Three-dimensional slope finite element self-adaptive partitioning method and device and computer readable storage medium

Abstract

The present application relates to a three-dimensional slope finite element adaptive subdivision method, device and computer readable storage medium, the method comprises the following steps: constructing a basic SDP model, implementing SDP double-quantization adaptive criterion global calculation; according to the double-coupling criterion, the finite element unit is marked as encryption, coarsening and reservation unit respectively, local grid encryption is executed on the encryption unit, and grid sparse processing is realized on the coarsening unit; generate the updated global finite element grid, output the adaptive grid and three-dimensional plastic slip band distribution, slope limit safety factor and global stress field visualization result. The present application distinguishes elastic, critical plastic and limit shear unit by convex optimization optimal condition and plastic energy double standard, and considers the calculation accuracy and grid calculation efficiency, and can be mainly used for three-dimensional soil slope, rock slope, earth-rock dam, deep foundation pit adaptive stability numerical calculation.

Description

Technical Field

[0001] This invention relates to a three-dimensional slope finite element adaptive meshing method, device, and computer-readable storage medium based on SDP complementary relaxation and plastic dissipation criteria, belonging to the technical fields of engineering numerical simulation, numerical optimization calculation, and stability calculation of geotechnical structures. Background Technology

[0002] The 3D slope finite element adaptive mesh technology uses the gradient of field variables such as stress and plastic strain as the error criterion. It can obtain the slope failure mode, sliding surface location, and plastic development range without pre-setting the sliding surface, which can effectively reduce mesh dependence, improve the solution accuracy of safety factor and limit state, and take into account computational efficiency. For example, Chinese patent document CN121191284A discloses a dynamic monitoring and early warning method for slope excavation based on digital twin, including the following steps: acquiring topographic point cloud, soil and rock stratification, and construction progress and performing preprocessing; establishing a 3D geometric twin and physical twin, using finite element simulation and completing boundary backpropagation and pore pressure rebalancing to form a twin baseline; calculating the observation residual and physical conservation residual and obtaining a highly consistent twin and assimilation sample set through joint updating; applying a topologically constrained sliding surface evolver and implementing adaptive mesh refinement and interface reconstruction in the critical zone; constructing a displacement and seepage pressure uncertainty cone domain based on the assimilation sample set and critical zone reinforcement model, outputting graded early warning results, and realizing highly consistent simulation and quantitative early warning of the entire slope excavation process. However, existing 3D slope finite element adaptive meshing technology still has some key shortcomings: First, the refinement criteria lack rigorous support from convex optimization theory: traditional adaptive refinement only uses equivalent plastic strain and deviatoric strain as single deformation scalars, without the support of SDP optimality conditions, and cannot quantitatively characterize the mathematical proximity of stress points to the Mohr-Coulomb yield cone; small strain elements in the elastic zone will be incorrectly refined, the mesh accuracy in the plastic slip zone is insufficient, the overall mesh number is redundant, and the computational efficiency drops significantly; Second, a single scalar cannot distinguish the strength of plastic shear: relying solely on strain cannot distinguish between small plastic deformations and the plastic concentration area of ​​the ultimate slip zone, and there is a lack of quantitative indicators based on the energy dimension; element plastic dissipation integrals The existing meshing algorithms do not use energy as a partitioning criterion to characterize the total accumulated energy of shear-plastic forces in the unit, resulting in low accuracy in slip zone identification and large errors in safety factor calculation. Thirdly, there is a lack of dual-criteria collaborative control logic for refinement / coarsening: only unidirectional refinement rules are set, lacking an automatic coarsening mechanism for the elastic zone mesh, leading to continuous refinement of the entire mesh, an explosion in the number of units, a single criterion, and poor reliability. Fourthly, there is no dynamic threshold adjustment mechanism for near-limit instability: slope... When the duality gap approaches zero and instability is imminent, the stress gradient of the slip zone increases sharply. The traditional adaptive mesh threshold is fixed throughout the process and cannot automatically improve the mesh resolution of the slip zone, resulting in distortion in the calculation of ill-conditioned slopes with high internal friction and no cohesion. Summary of the Invention

[0003] The purpose of this invention is to provide a three-dimensional slope finite element adaptive meshing method and apparatus based on the SDP complementary relaxation and plastic dissipation criterion.

