Robust topology optimization method for continuous fiber multi-lane containment capability

Abstract

The present application relates to the technical field of computer aided design and structural topology optimization data processing, and discloses a robust topology optimization method with continuous fiber multi-channel accommodation capacity, comprising: obtaining grid data and target structure width, constructing a physical density field through multi-threshold projection; solving a finite element equation to extract flexibility contribution and smooth truncation, performing anisotropic strip convolution integration according to the principal feature direction of the structure tensor to obtain a local effective width; calculating a smooth width gap and combining mechanical weighting to construct a differentiable manufacturing constraint function; solving a chain sensitivity to update design variables and output target topology data; the present application converts discrete fiber size into continuous differentiable constraints, guides material to actively converge in the main force transmission path, eliminates material dissipation in non-critical areas, and eliminates the accommodation bottleneck in the key load-bearing area while ensuring the stiffness of the structure.

Description

Technical Field

[0001] This invention belongs to the field of computer-aided design and structural topology optimization data processing technology, and particularly relates to a robust topology optimization method for the multi-channel capacity of continuous fibers. Background Technology

[0002] In structural topology optimization and computer-aided engineering numerical calculations, algorithms based on variable density material interpolation automatically generate lightweight structural topology density distribution data through finite element analysis and gradient search iteration, based on preset mechanical boundaries and material usage limits. This type of numerical method is widely used in the design of continuous fiber reinforced composite structures, aiming to determine clear mechanical force transmission paths through algorithmic optimization. Continuous fiber forming processes have clear requirements for single-pass width, inter-pass net distance, and matrix coverage, requiring the load-bearing components to have sufficient lateral solid dimensions to accommodate a preset number of fiber passes. Conventional topology optimization algorithms mainly aim at minimizing global flexibility and volume fraction. The optimization iteration only updates the element density based on mechanical stiffness sensitivity, and cannot perceive the local geometric dimensions' requirements for fiber laying during calculation. This leads to thin rods and narrow neck defects in the generated topology data in the main force transmission branches. If the fiber path is corrected or manually reinforced after topology generation, it can easily cause excessive local bending of the fibers or even destroy the original mechanical force transmission configuration.

[0003] To eliminate narrow features, existing technologies often introduce global morphological filtering or isotropic minimum size constraint operators. However, when the total volume of the structure is limited, the global indiscriminate size penalty causes material to diffuse towards the low-load edge, resulting in insufficient material distribution in the main force transmission branches and increased flexibility. At the same time, it is difficult to backpropagate analytical derivatives from discrete skeleton-based size measurements to continuous topological variables, which easily leads to optimization iteration oscillations. Existing topology optimization data processing methods mainly have the following defects: 1. Discrete multi-fiber dimensions are difficult to establish continuous differentiable mathematical proxies, resulting in the inability to participate in the analytical sensitivity solution of design variables through the chain rule for accommodating gaps; 2. Global uniform size constraints lack spatial weighting adjustment based on local strain energy distribution, resulting in ineffective material dissipation to non-critical areas and weakening the load-bearing capacity of critical paths; 3. The strain energy values ​​of boundary supports and load concentration areas easily dominate the global constraint response, causing the optimization algorithm to oscillate in the search direction and reducing the computational convergence stability.

[0004] Therefore, the technical problem to be solved by this invention is how to transform the multi-stage forming dimensions of continuous fibers into continuous differentiable geometric proxies, and combine the contribution of local mechanical bearing capacity to adaptively guide the material to directionally supplement the main force transmission branch in the optimization iteration. Summary of the Invention

