A finite element deformation analysis method for DLP light-cured 3D printing

Abstract

The application discloses a finite element deformation analysis method for DLP light curing 3D printing, and belongs to the technical field of additive manufacturing process simulation. The application constructs an integrated analysis mechanism which is coupled with macro layer equivalent curing and discrete support release and takes the unified finite element analysis core as the pivot. The whole grid layer is avoided to be divided layer by layer to avoid complex model geometric division, and the analysis step quantity is reduced to improve the solving efficiency by relying on the macro layer equivalent curing. The material stiffness evolution and intrinsic shrinkage strain loading are realized simultaneously based on the curing degree field variable, and the discrete support nodes are automatically identified by combining the adjacent macro layer geometric projection relationship. The residual stress evolution process under the real printing condition is restored through the support continuous constraint and unified release. Through the two-way dynamic coupling and cooperation of each link, the technical problems of low simulation calculation efficiency, poor grid modeling stability and insufficient deformation prediction accuracy after removing the support for the medium and large size complex curved surface components are solved synchronously. The surface node displacement field can be accurately output, and reliable basis is provided for the reverse geometric compensation and process optimization of the DLP light curing 3D printing model.

Description

Technical Field

[0001] This invention belongs to the field of additive manufacturing process simulation technology, specifically relating to a finite element deformation analysis method for DLP photopolymerization 3D printing. Background Technology

[0002] DLP (Digital Light Processing) photopolymerization 3D printing technology is an additive manufacturing process that uses digital micromirrors to selectively expose and cure liquid photosensitive resin layer by layer to construct three-dimensional objects. This technology is widely used in precision manufacturing, medical devices, and shoe molds and lasts due to its advantages such as high forming accuracy, good surface quality, and the ability to manufacture complex structures. During the actual printing process, the photosensitive resin undergoes chemical shrinkage during the photo-initiated polymerization reaction. This shrinkage, combined with the layer-by-layer accumulation and the support structure, generates residual stress within the printed part. After printing is completed and the support is removed, the release of this residual stress can cause warping, shrinkage, and other deformations in the printed part, directly affecting the dimensional accuracy of the product. To control such deformation, existing technologies employ finite element methods to numerically simulate the printing process and then use the simulation results to perform reverse compensation on the model. This approach is currently a common research direction for accuracy control.

[0003] However, existing deformation prediction methods based on finite element analysis still have significant shortcomings in practical applications. Firstly, many schemes employ a layer-by-layer modeling approach with the same number of layers as the actual printed parts. For larger printed parts, the number of analysis steps is typically hundreds or even thousands, resulting in a massive computational scale that makes it difficult to complete the simulation within an acceptable timeframe. Secondly, in handling boundary conditions, existing schemes often fix the bottom surface of the printed part entirely to the printing platform to simplify modeling. However, in DLP (Digital Persistent Light) processes, the printed part is actually connected to the platform through discrete support structures, which need to be removed after printing. This method of fixing the bottom surface excessively restricts the free contraction of the model's bottom, leading to significant deviations between the simulation results of stress accumulation and final deformation release and the actual printed results. Thirdly, for industrial parts containing free-form surfaces or complex overhanging structures, existing schemes involve complex preprocessing in terms of layer-by-layer geometric modeling, mesh generation, and support position setting, making stable application difficult. Therefore, improvements to existing technologies are needed to address the technical problems of low computational efficiency when handling complex printed parts, distortion in simulating real support conditions, and difficulty in accurately predicting the final deformation after support removal. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a finite element deformation analysis method for DLP photopolymerization 3D printing, so as to solve the core technical problem that existing simulation methods cannot simultaneously take into account computational efficiency, prediction accuracy and pre-processing success rate when processing large-sized complex industrial printed parts.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: The present invention provides a finite element deformation analysis method for DLP photopolymerization 3D printing, comprising: constructing an integrated finite element analysis framework with a unified finite element analysis core as the hub and macro-layer equivalent curing and discrete support release coupled together, the framework comprising a macro-layer equivalent partitioning module, an overall mesh layering module, a curing shrinkage loading module, and a discrete support continuous constraint and release module that work collaboratively around the unified finite element analysis core; The method includes: dividing the 3D model to be printed into a preset number of macrolayers along the printing direction using the macrolayer equivalent partitioning module to compress the number of analysis steps; performing overall finite element meshing on the 3D model to be printed using the overall mesh layering module and assigning each mesh unit to the corresponding macrolayer according to its printing direction position; integrating the unified finite element analysis core to form a unified analysis model including the overall mesh, macrolayer assignment, and analysis step scheduling; establishing an initial analysis step in the unified finite element analysis core using the curing shrinkage loading module and assigning initial material properties and curing degree field variables of the uncured state to all mesh units; sequentially executing macrolayer-by-macrolayer printing analysis steps corresponding to each macrolayer from bottom to top; updating the curing degree field variables of the current macrolayer mesh unit in each macrolayer printing analysis step to achieve macrolayer-level equivalent simulation of layer-by-layer curing; simultaneously updating the material elastic modulus in real time according to the curing degree in the user material subroutine and applying intrinsic shrinkage strain when a preset gel point is reached, so that the material evolution, shrinkage loading, and macrolayer curing progress are synchronized; during the execution of each macrolayer-by-macrolayer printing analysis step... The discrete support continuous constraint and release module automatically identifies the overhanging region and generates a discrete support node set based on the geometric projection relationship between the current macrolayer and the underlying cured macrolayer. Displacement constraints are applied to all nodes in the support node set and maintained continuously in all subsequent macrolayer-by-macrolayer printing analysis steps. The discrete support continuous constraint and release module and the curing shrinkage loading module form a bidirectional dynamic coupling in the unified finite element analysis core: the geometry of the current macrolayer and the deformation field generated by curing shrinkage together provide the basis for the identification and constraint application of the support nodes. The stress distribution generated by the support constraints reacts to the stress accumulation and deformation development in the subsequent curing process. After all macrolayer-by-macrolayer printing analysis steps are completed, the unified finite element analysis core uniformly schedules and establishes a release analysis step. The discrete support continuous constraint and release module uniformly releases all applied support node displacement constraints, allowing the printed part to undergo free deformation under the action of the accumulated residual stress field to restore the real stress release process after the support is removed. Finally, the surface node displacement field at the end of the release analysis step is extracted as the deformation prediction result output.