[0004] The technical solution of this invention is: a three-dimensional slope finite element adaptive meshing method, comprising the following steps:

[0005] S1. Basic SDP Model Construction: Based on the three-dimensional slope geometry model, an initial finite element mesh is generated using a coarse mesh, and the global discrete equilibrium operator is extracted. Three-dimensional symmetric stress tensor A three-dimensional Mohr-Coulomb primitive-dual positive semidefinite programming (SDP) model for SSR intensity reduction is established, defining two sets of positive semidefinite cones: , Dual positive semidefinite variables: , ;

[0006] S2. SDP Dual Quantization Adaptive Criterion Global Calculation: Traversing all Gaussian integration points and solving for complementary relaxation residuals at all finite element Gaussian integration points. ; Traverse all the three-dimensional element integration weights and integrate to obtain the element plastic dissipation integral. ;

[0007] S3. Finite element element classification (partitioning) marking: preset encryption threshold (This can be called the complementary relaxation residual encryption threshold) and (This can be referred to as the plastic dissipation integral refinement threshold) and coarsening threshold. (This can be called the complementary relaxation residual coarsening threshold) and (This can be called the plastic dissipation integral coarsening threshold). Element partitioning is completed based on the dual coupling criterion, where any Gaussian point within the element satisfies... Or the integral of unit plastic dissipation These are marked as encryption units (or refinement units); all integration points of the unit. and If the above conditions are not met (both the above encryption and coarsening conditions are not met), the cell can be marked as a reserved cell (or an invariant cell) or not marked (equivalent to being marked as a reserved cell, and no subsequent encryption or sparse processing is performed, and the mesh size remains unchanged).

[0008] S4. Adaptive Remeshing of 3D Mesh: Tetrahedral / hexahedral local mesh refinement is performed on the region containing refined elements (or the plastic region, or quasi-plastic region), and mesh sparsity is achieved by merging elements in the region containing coarsened elements (or the elastic region, or quasi-elastic region); the stress tensor between the old and new meshes is completed. Dual variables , Interpolation mapping generates an updated global finite element mesh;

[0009] S5. Output Results: Output the adaptive network (final adaptive mesh) and visualization results of the three-dimensional plastic slip zone distribution, slope ultimate safety factor, and global stress field. The three-dimensional plastic slip zone distribution, slope ultimate safety factor, and global stress field visualization results can be obtained by existing technology.

[0010] In step S2, the complementary relaxation residuals are solved based on the following formula. :

[0011]

[0012] in, , , , To correspond to the dual positive semidefinite matrix, This is for matrix trace operations.

[0013] The element plastic dissipation integral is obtained by integrating the following formula. :

[0014]

[0015] in, Let e ​​be the integration domain of the three-dimensional finite element, and the integration is implemented by Gaussian weighted summation discretization.

[0016] The coefficients (basic material coefficients) are calculated based on the following formula. , :

[0017] .

[0018] The original positive semidefinite programming expression, Primal-SDP, is as follows:

[0019]

[0020] The expression for the dual semidefinite programming method (Dual-SDP) is as follows:

[0021]

[0022] The duality gap is: .

[0023] In step S3, the threshold configuration rule is: encryption threshold , Take 0.6 to 0.8 times the average plastic dissipation of the global element; coarsening threshold. , Take 0.1 to 0.3 times the average value of plastic dissipation of the global element.

[0024] Furthermore, for sandy slopes with high internal friction and no cohesion, the densification threshold should be lowered simultaneously. and To increase the grid density of the slip zone.

[0025] In step S4, the interpolation method for the new and old mesh variables is: stress tensor and dual matrix , Second-order Lagrange form interpolation is used to ensure the continuity of SDP constraints. After interpolation, the complementary relaxation residuals at all integration points are recalculated. .

[0026] The adaptive loop termination condition is: dual gap If the relative change in the safety factor is less than 0.5% after two consecutive rounds of mesh partitioning, the adaptive iteration is stopped.

[0027] A three-dimensional slope finite element adaptive meshing device, used to execute any of the three-dimensional slope finite element adaptive meshing methods disclosed in this invention, comprising:

[0028] The basic SDP model building module is used to generate initial finite element meshes based on a 3D slope geometry model using a coarse mesh, and to extract global discrete equilibrium operators. Three-dimensional symmetric stress tensor A three-dimensional Mohr-Coulomb primitive-dual positive semidefinite programming (SDP) model for SSR intensity reduction is established, defining two sets of positive semidefinite cones: , Dual positive semidefinite variables: , ;

[0029] The SDP dual-quantization adaptive criterion global calculation module is used to traverse all Gaussian integration points and solve for complementary relaxation residuals at all finite element Gaussian integration points. ; Traverse all the three-dimensional element integration weights and integrate to obtain the element plastic dissipation integral. ;

[0030] Finite element element classification (partitioning) tagging module: used to load encryption thresholds. and and coarsening threshold and The cell partitioning is completed based on the dual coupling criterion, and any Gaussian point within the cell satisfies... Or the integral of unit plastic dissipation Marked as an encrypted unit; all integration points of the unit and , are marked as coarsened elements; if the above conditions are not met, they can be marked as retained elements or not marked.