[0005] In this technical solution, a robust topology optimization method for the multi-channel capacity of continuous fibers includes the following steps: Step S1: Obtain the design domain mesh data, load constraints, target fiber number, and target structural width calculated from single fiber forming width, inter-fiber spacing, matrix covering width, and manufacturing allowance. Step S2: Filter and perform multi-threshold projection calculations on the design variable field to obtain the erosion physical density field, nominal physical density field, and dilation physical density field. Step S3: Construct the finite element equilibrium equation based on the erosion physical density field, solve the displacement field and extract the compliance contribution of each mesh element, and perform smooth truncation on the compliance contribution to obtain the mechanical weighting coefficient. Step S4: Construct a structure tensor based on the density gradient of the nominal physical density field to determine the principal feature direction, and perform anisotropic strip convolution integral on the physical density distribution along the normal of the principal feature direction to obtain the local effective width of each grid cell. Step S5: Calculate the smooth width gap of each grid cell based on the local effective width and the target structure width, and perform weighted spatial aggregation of the smooth width gap using mechanical weighting coefficients to construct a differentiable manufacturing constraint function; Step S6: Solve the chain sensitivity of the structural compliance objective function and the differentiable manufacturing constraint function to the design variable field. Update the design variable field according to the chain sensitivity until convergence, and output the target topological physical density field data.

[0006] Preferably, step S2 includes the following sub-steps: Step S21, under a preset physical filtering radius, isotropic linear weighted filtering is applied to the design variable field to generate a filtering density field; Step S22, smoothing projection parameters are set, and the filtering density field is mapped to multiple thresholds using a hyperbolic tangent projection function; wherein, the erosion physical density field characterizing unfavorable manufacturing tolerances is obtained by using the first threshold projection, the nominal physical density field characterizing the theoretical geometric boundary is obtained by using the second threshold projection, and the expansion physical density field characterizing the maximum material boundary is obtained by using the third threshold projection, and the first threshold is greater than the second threshold, and the second threshold is greater than the third threshold.

[0007] Preferably, the process of constructing the structure tensor to determine the principal feature direction in step S4 includes the following sub-steps: Step S41, Gaussian smoothing filter is applied to the nominal physical density field to extract the smooth density gradient vector; Step S42, the second-order moment tensor matrix of the smooth density gradient vector is accumulated in the preset local neighborhood of each grid cell, and a regularization matrix is ​​superimposed to construct the local structure tensor; Step S43, the principal feature vector of the local structure tensor is solved, and it is used as the local normal vector representing the transverse boundary of the candidate fiber, and the direction orthogonal to the local normal vector is used as the tangential vector of the candidate fiber; Step S44, the direction vector between adjacent optimization iterations is smoothly tracked using a two-angle complex transformation to eliminate the sign jump of the principal feature vector.

[0008] Preferably, the process of performing anisotropic strip convolution integration of the physical density distribution along the normal direction of the main feature direction in step S4 includes the following sub-steps: Step S45, taking the center of each grid cell as the reference, setting a minor axis statistical window along the tangential vector of the candidate fiber, and setting equally spaced normal sampling sections along the local normal vector; Step S46, using anisotropic Gaussian kernel function to calculate the continuous weight between each normal sampling section and the neighboring grid cells, and obtaining the weighted average density at each normal sampling section; Step S47, calculating the material occupancy rate at each normal sampling section through a continuously differentiable monotonically smooth step function; Step S48, performing discrete integration of the material occupancy rate at each normal sampling section along the local normal vector, and obtaining the local effective width at each grid cell.

[0009] Preferably, the process of calculating the smooth width gap of each grid cell in step S5 includes the following sub-steps: Step S51, calculate the relative width deficiency between the local effective width and the target structure width at each grid cell; Step S52, input the relative width deficiency into a continuously differentiable smooth extremum approximation function, and output the smooth width gap at each grid cell; wherein, when the local effective width is greater than the target structure width, the smooth width gap monotonically decreases and approaches zero; when the local effective width is less than the target structure width, the smooth width gap monotonically increases linearly.

[0010] Preferably, the process of smoothing and truncating the compliance contribution to obtain the mechanical weighting coefficient in step S3 includes the following sub-steps: Step S31, construct the stiffness matrix based on the erosion physical density field and solve the finite element equation, calculate the element strain energy of each grid element, and use it as the untruncated compliance contribution; Step S32, extract the smoothed mean of the compliance contribution in the non-load-supported interface region, and set the upper limit truncation threshold of the compliance contribution; Step S33, use a continuously differentiable smoothing truncation function to perform extreme value suppression processing on the compliance contribution of each grid element, replace the values ​​exceeding the upper limit truncation threshold of the compliance contribution with the smoothing upper limit boundary value, and generate the mechanical weighting coefficient.