[0006] The present invention further proposes that dividing the 3D model to be printed into a predetermined number of macro layers along the printing direction specifically involves: extracting the minimum coordinate value of the 3D model to be printed in the printing direction. Z min and maximum coordinate value Z max Set the number of macro layers N layers Calculate the height of a single macro layer H layer =(Z max -Z min) / N layers The 3D model to be printed is divided into equal thickness sections along the printing direction. N layers One macro layer.

[0007] The present invention further proposes that the step of assigning each grid cell to the corresponding macro layer according to the printing direction position specifically involves: calculating the coordinate value of the centroid of each grid cell in the printing direction, and assigning each grid cell to a corresponding macro layer based on the macro layer height range in which the coordinate value is located.

[0008] The present invention further proposes that the duration of the initial analysis step is set to a minimum value to provide a uniform initial condition for subsequent macro-layer-by-macro-layer analysis; each macro-layer-by-macro-layer printing analysis step corresponds to a preset equivalent exposure time step to ensure that the update of the curing field variable has a step-by-step temporal relationship.

[0009] The present invention further proposes that the real-time updating of the material's elastic modulus based on the degree of curing specifically involves: based on the current degree of curing field variable, interpolation calculation is performed between the first elastic modulus representing the uncured state and the second elastic modulus representing the fully cured state to determine the actual elastic modulus at the current integration point.

[0010] The present invention further proposes that the automatic identification of overhanging regions based on the geometric projection relationship between the current macrolayer and the underlying solidified macrolayer specifically includes: extracting all nodes located on the free surface in the current macrolayer as candidate nodes; eliminating boundary nodes shared by the current macrolayer and the adjacent underlying macrolayer; constructing a contour envelope region based on the two-dimensional projections of all nodes in the adjacent underlying macrolayer; the contour envelope region is generated by constructing the convex hull of the two-dimensional projections of the nodes in the adjacent underlying macrolayer; determining whether the two-dimensional projection of the current macrolayer candidate node is located outside the contour envelope region, and if it is located outside, determining that the node is an overhanging candidate node.

[0011] The present invention further proposes that the generation of the discrete support node set specifically includes: spatial downsampling of the cantilever candidate nodes; calculating the number of target support nodes based on the span of the cantilever region in the horizontal direction and the preset support density; constructing a virtual grid based on the number of target support nodes, and dividing the cantilever candidate nodes into each grid according to their two-dimensional projection coordinates; selecting a representative node in each grid and removing the remaining nodes, thereby forming a uniformly distributed discrete support node set.

[0012] The present invention further proposes that applying displacement constraints to all nodes in the support node set specifically means applying fixed constraints to the translational degrees of freedom in the X, Y, and Z directions of each node in the support node set.

[0013] The present invention further proposes that the release analysis step is as follows: after all macro-layer printing analysis steps are completed, an independent analysis step is added. In this analysis step, the displacement constraints on all support nodes are uniformly removed, so that the printed part undergoes free deformation under the action of the existing residual stress field, in order to simulate the release process after the printed part leaves the printing platform and the support is removed.

[0014] The present invention further proposes that the surface node displacement field at the end of the extraction and release analysis step specifically involves: extracting the original coordinate values ​​of the surface nodes in the global coordinate system and the displacement components of each node in the X, Y and Z directions, and using the displacement components as printing deformation prediction values ​​to perform reverse geometric compensation on the three-dimensional model to be printed.

