii. The three ratios are squared and summed, and the square root of the sum is taken to obtain the normalized ellipsoidal distance. The normalized ellipsoidal distance is subtracted from 1 to obtain the ellipsoidal distance difference. When the ellipsoidal distance difference is greater than 0, it is used as the weighting coefficient of neighboring element j relative to central element i. When the difference in ellipsoidal distance is less than or equal to 0, Set to 0.

[0041] The local density influence factor is calculated by normalizing and weighting the pseudo-densities of all cells in the neighborhood using the obtained weight coefficients. For example, if a transitional connective subdomain cell is surrounded by 20 directional neighboring cells, with a total weight of 12.5 and a weighted pseudo-density product sum of 10.2, then the current local density influence factor of that cell is... =10.2 / 12.5=0.816.

[0042] In an optional embodiment, the step of performing topological connectivity analysis on the units to obtain the main load-bearing structural connectivity domain and setting isolation penalty terms for units that do not belong to the main load-bearing structural connectivity domain includes: Extract the units whose current pseudo-density variable value is greater than the connectivity threshold as entity units, and form a set of entity units; Based on the adjacency relationship of sharing a complete unit surface between entity units, the connected component search algorithm in graph theory is used to traverse the set of entity units to obtain several mutually independent continuous entity connected domains. For each continuous entity connected domain, determine whether the continuous entity connected domain contains a representative entity element corresponding to the load application point, and determine whether it contains a representative entity element corresponding to at least one structural support point. If the same continuous entity connected domain contains both the representative entity element corresponding to the load application point and the representative entity element corresponding to at least one structural support point, then the continuous entity connected domain is marked as the main load-bearing candidate connected domain, and the union of all main load-bearing candidate connected domains is set as the main load-bearing structural connected domain. Entity elements in the entity element set that do not belong to the connected domain of the main load-bearing structure are identified as island elements, and a penalty coefficient greater than 0 and less than 1 is set for the island elements as an isolation penalty term.

[0043] After each iteration completes the static solution, the global finite element mesh is traversed to extract the current pseudo-density variable value. Greater than the preset connectivity threshold The units are used as entity units to form a set of entity units, where The preferred value is 0.4; and a Boolean spatial adjacency matrix is ​​established based on whether the entity units share a complete unit surface; when two entity units share a complete unit surface, the corresponding element in the Boolean spatial adjacency matrix is ​​1, otherwise it is 0, and contact relationships that only share nodes or only share edges are not considered valid connectivity relationships. For each key node, the entity unit with the largest pseudo-density value in its corresponding local key functional subdomain is selected as the representative entity unit of the key node, which is used to determine the association relationship between the key node and the continuous entity connectivity domain.

[0044] Based on the Boolean spatial adjacency matrix, a graph theory connected component search algorithm, such as breadth-first search or depth-first search, is used to traverse the set of entity units. Starting from any unvisited entity unit, all entity units connected to it are found according to the adjacency relations with a value of 1 in the Boolean spatial adjacency matrix, and are grouped into the same continuous entity connected component. This process continues until all entity units have been traversed, resulting in several independent continuous entity connected components, for example, denoted as . , , .

[0045] For each continuous solid connected component, determine whether it contains a representative solid element corresponding to the load application point, and whether it contains a representative solid element corresponding to at least one structural support point. If the same continuous solid connected component contains both a representative solid element corresponding to the load application point and a representative solid element corresponding to at least one structural support point, then mark the continuous solid connected component as a primary load-bearing candidate connected component. When multiple primary load-bearing candidate connected components exist, the union of all primary load-bearing candidate connected components is taken as the primary load-bearing structural connected component. A continuous connected domain that does not simultaneously include the entity element representing the load application point and the entity element representing the structural support point is not marked as a main load-bearing structural connected domain.

[0046] Connect the solid element set to the connected domains that do not belong to the main load-bearing structure. The entity units are classified into the island unit set. .for For each unit in the code, a penalty coefficient greater than 0 and less than 1 is set as the isolation penalty term. For example, set... =0.1. The results of topological connectivity analysis and island unit identification during the iteration process are as follows: Figure 4 As shown.