[0011] Preferably, the process of constructing the differentiable manufacturing constraint function in step S5 includes the following sub-steps: Step S53, multiply the mechanical weighting coefficient at each grid cell by the corresponding smooth width gap point by point to calculate the weighted gap sum of the grid cells in the entire design domain; Step S54, calculate the sum of the mechanical weighting coefficients of the grid cells in the entire design domain, and divide the weighted gap sum by the sum of the mechanical weighting coefficients to generate the load-bearing weighted average containment gap; Step S55, construct the difference between the load-bearing weighted average containment gap and the preset manufacturing tolerance threshold as a scalar form of the differentiable manufacturing constraint function.

[0012] Preferably, the process of solving the chain sensitivity in step S6 includes the following sub-steps: Step S61, deriving the partial derivatives of the differentiable manufacturing constraint function with respect to the smooth width notch and the mechanical weighting coefficients; Step S62, combining the smooth extremum approximation function and the anisotropic strip convolution integral scheme, deriving the first partial derivative of the smooth width notch with respect to the physical density field; Step S63, solving the second partial derivative of the mechanical weighting coefficients with respect to the physical density field using the adjoint variable method; Step S64, combining the first and second partial derivatives to form the total partial derivative of the differentiable manufacturing constraint function with respect to the physical density field, and then backpropagating it to the design variable field through the transpose of the multi-threshold projection derivative and the filter convolution matrix to obtain the analytical manufacturing constraint sensitivity with respect to the design variable field.

[0013] Preferably, the process of updating the design variable field until convergence in step S6 includes the following sub-steps: Step S65, taking the minimization of structural compliance under the erosion physical density field as the objective function and the upper limit of material volume under the expansion physical density field as the volume constraint function, and jointly constructing a multi-constraint topology optimization model with the differentiable manufacturing constraint function; Step S66, based on the analytical sensitivity of each objective function and constraint function with respect to the design variable field, using the moving asymptote optimization algorithm to solve the convex quadratic problem within a preset design variable variation step size, and updating the design variable field; Step S67, gradually increasing the projection smoothing parameter in each optimization iteration step until the preset maximum continuous projection parameter, and terminating the iteration when the relative change of the objective function and the residual of the differentiable manufacturing constraint function both satisfy the preset convergence threshold, and outputting the final target topology physical density field data.

[0014] Compared with existing technologies, the robust topology optimization method for multi-channel capacity of continuous fibers described in this invention has the following advantages: 1. This invention decomposes the multi-fiber forming dimensions into continuous width requirements, combines the structural tensor of smooth physical density distribution to track local orientation, and uses anisotropic kernel functions to construct a continuous differentiable spatial strip geometric proxy. This transforms discrete process geometric gaps into smooth and continuous gap responses, establishes a direct analytical sensitivity feedback path for local accommodation indexes to design variables, eliminates the computational contradiction in structural topology optimization where discrete manufacturing dimensions are difficult to participate in gradient calculations, and enables the optimization algorithm to adaptively adjust the cross-sectional width of the force transmission branches during structural evolution, ensuring that the calculated topological density field directly possesses the geometric accommodation space required for multi-fiber laying.

[0015] 2. This invention obtains the load-bearing contribution of each element by extracting the strain energy density distribution of the finite element method, and introduces the load-bearing contribution as a spatial weighting factor into the aggregation function of the local width gap. This allows the update energy of the optimization gradient to actively converge on the main force transmission path. Under the condition of a given upper limit of material volume, it changes the problem of non-critical edge material accumulation and stiffness degradation in the main load-bearing area caused by uniform thickening across the entire domain. It enables the material to prioritize the compensation of the geometric width of the high stress transmission branch, achieving synergistic optimization of stiffness transmission efficiency and geometric accommodation size. It eliminates the width bottleneck of the main load-bearing area at a lower flexibility cost, and improves the overall mechanical load-bearing efficiency of the structure topology under the multi-fiber reinforcement layout.