[0015] The finite element deformation analysis method for DLP photopolymerization 3D printing disclosed in this invention is based on the construction of an integrated analysis framework with a unified finite element analysis core as the hub and macro-layer equivalent curing and discrete support release coupled together. Through bidirectional dynamic collaboration of each link, a complete technical system of rapid modeling, stable solution, accurate loading and real release is formed. Compared to existing technologies, this invention offers the following advantages: First, it achieves lightweight simulation through macro-layer equivalence, simplifying the hundreds to thousands of layers of actual printing into a small number of macro-layers for analysis. This significantly reduces the number of analysis steps and the scale of the solution, greatly improving computational speed and enabling stable simulation of medium-to-large-sized complex printed parts within a reasonable timeframe. Second, relying on overall mesh generation and element layering, it eliminates the need for layer-by-layer geometric decomposition of the model, enabling mesh modeling of complex free-form surfaces and large-span overhanging structures. This significantly improves preprocessing success rate and model applicability, reducing the risk of mesh generation failure. Third, by combining automatic discrete support identification, continuous constraints, and unified release, and through bidirectional dynamic coupling of solidification shrinkage and support constraints, it realistically recreates the support arrangement and removal conditions in industrial printing, avoiding constraint distortion caused by overall fixed bottom surfaces and effectively improving the final deformation prediction accuracy. In summary, this invention, through the organic synergy of each step, simultaneously solves the problem of traditional finite element simulation's difficulty in balancing computational speed, prediction accuracy, and modeling success rate. It provides a stable and reliable deformation prediction basis for error compensation, structural optimization, and industrial mass production in DLP photopolymerization 3D printing. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1This is a schematic diagram of the finite element deformation analysis framework for DLP photopolymerization 3D printing as described in an embodiment of the present invention; Figure 2 This is a schematic diagram of the three-dimensional model of the shoe mold to be printed in an embodiment of the present invention; Figure 3 This is a schematic diagram of the macro-layer division of the shoe mold model in an embodiment of the present invention; Figure 4 This is a schematic diagram of the overall finite element mesh generation of the shoe mold model in an embodiment of the present invention; Figure 5 This is a cloud map showing the displacement amplitude distribution of the shoe model after the support was removed in an embodiment of the present invention. Figure 6 This is a cloud map showing the total displacement distribution of the shoe mold model after the supports are removed in an embodiment of the present invention. Figure 7 This is a diagram illustrating the algorithm effect of the discrete support node boundary conditions for the simulated printed part in an embodiment of the present invention. Figure 8 This is a physical image of the actual printed support for the corresponding shoe last model in an embodiment of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0019] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0020] Finite element deformation analysis of DLP photopolymerization 3D printing faces three core challenges in applications involving medium to large-sized complex industrial parts: First, excessive layer-by-layer simulation steps lead to excessive computational load, making efficient solutions difficult; second, the fixed boundary conditions of the bottom surface do not match the actual discrete support conditions, resulting in insufficient deformation prediction accuracy; and third, layer-by-layer geometric decomposition and mesh generation are complex, leading to low success rates in preprocessing complex models. Based on these challenges, this invention provides a finite element deformation analysis method for DLP photopolymerization 3D printing, such as... Figure 1 As shown: An integrated finite element analysis framework is constructed, with a unified finite element analysis core as the hub and coupled with macro-layer equivalent solidification and discrete support release. The framework includes a macro-layer equivalent partitioning module, a global mesh layering module, a solidification shrinkage loading module, and a discrete support continuous constraint and release module that work collaboratively around the unified finite element analysis core. The method includes: The macro-layer equivalent partitioning module divides the 3D model to be printed into a preset number of macro-layers along the printing direction to reduce the number of analysis steps. The overall mesh layering module performs overall finite element meshing on the 3D model to be printed and assigns each mesh unit to the corresponding macro-layer according to its position in the printing direction. The unified finite element analysis core integrates these elements to form a unified analysis model that includes the overall mesh, macro-layer assignment, and analysis step scheduling. The curing shrinkage loading module establishes an initial analysis step in the unified finite element analysis core and assigns initial material properties and curing degree field variables to all mesh units in an uncured state. The macro-layer printing analysis steps, corresponding one-to-one with each macro-layer, are executed sequentially from bottom to top. In each macro-layer printing analysis step, the curing degree field variables of the current macro-layer mesh unit are updated to achieve macro-layer equivalent simulation of layer-by-layer curing. Simultaneously, the material elastic modulus is updated in real time according to the curing degree in the user material subroutine, and intrinsic shrinkage strain is applied when a preset gel point is reached, so that the material evolution, shrinkage loading, and macro-layer curing progress are synchronized. During the execution of each macro-layer printing analysis step, the following steps are performed: The discrete support continuous constraint and release module automatically identifies the overhanging region and generates a discrete support node set based on the geometric projection relationship between the current macrolayer and the underlying cured macrolayer. Displacement constraints are applied to all nodes in the support node set and maintained throughout all subsequent macrolayer-by-macrolayer printing analysis steps. The discrete support continuous constraint and release module and the curing shrinkage loading module form a bidirectional dynamic coupling within the unified finite element analysis core: the geometry of the current macrolayer and the deformation field generated by curing shrinkage jointly provide the basis for the identification and constraint application of the support nodes; the stress distribution generated by the support constraints reacts to the stress accumulation and deformation development in the subsequent curing process. After all macrolayer-by-macrolayer printing analysis steps are completed, the unified finite element analysis core uniformly schedules and establishes a release analysis step. The discrete support continuous constraint and release module uniformly releases all applied support node displacement constraints, allowing the printed part to undergo free deformation under the accumulated residual stress field to recreate the actual stress release process after support removal. Finally, the surface node displacement field at the end of the release analysis step is extracted as the deformation prediction result output.

[0021] The "macro-layer" processed by the macro-layer equivalent partitioning module refers to several analysis layers formed by merging hundreds or thousands of physical layers present in actual printing according to their height range. Each macro-layer represents the overall curing effect of all real printed layers within a certain thickness range. Macro-layers are used instead of real layers for analysis because simulating all physical layers layer by layer in macroscopic deformation analysis would incur a huge computational burden, while the merged macro-layers can still completely preserve the macroscopic laws of layer-by-layer curing accumulation. This module divides the 3D model to be printed into a preset number of macro-layers of equal thickness along the printing direction, and then transmits the simplified inter-layer topology to the unified finite element analysis core, providing a unified hierarchical benchmark for subsequent overall mesh layering and analysis step scheduling.

[0022] The overall meshing and layering module first generates a complete finite element mesh on the finished 3D model to be printed, using C3D10M tetrahedral elements. After generating the mesh, it calculates the coordinates of the centroid of each element in the printing direction. Based on the macrolayer height range of these coordinates, each mesh element is uniquely assigned to a corresponding macrolayer, and the data containing the overall mesh and element macrolayer affiliation is transmitted to the unified finite element analysis core. This method of first meshing the entire model and then layering it by element eliminates the need for layer-by-layer geometric decomposition of the model, naturally adapting to macrolayer division. It avoids the risk of preprocessing failure caused by layer-by-layer geometric decomposition, significantly improving the success rate of mesh generation for complex free-form surfaces and large-span overhanging structures.

[0023] The curing shrinkage loading module operates based on the unified analysis model provided by the unified finite element analysis core. First, an initial analysis step with a minimum duration is established, assigning initial elastic modulus and initial curing degree field variables representing the uncured state to all mesh elements. Then, in a bottom-up order, a macrolayer-by-macrolayer printing analysis step corresponding to each macrolayer is executed sequentially. Each macrolayer-by-macrolayer printing analysis step corresponds to a preset equivalent exposure time step. In each analysis step, only the curing degree field variable of the mesh element corresponding to the current macrolayer is updated to a high curing degree value representing the cured state, achieving equivalent simulation of macrolayer-level curing. Simultaneously, the module reads the current curing degree field variable at each integration point in real time through the user material subroutine, performs interpolation calculations between the uncured elastic modulus and the fully cured elastic modulus to update the elastic modulus, and applies intrinsic shrinkage strain to the integration point when the curing degree reaches the preset gel point, providing a driving force for deformation evolution synchronized with the macrolayer curing process. The current macrolayer geometry and deformation field calculated by the curing shrinkage loading module are transmitted to the unified finite element analysis core in real time, providing a basis for support identification for the discrete support continuous constraint and release module.