[0047] S3, calculate the sensitivity of each unit's pseudo-density variable and correct the sensitivity according to the local density influence factor and the isolation penalty term to obtain the corrected sensitivity. Based on the corrected sensitivity, update the pseudo-density variable values ​​of all units under the constraints of global volume and minimum material usage of the key functional subdomain. When the set iterative convergence conditions are met, output the final pseudo-density variable field. Generate the connection configuration of the power crossarm based on the final pseudo-density variable field.

[0048] The initial sensitivity is obtained by calculating the partial derivatives of the objective function with respect to the pseudo-density variables of each element based on the finite element response. The objective function is the global compliance of the power crossarm structure. The initial sensitivity is spatially smoothed using a local density influence factor, and an isolation penalty term is superimposed on isolated elements to reduce the influence of local numerical oscillations and non-connected suspended block materials on the optimization results, thus obtaining the corrected sensitivity.

[0049] An update operator is constructed using the optimal criterion method to calculate the total material volume corresponding to the current pseudo-density variable field and the local material volume of each local critical functional subdomain. An upper limit for the global target volume and a lower limit for the local target volume of each local critical functional subdomain are set. The feasibility between the minimum material usage constraint of the critical functional subdomain and the global volume constraint is assessed, ensuring that the sum of the minimum material volumes required for the local critical functional subdomains corresponding to each critical node does not exceed the globally allowed material volume. If this condition is not met, the subdomain partitioning radius is adjusted. Global volume fraction or lower volume threshold.

[0050] A Lagrangian function is constructed by introducing global volume Lagrange multipliers and local constraint Lagrange multipliers. A bisection method or nested bisection method is used to find Lagrange multipliers that satisfy both the global volume constraint and the minimum material usage constraint for the key functional subdomain. The found Lagrange multipliers and the corrected sensitivity are used to update the pseudo-density variable values ​​of all elements. Simultaneously, a moving limit is used to limit the maximum change in pseudo-density variable values ​​in a single iteration, and the updated pseudo-density variable values ​​are projected onto a preset pseudo-density value range.

[0051] After each iteration, the relative change in global compliance between the current iteration step and the previous iteration step is calculated, and the maximum change in all element pseudo-density variable values ​​between two adjacent iterations is also calculated. The relative change in global compliance is compared with a preset compliance convergence tolerance, and the maximum change is compared with a preset density convergence tolerance. It is then determined whether the current iteration count has reached a preset maximum iteration count. If both the relative change in global compliance and the maximum change are less than their respective convergence tolerances, or if the current iteration count has reached the preset maximum iteration count, the iteration is stopped, and the pseudo-density variable field of the current iteration step is output as the final pseudo-density variable field. Otherwise, the iteration counter is updated, and the process returns to execute the next pseudo-density update and finite element analysis.

[0052] After the topology optimization converges or reaches the preset maximum number of iterations, a configuration generation threshold is set. ,For example Set the value to 0.5. Iterate through the final pseudo-density variable field, selecting those with values ​​greater than 0.5. The unit cell is treated as a solid material unit, and the final pseudo density variable value is no greater than The unit is treated as a non-solid region; the structural surface contour is extracted based on the solid material unit, a three-dimensional surface mesh is generated using the moving cube algorithm, and the three-dimensional surface mesh is smoothed using the Laplacian smoothing algorithm to generate a smooth and continuous three-dimensional solid model of the power crossarm connection configuration, which serves as the structural model basis for engineering verification or manufacturing design.

[0053] In an optional embodiment, the step of calculating the sensitivity of each unit pseudo-density variable and correcting the sensitivity according to the local density influence factor and the isolation penalty term to obtain the corrected sensitivity includes: The initial sensitivity of the objective function to the pseudo-density variables of each unit is calculated based on the adjoint variable method. The initial sensitivity is spatially smoothed using the filtering function corresponding to the local density influence factor to obtain the smoothed sensitivity. When the cell is the islanded cell, the smoothing sensitivity is multiplied by the isolation penalty term to obtain the corrected sensitivity; When the cell is not the islanded cell, the smoothing sensitivity is used as the corrected sensitivity.