[0016] 3. This invention introduces a smooth cutoff function into the load-bearing weight mapping to suppress the abnormal strain energy values ​​generated by concentrated loads and constrained support regions through continuous differentiability. This maintains the monotonic transmission of the strain energy gradient in the internal region, eliminates the abnormal dominance of boundary local stress concentration singularities on the search direction of the moving asymptote optimization algorithm, avoids sensitivity oscillations and design variable update stagnation caused by weight mutations, maintains numerical stability and iterative smoothness when solving multiple manufacturing constraints collaboratively, significantly reduces the number of iterative oscillation steps of the optimization algorithm in non-convex constraint space, shortens the computation time of topology optimization, and improves the solution convergence reliability of the structural topology data calculation system. Attached Figure Description

[0017] Figure 1 This is a flowchart of the topology optimization process that integrates local effective width and mechanical weighting according to the present invention; Figure 2 This is a schematic diagram of the data interaction architecture between the multi-threshold density field and the optimization solution module of the present invention; Figure 3 This is a schematic diagram comparing the mechanical and geometric bottleneck performance of the present invention under different topological constraint conditions. Detailed Implementation

[0018] The technical solutions of the embodiments of this application will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application are within the scope of protection of this application.

[0019] A robust topology optimization method for multi-channel capacity of continuous fibers includes the following steps: Step S1: Obtain the design domain mesh data, load constraints, target fiber number, and target structural width calculated from single fiber forming width, inter-fiber spacing, matrix covering width, and manufacturing allowance. Step S2: Filter and perform multi-threshold projection calculations on the design variable field to obtain the erosion physical density field, nominal physical density field, and dilation physical density field. Step S3: Construct the finite element equilibrium equation based on the erosion physical density field, solve the displacement field and extract the compliance contribution of each mesh element, and perform smooth truncation on the compliance contribution to obtain the mechanical weighting coefficient. Step S4: Construct a structure tensor based on the density gradient of the nominal physical density field to determine the principal feature direction, and perform anisotropic strip convolution integral on the physical density distribution along the normal of the principal feature direction to obtain the local effective width of each grid cell. Step S5: Calculate the smooth width gap of each grid cell based on the local effective width and the target structure width, and perform weighted spatial aggregation of the smooth width gap using mechanical weighting coefficients to construct a differentiable manufacturing constraint function; Step S6: Solve the chain sensitivity of the structural compliance objective function and the differentiable manufacturing constraint function to the design variable field. Update the design variable field according to the chain sensitivity until convergence, and output the target topological physical density field data.

[0020] Preferably, step S2 includes the following sub-steps: Step S21, under a preset physical filtering radius, isotropic linear weighted filtering is applied to the design variable field to generate a filtering density field; Step S22, smoothing projection parameters are set, and the filtering density field is mapped to multiple thresholds using a hyperbolic tangent projection function; wherein, the erosion physical density field characterizing unfavorable manufacturing tolerances is obtained by using the first threshold projection, the nominal physical density field characterizing the theoretical geometric boundary is obtained by using the second threshold projection, and the expansion physical density field characterizing the maximum material boundary is obtained by using the third threshold projection, and the first threshold is greater than the second threshold, and the second threshold is greater than the third threshold.

[0021] Preferably, the process of constructing the structure tensor to determine the principal feature direction in step S4 includes the following sub-steps: Step S41, Gaussian smoothing filter is applied to the nominal physical density field to extract the smooth density gradient vector; Step S42, the second-order moment tensor matrix of the smooth density gradient vector is accumulated in the preset local neighborhood of each grid cell, and a regularization matrix is ​​superimposed to construct the local structure tensor; Step S43, the principal feature vector of the local structure tensor is solved, and it is used as the local normal vector representing the transverse boundary of the candidate fiber, and the direction orthogonal to the local normal vector is used as the tangential vector of the candidate fiber; Step S44, the direction vector between adjacent optimization iterations is smoothly tracked using a two-angle complex transformation to eliminate the sign jump of the principal feature vector.