[0024] The discrete support continuous constraint and release module operates based on the current macrolayer geometry and deformation field provided by the unified finite element analysis core: During each macrolayer-by-macrolayer printing analysis step, firstly, all nodes located on the free surface in the current macrolayer are extracted as candidate nodes, and boundary nodes shared by the current macrolayer and the adjacent lower macrolayer are eliminated; then, a convex hull contour envelope region is constructed based on the two-dimensional projection of all nodes in the adjacent lower macrolayer, and it is determined whether the two-dimensional projection of the current macrolayer candidate node is located outside the contour envelope region. If it is located outside, it is determined to be a cantilever candidate node; then, spatial downsampling is performed on the cantilever candidate nodes, and a virtual grid is constructed based on the horizontal span of the cantilever region and the preset support density. A representative node is selected in each grid to form a uniformly distributed discrete support node set; fixed constraints are applied to the translational degrees of freedom of all nodes in the support node set in the X, Y, and Z directions. This constraint takes effect from the current macrolayer-by-macrolayer printing analysis step and is maintained in all subsequent macrolayer-by-macrolayer printing analysis steps. The displacement constraints applied by this module are fed back to the curing shrinkage loading module as boundary conditions through the unified finite element analysis core. This feedback affects the stress accumulation and deformation development in the subsequent macro-layer curing process, forming a two-way dynamic coupling between curing shrinkage and support constraints.

[0025] After all macro-layer printing analysis steps are completed, the unified finite element analysis core schedules and establishes a release analysis step. Through the discrete support continuous constraint and release module, all applied support node displacement constraints are uniformly released, allowing the printed part to undergo free deformation under the accumulated residual stress field, accurately reproducing the actual stress release process after support removal. Finally, the original coordinate values ​​of the model surface nodes in the global coordinate system and the displacement components in the X, Y, and Z directions are extracted at the end of the release analysis step and output as the deformation prediction result. This displacement component can be directly used for reverse geometric compensation of the 3D model to be printed. The above modules achieve data interoperability and scheduling collaboration through the unified finite element analysis core, significantly reducing the number of analysis steps and improving calculation speed while ensuring the success rate of mesh generation and deformation prediction accuracy for complex models. This simultaneously solves the core problem of existing technologies struggling to balance efficiency, accuracy, and stability.

[0026] The present invention further proposes that dividing the 3D model to be printed into a predetermined number of macro layers specifically involves: extracting the minimum coordinate value of the 3D model to be printed in the printing direction. Z min and maximum coordinate value Z max Set the number of macro layers N layers Calculate the height of a single macro layer H layer =(Z max -Z min) / N layers The 3D model to be printed is divided into equal thickness sections along the printing direction. N layers One macro layer.

[0027] in, Z min and Z max These represent the positions of the bottom and top of the model in the printing direction, respectively; the difference between them is the total height of the model. Preset number of macro layers. N layers This is a parameter that can be adjusted as needed, and it directly determines the number of analysis steps in the entire simulation. Using equal thickness partitioning, meaning each macrolayer has the same height, offers the advantages of simplicity and even distribution of the computational load. The specific height of each macrolayer is obtained by dividing the total height by the number of macrolayers. In this way, the layer-by-layer simulation that originally required thousands of analysis steps is compressed into dozens, significantly reducing the computational scale.

[0028] As a specific implementation method, for a model with a total height of 100mm, if we assume... N layers =20, then H layer =5mm; if the model height is small or higher accuracy is required, it can also be set to 5mm. N layers =30, then H layer ≈3.33mm; conversely, if the model is very large and the main focus is on the overall deformation trend, it can be set to 3.33mm. N layers =10. These different values ​​can be flexibly selected according to actual needs, and all are within the protection scope of this invention.

[0029] The present invention further proposes to generate an overall finite element mesh of the three-dimensional model to be printed, calculate the coordinate value of the centroid of each mesh unit in the printing direction, and uniquely assign each mesh unit to a corresponding macro layer according to the macro layer height range in which the coordinate value is located.

[0030] The generation of the overall finite element mesh is completed in traditional finite element preprocessing software, eliminating the need for separate processing for each layer. After meshing, the software automatically calculates the coordinates of the centroid of each element. The printing direction coordinates (i.e., the Z-value) of the centroid determine the element's position in height. Since each macrolayer has a defined height range (e.g., macrolayer 1 corresponds to...), the software can automatically calculate the coordinates of the centroid's centroid. Z min arrive Z min +H layer Macro layer 2 corresponds toZ min + H layer arrive Z min +2 H layer (And so on). By comparing the Z-value of the element's centroid with these intervals, it can be determined which macrolayer the element belongs to. This attribution relationship is unique; that is, an element can only belong to one macrolayer. After attribution, each element is labeled with a "macrolayer number," which is used to control the update of field variables in subsequent analyses.

[0031] The present invention further proposes that the duration of the initial analysis step is set to a minimum value to provide a uniform initial condition for subsequent macro-layer-by-macro-layer analysis; each macro-layer-by-macro-layer printing analysis step corresponds to a preset equivalent exposure time step to ensure that the update of the curing field variable has a step-by-step temporal relationship.