[0054] The objective function is to minimize the overall structural compliance. At that time, the objective function is solved based on the adjoint variable method for the pseudo-density variable of element e. The initial sensitivity, when the lower limit of the elastic modulus of the void phase Elastic modulus relative to solid materials When the value is sufficiently small, the sensitivity can be approximated as: Where p is the SIMP interpolation penalty factor, preferably p=3, used to reduce the equivalent stiffness contribution of intermediate pseudo-density elements, so that the pseudo-density variable tends to the solid material state or void state during the iteration process. Let be the element stiffness matrix under full density conditions. Assume that in a certain iteration, the pseudo-density of element e is 0.6, and the local strain energy is 3.2 × 10⁻⁶. -4 J, and the local strain energy of the element is equal to 1 / 2· Therefore, the initial sensitivity is calculated to be -3 × 0.6. 2 ×(2×3.2×10 -4 )≈-6.91×10 -4 .

[0055] Local density influence factor As the density continuity correction coefficient for the central unit i, the filtering formula is: ,in To evaluate the weighting coefficients of the neighborhood computation, the minimum constant γ = 10. -3 The smooth sensitivity of the unit is output after this process. .

[0056] After calculating the smoothing sensitivity, the topology status identifier of each cell is queried. When a cell is identified as belonging to an islanded cell set, the result is obtained. At that time, i.e., in an independent domain where no effective load-bearing connection has been formed, the smoothing sensitivity and isolation penalty term of this unit are considered. ,For example Multiplying by 0.1 yields the corrected sensitivity. This reduces the absolute value of the sensitivity of isolated cells, thus lowering their retention priority during material updates.

[0057] When a cell is identified as not being an isolated cell, the smoothing sensitivity value remains unchanged. This strategy, through gradient scaling, helps to reduce the tendency for free material blocks to continue growing.

[0058] In an optional embodiment, updating the pseudo-density variable values ​​of all cells based on the modified sensitivity under global volume constraints and minimum material usage constraints of the key functional subdomains includes: Construct a Lagrangian function that includes global volume constraints, local volume constraints, and pseudo density upper and lower bound constraints; The optimal criterion method or the moving asymptote method is used as the optimization algorithm to update the Lagrange multipliers based on the modified sensitivity. Calculate the pseudo-density update of each cell in the current iteration step based on the updated Lagrange multipliers; The pseudo-density update amount is superimposed on the current pseudo-density variable value to obtain the updated pseudo-density variable value.

[0059] In the variable update stage of the optimization iteration, the Lagrange function of the constrained optimization problem is constructed based on the Lagrange multiplier method. The objective function c(ρ) represents compliance, and the global volume constraint is weighted by Lagrange multipliers Λ, requiring that the current total material volume V(ρ) is not greater than a set volume fraction. ,like =0.3 and initial total volume The product; local volume constraints are determined by Lagrange multipliers. Weighting ensures that each critical node retains sufficient entity material within its corresponding local critical functional subdomain, such as the local constraint lower limit ratio. =0.85; Superimposed constraints ∈[0.001,1].

[0060] Using the optimality criterion method based on duality theory, the KKT condition equations are constructed at the current iteration step t using the aforementioned modified sensitivity. Then, the global multiplier satisfying the global volume constraint and each local volume constraint is found through an inner-level bisection method or a nested search approach. and each local multiplier In the interval [0, 10 5 Internal iterative optimization until the constraint function residual is less than 10. -5 Find the convergent Lagrange multipliers.

[0061] After obtaining the Lagrange multipliers that satisfy the constraints, the target metric for each unit is calculated based on the corrected sensitivity. Specifically, for unit i, the negative of the corrected sensitivity is first taken; if unit i belongs to a local critical functional subdomain corresponding to a critical node, the Lagrange multiplier corresponding to the local critical functional subdomain is multiplied by the unit's intrinsic volume, and the resulting product is added to the negative of the corrected sensitivity; if unit i does not belong to any local critical functional subdomain, the local constraint term is not added. Then, the above superposition result is divided by the product of the Lagrange multiplier corresponding to the global volume constraint and the unit's intrinsic volume, and a preset minimum positive number is added to the denominator to avoid the denominator being zero, thus obtaining the target metric for unit i. When the calculated target metrics are... Less than the preset minimum positive number At that time, Revised to Since local volume constraints are used to limit the material usage of each key node's corresponding local key functional subdomain to a minimum, the local constraint terms participate in the target metric calculation within the key functional subdomain by increasing the material retention tendency.