[0022] Preferably, the process of performing anisotropic strip convolution integration of the physical density distribution along the normal direction of the main feature direction in step S4 includes the following sub-steps: Step S45, taking the center of each grid cell as the reference, setting a minor axis statistical window along the tangential vector of the candidate fiber, and setting equally spaced normal sampling sections along the local normal vector; Step S46, using anisotropic Gaussian kernel function to calculate the continuous weight between each normal sampling section and the neighboring grid cells, and obtaining the weighted average density at each normal sampling section; Step S47, calculating the material occupancy rate at each normal sampling section through a continuously differentiable monotonically smooth step function; Step S48, performing discrete integration of the material occupancy rate at each normal sampling section along the local normal vector, and obtaining the local effective width at each grid cell.

[0023] Preferably, the process of calculating the smooth width gap of each grid cell in step S5 includes the following sub-steps: Step S51, calculate the relative width deficiency between the local effective width and the target structure width at each grid cell; Step S52, input the relative width deficiency into a continuously differentiable smooth extremum approximation function, and output the smooth width gap at each grid cell; wherein, when the local effective width is greater than the target structure width, the smooth width gap monotonically decreases and approaches zero; when the local effective width is less than the target structure width, the smooth width gap monotonically increases linearly.

[0024] Preferably, the process of smoothing and truncating the compliance contribution to obtain the mechanical weighting coefficient in step S3 includes the following sub-steps: Step S31, construct the stiffness matrix based on the erosion physical density field and solve the finite element equation, calculate the element strain energy of each grid element, and use it as the untruncated compliance contribution; Step S32, extract the smoothed mean of the compliance contribution in the non-load-supported interface region, and set the upper limit truncation threshold of the compliance contribution; Step S33, use a continuously differentiable smoothing truncation function to perform extreme value suppression processing on the compliance contribution of each grid element, replace the values ​​exceeding the upper limit truncation threshold of the compliance contribution with the smoothing upper limit boundary value, and generate the mechanical weighting coefficient.

[0025] Preferably, the process of constructing the differentiable manufacturing constraint function in step S5 includes the following sub-steps: Step S53, multiply the mechanical weighting coefficient at each grid cell by the corresponding smooth width gap point by point to calculate the weighted gap sum of the grid cells in the entire design domain; Step S54, calculate the sum of the mechanical weighting coefficients of the grid cells in the entire design domain, and divide the weighted gap sum by the sum of the mechanical weighting coefficients to generate the load-bearing weighted average containment gap; Step S55, construct the difference between the load-bearing weighted average containment gap and the preset manufacturing tolerance threshold as a scalar form of the differentiable manufacturing constraint function.

[0026] Preferably, the process of solving the chain sensitivity in step S6 includes the following sub-steps: Step S61, deriving the partial derivatives of the differentiable manufacturing constraint function with respect to the smooth width notch and the mechanical weighting coefficients; Step S62, combining the smooth extremum approximation function and the anisotropic strip convolution integral scheme, deriving the first partial derivative of the smooth width notch with respect to the physical density field; Step S63, solving the second partial derivative of the mechanical weighting coefficients with respect to the physical density field using the adjoint variable method; Step S64, combining the first and second partial derivatives to form the total partial derivative of the differentiable manufacturing constraint function with respect to the physical density field, and then backpropagating it to the design variable field through the transpose of the multi-threshold projection derivative and the filter convolution matrix to obtain the analytical manufacturing constraint sensitivity with respect to the design variable field.