[0032] The initial analysis step has an extremely short duration, and its physical meaning does not correspond to actual time. It merely serves to establish an initial stress and cure degree field in the finite element model, encompassing all elements in an uncured state. This extremely small time value (on the order of 10^-5 seconds) ensures that the model stably proceeds to the next analysis step without any loading. For each macrolayer-by-macrolayer printing analysis step, an equivalent exposure time step is assigned. This time represents the total cumulative curing time of the actual printed layers covered by that macrolayer. Through this time step setting, the updates to the cure degree field variables have a clear sequence: the cure degree of the first macrolayer is updated first, then after one time step, the cure degree of the second macrolayer is updated, and so on. This temporal relationship simulates the actual layer-by-layer printing sequence.

[0033] As a specific implementation method, the duration of the initial analysis step can be set to 1.0 × 10^-5 seconds; the equivalent exposure time step of each macrolayer-by-macrolayer analysis step can be set to 3.0 seconds. This 3.0 seconds is not required to be exactly the same as the physical exposure time, but is used as a relative value to control the stepping rhythm of material evolution and shrinkage loading.

[0034] The present invention further proposes that the real-time updating of the elastic modulus in the user material subroutine is specifically as follows: based on the current curing degree field variable, interpolation calculation is performed between the first elastic modulus representing the uncured state and the second elastic modulus representing the fully cured state to determine the actual elastic modulus at the current integration point.

[0035] The first elastic modulus corresponds to the soft material state of the resin before it has cured; its value is very small, making the model almost unresistant to deformation in the initial analysis step. The second elastic modulus corresponds to the hard material state of the resin after it has fully cured; its value is larger. Interpolation can be performed using linear interpolation or a nonlinear function depending on the curing kinetics of the specific resin. As the value of the curing degree field variable gradually increases from 0 to 1, the elastic modulus also increases accordingly, transitioning continuously. This approach avoids the numerical oscillations caused by the sudden appearance or disappearance of elements in the traditional "birth and death element" method, and is more consistent with the gradual change of the physical properties of the resin during photocuring.

[0036] In one specific implementation, the first elastic modulus is taken as 5.0 MPa, the second elastic modulus as 1205 MPa, and the Poisson's ratio as 0.35. The linear interpolation formula is: E =5.0+(1205-5.0)× ,in Current degree of cure (0≤ ≤1). When When =0, E =5.0MPa; when When =0.85, E ≈5.0 + 1200 × 0.85 = 1025 MPa. Furthermore, the gel point threshold is set to 0.15, only when... Intrinsic shrinkage strain is applied only when the value is greater than 0.15, and the shrinkage strain value is set to 0.0065 (i.e., linear shrinkage rate of 0.65%). This setting avoids numerical instability caused by prematurely applying shrinkage before the material has developed sufficient strength.

[0037] The present invention further proposes that automatically identifying the overhanging region that needs support below the current macrolayer specifically includes: extracting all nodes located on the free surface in the current macrolayer as candidate nodes; eliminating boundary nodes shared by the current macrolayer and the adjacent lower macrolayer; constructing a contour envelope region based on the two-dimensional projections of all nodes in the adjacent lower macrolayer; the contour envelope region is generated by constructing the convex hull of the two-dimensional projections of the nodes in the adjacent lower macrolayer; determining whether the two-dimensional projection of the current macrolayer candidate node is located outside the contour envelope region, and if it is located outside, determining that the node is an overhanging candidate node.

[0038] "Free surface nodes" refer to nodes that belong to at least one outer surface element, which can be obtained through the surface extraction function of the finite element model. "Adjacent lower macrolayers" refer to the macrolayer immediately below the current macrolayer. Boundary nodes are removed to avoid misclassifying normal contact surfaces between two macrolayers as suspended surfaces. The method for constructing the 2D projection is to extract the X and Y coordinates of all nodes, ignoring the Z coordinate, and then calculate the convex hull of these points on the XY plane. The convex hull is the smallest convex polygon containing all these points. If the projection point of a candidate node on the XY plane falls outside this convex hull, it means that, vertically, it is not supported by solid material from an adjacent macrolayer below it, and therefore it should be marked as a suspended candidate node requiring support.

[0039] The present invention further proposes that generating a discrete set of support nodes on the overhanging region specifically includes: spatial downsampling of the overhanging candidate nodes; calculating the number of target support nodes based on the horizontal span of the overhanging region and a preset support density; constructing a virtual grid based on the number of target support nodes, and dividing the overhanging candidate nodes into each grid according to their two-dimensional projection coordinates; selecting a representative node in each grid and removing the remaining nodes, thereby forming the evenly distributed discrete set of support nodes.

[0040] The number of cantilever candidate nodes is often large. Applying constraints to all of them would lead to overly dense constraints, reduced solution efficiency, and inconsistent with the sparse support arrangement in actual printing. Therefore, downsampling is necessary. First, the horizontal range (i.e., the span in the X and Y directions) covered by the 2D projection of all cantilever candidate nodes is calculated. The preset support density is a ratio, such as 50%, meaning that about half of the candidate points are retained. Based on the product of the target number of retained nodes and the span, the size of the virtual grid can be determined: the number of grids is approximately equal to the target number of support nodes. Then, each candidate node is assigned to a grid according to its projected coordinates. Within each grid, only one representative node is retained (e.g., the center point of the grid or the candidate node closest to the center), and other nodes are discarded. The final result is a relatively evenly distributed and reasonably numbered set of discrete support nodes.

[0041] As a specific implementation method, the preset support density is set to 50%. If the overhanging area spans 30mm in the X direction and 20mm in the Y direction, and there are 200 initial candidate nodes, then 100 nodes are selected as the target. Based on this, a virtual grid of approximately 10×10 (100 cells in total) can be constructed, with each cell measuring approximately 3mm×2mm. One representative node is retained within each cell, resulting in a support node set that offers good coverage without being overly dense.

[0042] The present invention further proposes that applying displacement constraints to all nodes in the support node set specifically involves applying fixed constraints to the translational degrees of freedom in the X, Y, and Z directions of each node in the support node set; the displacement constraints take effect from the current macrolayer printing analysis step and are maintained in all subsequent macrolayer printing analysis steps.