[0062] In obtaining target metrics Next, calculate the target metrics. The result is raised to the power of η and compared with the pseudo-density variable value of the current iteration step. Multiply to obtain the target pseudo-density value of cell i; then subtract the pseudo-density variable value of the current iteration step from the target pseudo-density value. The pseudo density to be updated for unit i is obtained, where η is the damping coefficient, preferably 0.5. If the pseudo density to be updated is greater than the movement limit m, the pseudo density update amount is set to +m; if the pseudo density to be updated is less than -m, the pseudo density update amount is set to -m; if the pseudo density to be updated is between -m and +m, the pseudo density to be updated is directly used as the pseudo density update amount.

[0063] The pseudo-density update is added to the current pseudo-density variable value, and the projection is truncated by upper and lower limits to ensure that the updated pseudo-density variable value is not less than the preset pseudo-density lower limit. And not greater than 1, to obtain the pseudo-density variable value for the next iteration. For example, if the current density of a cell is 0.5, the target metric is calculated after multiplication. =1.2, not reaching the movement limit, then update according to the formula to obtain the pseudo-density value of 0.547 for the next iteration. This process completes the synchronous evolution of all variables under the dual volume constraints.

[0064] In the second embodiment, the present invention also proposes a topology for the connection configuration of key nodes of power crossarms and its optimization design system, comprising the following modules: The acquisition module is used to acquire the initial design domain of the power crossarm and the preset key node location information. The key nodes include load application points and structural support points. Based on the initial design domain, finite element mesh is performed to obtain a set of finite element elements. Based on the full solid model of the initial design domain, initial static analysis is performed to obtain the initial strain energy density of each element and the initial pseudo density variable field is set according to the initial strain energy density. The calculation module is used to enter the iterative optimization calculation. In each iteration, the initial design domain is divided into key functional subdomains and transition connection subdomains based on the key node location information. Finite element analysis is performed on the current configuration based on the current pseudo density variable field to obtain the response of each element. An evaluation neighborhood is set based on the subdomain type to which the element belongs and the local density influence factor is calculated according to the evaluation neighborhood. Topological connectivity analysis is performed on the elements to obtain the main load-bearing structure connectivity domain and an isolation penalty term is set for elements that do not belong to the main load-bearing structure connectivity domain. The output module is used to calculate the sensitivity of each unit's pseudo-density variable and correct the sensitivity according to the local density influence factor and the isolation penalty term to obtain the corrected sensitivity. Based on the corrected sensitivity, the pseudo-density variable values ​​of all units are updated under the constraints of global volume and minimum material usage of the key functional subdomain. When the set iterative convergence conditions are met, the final pseudo-density variable field is output, and the connection configuration of the power crossarm is generated based on the final pseudo-density variable field.

[0065] The above description represents the preferred embodiments of the present invention. It should be noted that, for those skilled in the art, various improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A topology for the connection configuration of key nodes in a power crossarm and its optimization design method, characterized in that, Includes the following steps: The initial design domain and preset key node location information of the power crossarm are obtained. The key nodes include load application points and structural support points. Finite element mesh is generated based on the initial design domain to obtain a set of finite element elements. Initial static analysis is performed based on the full solid model of the initial design domain to obtain the initial strain energy density of each element and the initial pseudo density variable field is set according to the initial strain energy density. Entering iterative optimization calculation, in each iteration, the initial design domain is divided into key functional subdomains and transition connection subdomains based on the key node location information. Finite element analysis is performed on the current configuration based on the current pseudo density variable field to obtain the response of each element. An evaluation neighborhood is set based on the subdomain type to which the element belongs, and the local density influence factor is calculated according to the evaluation neighborhood. Topological connectivity analysis is performed on the elements to obtain the main load-bearing structure connectivity domain, and an isolation penalty term is set for elements that do not belong to the main load-bearing structure connectivity domain. The sensitivity of each unit's pseudo-density variable is calculated, and the sensitivity is corrected according to the local density influence factor and the isolation penalty term to obtain the corrected sensitivity. Based on the corrected sensitivity, the pseudo-density variable values ​​of all units are updated under the constraints of global volume and minimum material usage of the key functional subdomain. When the set iterative convergence conditions are met, the final pseudo-density variable field is output, and the connection configuration of the power crossarm is generated based on the final pseudo-density variable field.