[0027] Preferably, the process of updating the design variable field until convergence in step S6 includes the following sub-steps: Step S65, taking the minimization of structural compliance under the erosion physical density field as the objective function and the upper limit of material volume under the expansion physical density field as the volume constraint function, and jointly constructing a multi-constraint topology optimization model with the differentiable manufacturing constraint function; Step S66, based on the analytical sensitivity of each objective function and constraint function with respect to the design variable field, using the moving asymptote optimization algorithm to solve the convex quadratic problem within a preset design variable variation step size, and updating the design variable field; Step S67, gradually increasing the projection smoothing parameter in each optimization iteration step until the preset maximum continuous projection parameter, and terminating the iteration when the relative change of the objective function and the residual of the differentiable manufacturing constraint function both satisfy the preset convergence threshold, and outputting the final target topology physical density field data.

[0028] Example 1: This example combines Figures 1 to 3 A robust topology optimization method for multi-channel capacity of continuous fibers is described, such as... Figure 1 As shown, the design domain mesh data and parameters are obtained, along with load constraints, target fiber count, and target structural width. Filtering and multi-threshold projection calculations are performed on the obtained mesh data and parameters to generate erosion physical density fields, nominal physical density fields, and dilatation physical density fields. The erosion physical density field is input into a compliance contribution smoothing and truncation processing module to extract the compliance contribution of each mesh element and perform smoothing and truncation to obtain mechanical weighting coefficients. The nominal physical density field is input into an anisotropic strip convolution integration module to determine the principal characteristic direction based on the structural tensor, and integral along the normal direction of the principal characteristic direction to obtain the local effective width of each mesh element. A differentiable manufacturing constraint function is constructed based on the mechanical weighting coefficients and the local effective width of each mesh element to calculate the smooth width gap, and weighted space aggregation is performed in conjunction with the mechanical weighting coefficients. Chain sensitivity solving and updating are performed based on the constructed differentiable manufacturing constraint function, calculating the chain sensitivity and updating the design variable field. If the updated design variable field does not converge, the non-converged updated design variable field is executed and returned to the filtering and multi-threshold projection calculations. When the updated design variable field meets the convergence threshold, the target topological physical density field data is output.

[0029] like Figure 2 As shown, multi-threshold projection calculations generate erosion physical density fields, nominal physical density fields, and dilatational physical density fields. The finite element equation includes compliance contributions and flows unidirectionally from top to bottom to the mechanical weighting coefficients. The structural tensor includes principal characteristic directions and flows unidirectionally from top to bottom to the local effective width. The moving asymptote optimization algorithm includes differentiable manufacturing constraint functions, chain sensitivity, and target topological physical density field data, presenting a top-down flow output structure. The erosion physical density field in the multi-threshold projection calculation is unidirectionally transmitted to the compliance contributions in the finite element equation through dashed lines. The nominal physical density field is unidirectionally transmitted to the principal characteristic directions in the structural tensor through dashed lines. The dilatational physical density field is directly transmitted to the differentiable manufacturing constraint functions in the moving asymptote optimization algorithm through vertical dashed lines. The output of the finite element equation is unidirectionally connected to the chain sensitivity in the moving asymptote optimization algorithm through dashed lines. The output of the structural tensor is unidirectionally connected to the target topological physical density field data in the moving asymptote optimization algorithm through dashed lines. The final data output flow is led out from the bottom of the moving asymptote optimization algorithm.

[0030] like Figure 3 As shown, the nominal flexibility change rate and the high load-bearing three-bottleneck elimination rate exhibit a comparative response distribution under three working conditions: no fiber channel constraint, global uniform thickening, and load-bearing weighted directional widening. In the nominal flexibility change rate index, with the relative unconstrained baseline (%) as the vertical axis scale, no fiber channel constraint corresponds to 0% baseline, global uniform thickening corresponds to 4.5% column height, and load-bearing weighted directional widening corresponds to 2.5% column height. In the high load-bearing three-bottleneck elimination rate index, with the bottleneck length elimination rate (%) as the vertical axis scale and a 0.0% horizontal baseline set, no fiber channel constraint is located on the baseline, global uniform thickening extends downward to the -10.5% scale position, and load-bearing weighted directional widening extends upward to the 6.0% scale position. Under the condition that the nominal flexibility change rate of the relative unconstrained baseline is maintained at 2.5% column height, the load-bearing weighted directional widening corresponds to a high load-bearing three-bottleneck elimination rate in the positive distribution range of 6.0%.