[0043] In this context, a fixed constraint restricts all three translational degrees of freedom of the node to zero displacement. Once applied, this constraint remains in place until the analysis step is released. In actual DLP printing, the support structure is generated layer by layer during the printing process, and once generated, it continuously constrains the shrinkage of subsequent cured layers. This physical process is simulated here by "taking effect from the current macrolayer and persisting in subsequent analysis steps." For example, if a support node is identified in the 3rd macrolayer analysis step, then the fixed constraint for this node starts from the 3rd macrolayer analysis step and persists in the 4th, 5th, and all the way to the last macrolayer analysis step.

[0044] The present invention further proposes that the release analysis step is specifically as follows: after all macro-layer printing analysis steps are completed, an independent analysis step is added. In this analysis step, the displacement constraints on all support nodes are uniformly removed, so that the printed part undergoes free deformation under the action of the existing residual stress field, in order to simulate the release process after the printed part leaves the printing platform and the support is removed.

[0045] The release analysis step is specifically designed to simulate the process of removing supports. In this step, no new curing or shrinkage is introduced; all previously applied constraints on the support nodes are simply removed. Residual stresses within the model (accumulated from curing shrinkage) are no longer counteracted by constraints, driving the model to elastically rebound and deform until a new static equilibrium is reached. This step is crucial because if supports are not released, the model's deformation will be suppressed by constraints, failing to reflect the warping or shrinkage of a real printed part after support removal.

[0046] As a specific implementation method, the duration of the release analysis step can be set to 1.0 second, which is a quasi-static duration sufficient for the model to re-equilibrium. In this analysis step, the boundary conditions of all previous support nodes are set to "inactive" or deleted directly, and then the solution is submitted. After the solution is completed, the shape of the model is the predicted final deformation form.

[0047] The present invention further proposes that the output surface node displacement field includes: the original coordinate values ​​of the surface nodes in the global coordinate system and the displacement components of each node in the X, Y and Z directions. The displacement components are used as printing deformation prediction values ​​to perform reverse geometric compensation on the three-dimensional model to be printed.

[0048] The surface nodal displacement field can be directly extracted from the finite element analysis results. The original coordinate values ​​refer to the nodal positions of the model before deformation, and the displacement components are the changes in the nodal position from its original position to its deformed position. By taking the inverse of these displacement components and adding them to the corresponding nodal coordinates of the original model, a new model with inverse compensation is obtained. Using this compensated model for printing allows the actual deformation to cancel out the predicted deformation, effectively improving the dimensional accuracy of the printed parts.

[0049] To further verify the implementation effect of the integrated analysis framework described in this invention, which uses a unified finite element analysis core as the hub and couples macro-layer equivalent solidification with discrete support release, a shoe mold model is used as an example for detailed explanation. The relevant processes and results are as follows: Figures 2 to 6 As shown.

[0050] Figure 2 The model is a 3D model of a shoe mold to be printed. It is a typical industrial part with complex curved surfaces and large-span overhanging structures, which is suitable for the application scenarios of medium and large-sized DLP photopolymerization 3D printed parts.

[0051] First, the shoe mold model is divided into macro layers along the printing direction using the macro layer equivalent partitioning module, such as... Figure 3 As shown, the total height of the model is divided into 20 macro-layers to form the hierarchical basis for lightweight analysis, significantly reducing the number of subsequent analysis steps. Then, the shoe model is meshed using the overall meshing module, as shown below. Figure 4 As shown, a complete mesh is generated in one go using C3D10M tetrahedral elements, and then each element is assigned to its corresponding macro layer based on the printing direction coordinates of its centroid. The unified finite element analysis core integrates the above macro layer division results and mesh layering results to form a unified analysis model that includes the overall mesh, macro layer assignment, and analysis step scheduling. This eliminates the need to decompose complex surfaces layer by layer, effectively improving the success rate of preprocessing.

[0052] An initial analysis step is established in the unified finite element analysis core using the curing shrinkage loading module, assigning initial material properties and curing degree field variables to all elements in their uncured state. Each macrolayer-by-macrolayer printing analysis step is executed sequentially from bottom to top, achieving a macrolayer-level equivalent simulation of the layer-by-layer curing process by updating the curing degree field variables of the current macrolayer mesh elements. Simultaneously, in the user material subroutine, the elastic modulus is dynamically updated based on the curing degree, and intrinsic shrinkage strain is applied when a preset gel point is reached, providing a driving force for deformation evolution synchronized with the macrolayer curing process. During each macrolayer-by-macrolayer printing analysis step, the calculation results from the curing shrinkage loading module are transmitted in real-time to the discrete support continuous constraint and release module through the unified finite element analysis core. This module automatically identifies the overhanging region and generates a discrete support node set based on the geometric projection relationship between the current macrolayer and the underlying cured macrolayer, establishing a continuous constraint mechanism between the discrete support and the macrolayer curing. This constraint is fed back to the curing shrinkage loading module through the unified finite element analysis core, acting in response to the stress accumulation and deformation development of the subsequent macrolayer curing process, forming a two-way dynamic coupling between curing shrinkage and support constraints. After all macro-level analyses are completed, a release analysis step is established by the unified finite element analysis core. The displacement constraints of all support nodes are released in a unified manner through the discrete support continuous constraint and release module, restoring the support removal condition of real industrial printing. Finally, the surface node displacement field at the end of the release analysis step is extracted.

[0053] Figure 5 To show the distribution contour map of the total displacement of the model after removing the supports. Figure 6 The model displacement amplitude distribution cloud map after removing the support is represented by different colors. The red area corresponds to the maximum displacement, which is mainly concentrated at the front overhang of the model. This is completely consistent with the phenomenon that the area is prone to warping and deformation due to insufficient support constraints and residual stress release in actual printing. This verifies the accurate ability of the coupling frame of the present invention to capture the deformation distribution characteristics of the overhang structure.