2. The method according to claim 1, characterized in that, The initial static analysis of the full solid model based on the initial design domain to obtain the initial strain energy density of each element, and the setting of the initial pseudo-density variable field based on the initial strain energy density, includes: A fixed displacement boundary condition is applied based on the structural support point, and a load vector under rated working conditions is applied based on the load application point; Construct the overall stiffness matrix of the full solid model and assemble the load vector, solve the finite element equilibrium equations to obtain the global nodal displacement vector, and extract the local nodal displacement corresponding to each element; The strain tensor and stress tensor of each element are calculated based on the nodal displacements, and the initial strain energy density of each element is obtained. The initial strain energy density of each element is normalized, and the normalized values ​​are mapped to initial pseudo-density variables in the interval greater than 0 and less than or equal to 1, thus obtaining the initial pseudo-density variable field.

3. The method according to claim 2, characterized in that, The process of dividing the initial design domain into a key functional subdomain and a transitional connection subdomain based on the key node location information in each iteration includes: Calculate the Euclidean distance from the center of each element to the nearest critical node within the initial design domain; When the Euclidean distance is less than or equal to the preset subdomain division radius, the corresponding unit is assigned to the key functional subdomain and the corresponding unit is assigned to the local key functional subdomain corresponding to the nearest key node. When the Euclidean distance is greater than the preset subdomain division radius, the corresponding unit is assigned to the transition connection subdomain. A lower volume limit threshold is set for each local key functional subdomain corresponding to each key node, and a local volume constraint equation is constructed for each local key functional subdomain as the minimum material usage constraint.

4. The method according to claim 1, characterized in that, The process of setting an evaluation neighborhood based on the subdomain type to which the unit belongs and calculating a local density influence factor based on the evaluation neighborhood includes: When a unit belongs to a key functional subdomain, a circular or spherical region is constructed with the center of the unit as the center and a preset isotropic filtering radius as the radius, and all units within the region are regarded as geometrically neighboring units. When a unit belongs to a transitional connection subdomain, an elliptical or ellipsoidal region with a major-minor axis ratio greater than 1 is constructed with the current principal stress direction of the unit as the major axis direction and the principal stress direction orthogonal to the current principal stress direction as the minor axis direction. All units within the region are considered as directional neighboring units. The weighting coefficients are calculated based on the distances between each neighboring cell and the central cell within the evaluation neighborhood. The pseudo-densities of the neighboring cells are then weighted and summed using these weighting coefficients to obtain the local density influence factor.

5. The method according to claim 1, characterized in that, The step of performing topological connectivity analysis on the units to obtain the main load-bearing structural connectivity domain and setting isolation penalty terms for units that do not belong to the main load-bearing structural connectivity domain includes: Extract the units whose current pseudo-density variable value is greater than the connectivity threshold as entity units, and form a set of entity units; Based on the adjacency relationship of sharing a complete unit surface between entity units, the connected component search algorithm in graph theory is used to traverse the set of entity units to obtain several mutually independent continuous entity connected domains. For each continuous entity connected domain, determine whether the continuous entity connected domain contains a representative entity element corresponding to the load application point, and determine whether it contains a representative entity element corresponding to at least one structural support point. If the same continuous entity connected domain contains both the representative entity element corresponding to the load application point and the representative entity element corresponding to at least one structural support point, then the continuous entity connected domain is marked as the main load-bearing candidate connected domain, and the union of all main load-bearing candidate connected domains is set as the main load-bearing structural connected domain. Entity elements in the entity element set that do not belong to the connected domain of the main load-bearing structure are identified as island elements, and a penalty coefficient greater than 0 and less than 1 is set for the island elements as an isolation penalty term.