[0031] The embodiments of this application have been described above with reference to the accompanying drawings. Unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other. This application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of this application.

Claims

1. A robust topology optimization method for the multi-channel capacity of continuous fibers, characterized in that, Includes the following steps: Step S1: Obtain the design domain mesh data, load constraints, target fiber number, and target structural width calculated from single fiber forming width, inter-fiber spacing, matrix covering width, and manufacturing allowance. Step S2: Filter and perform multi-threshold projection calculations on the design variable field to obtain the erosion physical density field, nominal physical density field, and dilation physical density field. Step S3: Construct the finite element equilibrium equation based on the erosion physical density field, solve the displacement field and extract the compliance contribution of each mesh element, and perform smooth truncation on the compliance contribution to obtain the mechanical weighting coefficient. Step S4: Construct a structure tensor based on the density gradient of the nominal physical density field to determine the principal feature direction, and perform anisotropic strip convolution integral on the physical density distribution along the normal of the principal feature direction to obtain the local effective width of each grid cell. Step S5: Calculate the smooth width gap of each grid cell based on the local effective width and the target structure width, and perform weighted spatial aggregation of the smooth width gap using mechanical weighting coefficients to construct a differentiable manufacturing constraint function; Step S6: Solve the chain sensitivity of the structural compliance objective function and the differentiable manufacturing constraint function to the design variable field. Update the design variable field according to the chain sensitivity until convergence, and output the target topological physical density field data.

2. The robust topology optimization method for multi-channel capacity of continuous fibers according to claim 1, characterized in that, Step S2 includes the following sub-steps: Step S21, under a preset physical filtering radius, the design variable field is subjected to isotropic linear weighted filtering to generate a filtering density field; Step S22, set smoothing projection parameters and use the hyperbolic tangent projection function to perform multi-threshold mapping on the filtering density field; wherein, the first threshold projection is used to obtain the erosion physical density field characterizing unfavorable manufacturing tolerances, the second threshold projection is used to obtain the nominal physical density field characterizing the theoretical geometric boundary, and the third threshold projection is used to obtain the expansion physical density field characterizing the maximum material boundary, and the first threshold is greater than the second threshold, and the second threshold is greater than the third threshold.

3. The robust topology optimization method for multi-channel capacity of continuous fibers according to claim 1, characterized in that, The process of constructing the structure tensor to determine the principal feature direction in step S4 includes the following sub-steps: Step S41, Gaussian smoothing filter is applied to the nominal physical density field to extract the smooth density gradient vector; Step S42, the second-order moment tensor matrix of the smooth density gradient vector is accumulated in the preset local neighborhood of each grid cell, and a regularization matrix is ​​superimposed to construct the local structure tensor; Step S43, the principal feature vector of the local structure tensor is solved, and it is used as the local normal vector representing the lateral boundary of the candidate fiber, and the direction orthogonal to the local normal vector is used as the tangential vector of the candidate fiber; Step S44, the direction vector between adjacent optimization iterations is smoothly tracked using a two-angle complex transformation.

4. The robust topology optimization method for multi-channel capacity of continuous fibers according to claim 3, characterized in that, The process of performing anisotropic strip convolution integral of the physical density distribution along the normal direction of the main feature direction in step S4 includes the following sub-steps: Step S45, with the center of each grid cell as the reference, set the minor axis statistical window along the tangential vector of the candidate fiber, and set equally spaced normal sampling sections along the local normal vector; Step S46, use the anisotropic Gaussian kernel function to calculate the continuous weight between each normal sampling section and the neighboring grid cells to obtain the weighted average density at each normal sampling section; Step S47, calculate the material occupancy rate at each normal sampling section through a continuously differentiable monotonically smooth step function; Step S48, perform discrete integral of the material occupancy rate at each normal sampling section along the local normal vector to obtain the local effective width at each grid cell.