[0054] This implementation process fully covers the core aspects such as equivalent macro-layer division, overall mesh stratification, curing degree-driven material evolution, discrete support constraints and release, etc. It verifies the effectiveness of the collaborative working mechanism of each module with the unified finite element analysis core as the hub, and can provide a reliable deformation prediction basis for error compensation and process optimization of DLP photopolymerization 3D printing.

[0055] To further quantitatively verify the effectiveness of the coupling framework of this invention in predicting deformation and compensating errors in printed parts, simulation prediction and actual printing comparison tests were conducted on five groups of complex free-form surface components of shoe molds with different structures. The geometric deviation between the nominal model, the simulation compensation model obtained based on the framework of this invention, and the actual printed parts was used as the evaluation index. Mean point Euclidean error (AEE) and root mean square error (RMSE) were used for quantitative evaluation. The deviation levels of the directly printed nominal model (NR) and the printed model compensated using the simulation results of this invention (SR) were compared. The results are shown in Table 1. Table 1. Quantitative Comparison of Error Compensation Effects of the Method of the Invention Wherein, N-RAEE represents the average point Euclidean error between the nominal model and the actual printed part, S-RAEE represents the average point Euclidean error between the printed part and the actual printed part after compensation using the simulation results of this invention, and the AEE reduction rate reflects the error compensation effect. The test results show that after compensation using the method of this invention, the S-RAEE of all five groups of samples is significantly lower than N-RAEE, with an average reduction rate of 71.06%. Simultaneously, S-RRMSE also decreased from an average of 0.5191 mm for NR to 0.2052 mm, indicating that the method of this invention can accurately predict the deformation distribution of the printed part, providing a reliable basis for reverse geometric compensation of the model and significantly reducing the geometric deviation between the actual printed part and the nominal model. The above test results fully verify the effectiveness and engineering practicality of the method of this invention in deformation prediction and error compensation for DLP photopolymerization 3D printing of medium-to-large-sized complex industrial parts.

[0056] To verify the stability and applicability of the coupling framework of this invention in industrial batch applications, 100 random shoe last models with different structures were selected for comparative testing. The success rates of the layer-by-layer geometric slicing modeling method, the overall mesh + real layer unit activation method and the present method were compared in each key step. The results are shown in Table 2.

[0057] Table 2. Applicability verification results of the method of the present invention on random shoe last models. As shown in Table 2, the success rate of the three methods in the 3D model reading and geometric inspection stages is 98%, indicating that the quality of the initial model data has a basically consistent impact on each method. The performance differences are mainly reflected in the subsequent finite element modeling, support generation, and solidification shrinkage solution stages.

[0058] The success rate of the layer-by-layer geometric slicing modeling method in the finite element mesh generation stage is only 21%. This is because after the complex shoe last model is cut into a large number of thin geometric layers according to the actual printing layer thickness, it is very easy to generate small fragments, non-manifold boundaries and local degenerate surfaces, which leads to a significant decrease in mesh generation stability. Since a large number of models have failed in the preprocessing stage, the success rate of subsequent support node generation is only 21%, and the final solidification shrinkage solution success rate further drops to 4%. This indicates that this type of method cannot be stably applied to the batch simulation of medium and large-sized complex free-form surface components.

[0059] The overall mesh + real layer element activation method avoids layer-by-layer geometric decomposition, thus increasing the finite element mesh generation success rate to 55% and the support node generation success rate to 48%, which is a significant improvement compared to the layer-by-layer slicing method. However, this method still requires the establishment of thousands of elements to activate the analysis steps according to the real printing layer. The excessive number of analysis steps and frequent material state switching can easily lead to numerical convergence difficulties. Therefore, the solidification shrinkage solution success rate is only 15%, indicating that simply canceling the layer-by-layer geometric slicing cannot completely solve the stable solution problem of complex DLP printed parts simulation.

[0060] In contrast, this invention fundamentally solves the above problems through an integrated coupled framework centered on a unified finite element analysis core: It achieves automatic element layering without geometric splitting through a global meshing module, increasing the finite element meshing success rate to 97%; it compresses thousands of real layers into dozens of macro-layer analysis steps through a macro-layer equivalent partitioning module, significantly reducing the risk of solution convergence; and it automatically generates support nodes based on macro-layer projection relationships through a discrete support continuous constraint and release module, maintaining a support node generation success rate of 97%. Figure 7 The image shown is a simulation result of the discrete support node boundary condition algorithm obtained by the method of this invention. Figure 8 The actual printed support diagrams corresponding to the shoe last model show a high degree of match between the support layout area and distribution density, which intuitively verifies the consistency between the discrete support constraint simulation of this invention and the actual printing conditions. This is also an important reason why the success rate of solidification shrinkage solution of this method has been improved to 96%.

[0061] The two sets of verification results above together show that the method of the present invention not only has high-precision deformation prediction and error compensation capabilities, but also significantly outperforms existing methods in terms of overall process stability and batch applicability. It can meet the batch simulation requirements of industrial-grade DLP photopolymerization 3D printing and provide comprehensive and reliable technical support for error compensation, process optimization and mass production.