6. The method according to claim 1, characterized in that, The process of calculating the sensitivity of each unit's pseudo-density variable and correcting the sensitivity based on the local density influence factor and the isolation penalty term to obtain the corrected sensitivity includes: The initial sensitivity of the objective function to the pseudo-density variables of each unit is calculated based on the adjoint variable method. The initial sensitivity is spatially smoothed using the filtering function corresponding to the local density influence factor to obtain the smoothed sensitivity. When the cell is the islanded cell, the smoothing sensitivity is multiplied by the isolation penalty term to obtain the corrected sensitivity; When the cell is not the islanded cell, the smoothing sensitivity is used as the corrected sensitivity.

7. The method according to claim 1, characterized in that, The process of updating the pseudo-density variable values ​​of all elements based on the corrected sensitivity under the constraints of global volume and minimum material usage in the key functional subdomains includes: Construct a Lagrangian function that includes global volume constraints, local volume constraints, and pseudo density upper and lower bound constraints; The optimal criterion method or the moving asymptote method is used as the optimization algorithm to update the Lagrange multipliers based on the modified sensitivity. Calculate the pseudo-density update of each cell in the current iteration step based on the updated Lagrange multipliers; The pseudo-density update amount is superimposed on the current pseudo-density variable value to obtain the updated pseudo-density variable value.

8. A topology for the connection configuration of key nodes of a power crossarm and its optimization design system, characterized in that, Includes the following modules: The acquisition module is used to acquire the initial design domain of the power crossarm and the preset key node location information. The key nodes include load application points and structural support points. Based on the initial design domain, finite element mesh is performed to obtain a set of finite element elements. Based on the full solid model of the initial design domain, initial static analysis is performed to obtain the initial strain energy density of each element and the initial pseudo density variable field is set according to the initial strain energy density. The calculation module is used to enter the iterative optimization calculation. In each iteration, the initial design domain is divided into key functional subdomains and transition connection subdomains based on the key node location information. Finite element analysis is performed on the current configuration based on the current pseudo density variable field to obtain the response of each element. An evaluation neighborhood is set based on the subdomain type to which the element belongs and the local density influence factor is calculated according to the evaluation neighborhood. Topological connectivity analysis is performed on the elements to obtain the main load-bearing structure connectivity domain and an isolation penalty term is set for elements that do not belong to the main load-bearing structure connectivity domain. The output module is used to calculate the sensitivity of each unit's pseudo-density variable and correct the sensitivity according to the local density influence factor and the isolation penalty term to obtain the corrected sensitivity. Based on the corrected sensitivity, the pseudo-density variable values ​​of all units are updated under the constraints of global volume and minimum material usage of the key functional subdomain. When the set iterative convergence conditions are met, the final pseudo-density variable field is output, and the connection configuration of the power crossarm is generated based on the final pseudo-density variable field.

9. The system according to claim 8, characterized in that, The initial static analysis of the full solid model based on the initial design domain to obtain the initial strain energy density of each element, and the setting of the initial pseudo-density variable field based on the initial strain energy density, includes: A fixed displacement boundary condition is applied based on the structural support point, and a load vector under rated working conditions is applied based on the load application point; Construct the overall stiffness matrix of the full solid model and assemble the load vector, solve the finite element equilibrium equations to obtain the global nodal displacement vector, and extract the local nodal displacement corresponding to each element; The strain tensor and stress tensor of each element are calculated based on the nodal displacements, and the initial strain energy density of each element is obtained. The initial strain energy density of each element is normalized, and the normalized values ​​are mapped to initial pseudo-density variables in the interval greater than 0 and less than or equal to 1, thus obtaining the initial pseudo-density variable field.

10. The system according to claim 8, characterized in that, The process of dividing the initial design domain into a key functional subdomain and a transitional connection subdomain based on the key node location information in each iteration includes: Calculate the Euclidean distance from the center of each element to the nearest critical node within the initial design domain; When the Euclidean distance is less than or equal to the preset subdomain division radius, the corresponding unit is assigned to the key functional subdomain and the corresponding unit is assigned to the local key functional subdomain corresponding to the nearest key node. When the Euclidean distance is greater than the preset subdomain division radius, the corresponding unit is assigned to the transition connection subdomain. A lower volume limit threshold is set for each local key functional subdomain corresponding to each key node, and a local volume constraint equation is constructed for each local key functional subdomain as the minimum material usage constraint.

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