5. A robust topology optimization method for multi-channel capacity of continuous fibers according to claim 1, characterized in that, The process of calculating the smooth width gap of each grid cell in step S5 includes the following sub-steps: Step S51, calculate the relative width deficiency between the local effective width and the target structure width at each grid cell; Step S52, input the relative width deficiency into a continuously differentiable smooth extremum approximation function, and output the smooth width gap at each grid cell; wherein, when the local effective width is greater than the target structure width, the smooth width gap monotonically decreases and approaches zero; when the local effective width is less than the target structure width, the smooth width gap monotonically increases linearly.

6. The robust topology optimization method for multi-channel capacity of continuous fibers according to claim 1, characterized in that, The process of smoothing and truncating the compliance contribution in step S3 to obtain the mechanical weighting coefficient includes the following sub-steps: Step S31, construct the stiffness matrix based on the erosion physical density field and solve the finite element equation, calculate the element strain energy of each grid element, and use it as the untruncated compliance contribution. Step S32: Extract the smoothed mean value of the compliance contribution in the non-load-supported interface region and set the upper limit truncation threshold of the compliance contribution; Step S33: Use a continuously differentiable smoothing truncation function to perform extreme value suppression processing on the compliance contribution of each grid element, replace the values ​​exceeding the upper limit truncation threshold of the compliance contribution with the smoothing upper limit boundary value, and generate mechanical weighting coefficients.

7. A robust topology optimization method for multi-channel capacity of continuous fibers according to claim 1, characterized in that, The process of constructing the differentiable manufacturing constraint function in step S5 includes the following sub-steps: Step S53, multiply the mechanical weighting coefficient at each grid cell by the corresponding smooth width gap point by point to calculate the weighted gap sum of the grid cells in the entire design domain; Step S54, calculate the sum of the mechanical weighting coefficients of the grid cells in the entire design domain, and divide the weighted gap sum by the sum of the mechanical weighting coefficients to generate the load-bearing weighted average containment gap; Step S55, construct the difference between the load-bearing weighted average containment gap and the preset manufacturing tolerance threshold as a scalar form of the differentiable manufacturing constraint function.

8. A robust topology optimization method for multi-channel capacity of continuous fibers according to claim 1, characterized in that, The process of solving the chain sensitivity in step S6 includes the following sub-steps: Step S61, derive the partial derivatives of the differentiable manufacturing constraint function with respect to the smooth width notch and the mechanical weighting coefficients; Step S62, combine the smooth extremum approximation function and the anisotropic strip convolution integral scheme to derive the first partial derivative of the smooth width notch with respect to the physical density field; Step S63, use the adjoint variable method to solve the second partial derivative of the mechanical weighting coefficients with respect to the physical density field; Step S64, combine the first and second partial derivatives to synthesize the total partial derivative of the differentiable manufacturing constraint function with respect to the physical density field, and backpropagate it to the design variable field through the multi-threshold projection derivative and the transpose of the filter convolution matrix to obtain the analytical manufacturing constraint sensitivity with respect to the design variable field.

9. A robust topology optimization method for multi-channel capacity of continuous fibers according to claim 1, characterized in that, The process of updating the design variable field until convergence in step S6 includes the following sub-steps: Step S65, with minimizing the structural compliance under the erosion physical density field as the objective function and the upper limit of the material volume under the expansion physical density field as the volume constraint function, a multi-constraint topology optimization model is constructed in conjunction with the differentiable manufacturing constraint function; Step S66, based on the analytical sensitivity of each objective function and constraint function with respect to the design variable field, the moving asymptote optimization algorithm is used to solve the convex quadratic problem within the preset design variable variation step size, and the design variable field is updated; Step S67, the projection smoothing parameter is gradually increased in each optimization iteration step until the preset maximum continuous projection parameter is reached, and the iteration is terminated when the relative change of the objective function and the residual of the differentiable manufacturing constraint function both meet the preset convergence threshold, and the final target topology physical density field data is output.

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