[0062] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A finite element deformation analysis method for DLP photopolymerization 3D printing, characterized in that, An integrated finite element analysis framework is constructed, with a unified finite element analysis core as the hub and coupled with macro-layer equivalent solidification and discrete support release. The framework includes a macro-layer equivalent partitioning module, a global mesh layering module, a solidification shrinkage loading module, and a discrete support continuous constraint and release module that work collaboratively around the unified finite element analysis core. The method includes: The macro-layer equivalent partitioning module divides the 3D model to be printed into a preset number of macro-layers along the printing direction to reduce the number of analysis steps. The overall mesh layering module performs overall finite element meshing on the 3D model to be printed and assigns each mesh unit to the corresponding macro-layer according to its position in the printing direction. The unified finite element analysis core integrates these elements to form a unified analysis model that includes the overall mesh, macro-layer assignment, and analysis step scheduling. The curing shrinkage loading module establishes an initial analysis step in the unified finite element analysis core and assigns initial material properties and curing degree field variables to all mesh units in an uncured state. The macro-layer printing analysis steps, corresponding one-to-one with each macro-layer, are executed sequentially from bottom to top. In each macro-layer printing analysis step, the curing degree field variables of the current macro-layer mesh unit are updated to achieve macro-layer equivalent simulation of layer-by-layer curing. Simultaneously, the material elastic modulus is updated in real time according to the curing degree in the user material subroutine, and intrinsic shrinkage strain is applied when a preset gel point is reached, so that the material evolution, shrinkage loading, and macro-layer curing progress are synchronized. During the execution of each macro-layer printing analysis step, the following steps are performed: The discrete support continuous constraint and release module automatically identifies the overhanging region and generates a discrete support node set based on the geometric projection relationship between the current macrolayer and the underlying cured macrolayer. Displacement constraints are applied to all nodes in the support node set and maintained throughout all subsequent macrolayer-by-macrolayer printing analysis steps. The discrete support continuous constraint and release module and the curing shrinkage loading module form a bidirectional dynamic coupling within the unified finite element analysis core: the geometry of the current macrolayer and the deformation field generated by curing shrinkage jointly provide the basis for the identification and constraint application of the support nodes; the stress distribution generated by the support constraints reacts to the stress accumulation and deformation development in the subsequent curing process. After all macrolayer-by-macrolayer printing analysis steps are completed, the unified finite element analysis core uniformly schedules and establishes a release analysis step. The discrete support continuous constraint and release module uniformly releases all applied support node displacement constraints, allowing the printed part to undergo free deformation under the accumulated residual stress field to recreate the actual stress release process after support removal. Finally, the surface node displacement field at the end of the release analysis step is extracted as the deformation prediction result output.

2. The finite element deformation analysis method for DLP photopolymerization 3D printing according to claim 1, characterized in that, The process of dividing the 3D model to be printed into a preset number of macro layers along the printing direction specifically involves: extracting the minimum coordinate value of the 3D model to be printed in the printing direction. Z min and maximum coordinate value Z max Set the number of macro layers N layers Calculate the height of a single macro layer H layer =(Z max -Z min ) / N layers The 3D model to be printed is divided into equal thickness sections along the printing direction. N layers One macro layer.

3. The finite element deformation analysis method for DLP photopolymerization 3D printing according to claim 1, characterized in that, The specific steps of assigning each grid cell to the corresponding macro layer according to its printing direction position are as follows: calculate the coordinate value of the centroid of each grid cell in the printing direction, and assign each grid cell to a corresponding macro layer based on the macro layer height range in which the coordinate value is located.

4. The finite element deformation analysis method for DLP photopolymerization 3D printing according to claim 1, characterized in that, The duration of the initial analysis step is set to a minimum value to provide uniform initial conditions for subsequent macro-layer-by-macro-layer analysis; each macro-layer-by-macro-layer printing analysis step corresponds to a preset equivalent exposure time step to ensure that the update of the curing field variable has a step-by-step temporal relationship.

5. The finite element deformation analysis method for DLP photopolymerization 3D printing according to claim 1, characterized in that, The method of updating the material's elastic modulus in real time based on the degree of curing is as follows: based on the current degree of curing field variable, interpolation calculation is performed between the first elastic modulus representing the uncured state and the second elastic modulus representing the fully cured state to determine the actual elastic modulus at the current integration point.

6. The finite element deformation analysis method for DLP photopolymerization 3D printing according to claim 1, characterized in that, The automatic identification of overhanging regions based on the geometric projection relationship between the current macrolayer and the underlying solidified macrolayer specifically includes: extracting all nodes located on the free surface in the current macrolayer as candidate nodes; eliminating boundary nodes shared by the current macrolayer and the adjacent underlying macrolayer; constructing a contour envelope region based on the two-dimensional projections of all nodes in the adjacent underlying macrolayer; the contour envelope region is generated by constructing the convex hull of the two-dimensional projections of the nodes in the adjacent underlying macrolayer; determining whether the two-dimensional projection of the current macrolayer candidate node is located outside the contour envelope region, and if it is located outside, determining that the node is an overhanging candidate node.

7. The finite element deformation analysis method for DLP photopolymerization 3D printing according to claim 6, characterized in that, The specific steps of generating the discrete support node set include: spatial downsampling of the cantilever candidate nodes; calculating the number of target support nodes based on the horizontal span of the cantilever region and the preset support density; constructing a virtual grid based on the number of target support nodes, and dividing the cantilever candidate nodes into each grid according to their two-dimensional projection coordinates; selecting a representative node in each grid and removing the remaining nodes, thereby forming a uniformly distributed discrete support node set.

8. The finite element deformation analysis method for DLP photopolymerization 3D printing according to claim 1, characterized in that, The specific method of applying displacement constraints to all nodes in the support node set is to apply fixed constraints to the translational degrees of freedom in the X, Y, and Z directions of each node in the support node set.

9. The finite element deformation analysis method for DLP photopolymerization 3D printing according to claim 1, characterized in that, The release analysis step is as follows: After all macro-layer printing analysis steps are completed, an independent analysis step is added. In this analysis step, the displacement constraints on all support nodes are uniformly removed, so that the printed part undergoes free deformation under the action of the existing residual stress field, in order to simulate the release process after the printed part leaves the printing platform and the support is removed.

10. The finite element deformation analysis method for DLP photopolymerization 3D printing according to claim 1, characterized in that, The surface node displacement field at the end of the extraction and release analysis step specifically involves: extracting the original coordinate values ​​of the surface nodes in the global coordinate system and the displacement components of each node in the X, Y, and Z directions. The displacement components are used as printing deformation prediction values ​​to perform reverse geometric compensation on the three-dimensional model to be printed.

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