[0031] The 3D mesh adaptive re-meshing module is used to perform tetrahedral / hexahedral local mesh refinement in the region where the refined elements are located (also known as the plastic region or quasi-plastic region), and to achieve mesh sparsity processing by merging elements in the region where the coarsened elements are located (also known as the elastic region or quasi-elastic region); it also completes the stress tensor between the old and new meshes. Dual variables , Interpolation mapping generates an updated global finite element mesh (adaptive network); depending on the software architecture design, if necessary, calculations can also be performed on the three-dimensional plastic slip zone distribution, slope ultimate safety factor, and global stress field visualization results, and the specific calculation methods can adopt existing technologies;

[0032] The results output module is used to output the adaptive network (final adaptive mesh). When necessary, it can also be used to output the three-dimensional plastic slip zone distribution, slope ultimate safety factor, and global stress field visualization results.

[0033] A computer-readable storage medium storing a computer program that, when executed by a processor, implements any of the three-dimensional slope finite element adaptive subdivision methods disclosed in this invention.

[0034] This invention integrates the optimal condition of complementary relaxation using SDP and the dual quantization criterion of plastic dissipative energy integral to construct a bidirectional refinement-coarsening adaptive mesh generation system. It is coupled with dual-parameter homotopy SSR iteration based on dual gap and external force work, dynamically updating the mesh in each round of homotopy correction. Near instability, the refinement threshold is automatically lowered to enhance the accuracy of the slip zone mesh. This effectively solves the related technical problems of existing adaptive meshes and has the following effective effects:

[0035] 1) A balance between mesh accuracy and computational efficiency: automatic refinement of plastic slip zones and automatic coarsening of deep elastic zones, reducing mesh size by 15% to 20% under the same computational error;

[0036] 2) Rigorous criterion theory: Based on the SDP original dual optimal complementary relaxation condition, it distinguishes itself from purely empirical strain indices, and the slip zone positioning error is less than 1%;

[0037] 3) Dynamic matching plastic evolution: The mesh is updated synchronously in each round of homotopy iteration, and the expansion shear band is tracked synchronously as the intensity decreases;

[0038] 4) Stable adaptation to severe adverse conditions: Automatically densifies slip zones near instability of high internal friction, zero cohesion sandy slopes, with a relative error of less than 0.8% in the safety factor;

[0039] 5) High degree of automation, no need for manual preset of grid size, can perform batch layered three-dimensional adaptive calculation of slopes, foundation pits and earth-rock dams.

[0040] This invention employs a three-dimensional slope finite element adaptive meshing method based on SDP complementary relaxation and plastic dissipation criteria. It distinguishes elastic, critical plastic, and ultimate shear elements using convex optimization optimal conditions and plastic energy as dual standards, balancing computational accuracy and mesh computation efficiency. It can be mainly used for adaptive stability numerical calculation of three-dimensional soil slopes, rock slopes, earth-rock dams, and deep foundation pits. Attached Figure Description

[0041] Figure 1 This is the complete flowchart of adaptive partitioning;

[0042] Figure 2 This is the flowchart of the unit marker sub-flowchart for step S3;

[0043] Figure 3 This is the molecular flowchart for mesh resection in step S4;

[0044] Figure 4 This is a schematic diagram comparing the initial coarse mesh and the adaptively refined mesh of a 3D slope. The left image shows the initial coarse mesh, and the right image shows the adaptively refined mesh. Detailed Implementation

[0045] The present invention will be further described below with reference to the embodiments.

[0046] (I) Target Groups

[0047] Three-dimensional homogeneous soil slope, geometric height 10m, slope angle 45°; geotechnical parameters Bottom fully constrained, side normal constrained.

[0048] (II) Implementation Steps

[0049] 1) Modeling and Initial Mesh: Establish a 3D slope geometric model and input layered geotechnical parameters. (cohesion c, internal friction angle) (Including shear dilatation angle ψ, elastic modulus E, Poisson's ratio ν), displacement boundary, self-weight, and external load; initial meshing is generated using coarse tetrahedral mesh; SSR Mohr-Coulomb original / dual SDP model is built;

[0050] 2) Dual-criteria global calculation: Solving by traversing all Gaussian integration points. The unit Gaussian weighted integral is obtained Preset encryption threshold , coarsening threshold , ;in, This represents the element plastic dissipation integral of all finite element elements. The arithmetic mean, i.e. , The total number of finite element elements in the current mesh. The plastic dissipation integral of the e-th element;

[0051] 3) Unit label: or Marking encryption units; all integration points And dissipation is lower than Mark the coarsened units; retain the rest;

[0052] 4) Adaptive re-subdivision: Tetrahedral dichotomy refinement of the densified elements, coarsening by merging the elastic region elements; second-order Lagrange interpolation transfer. , , ;

[0053] 5) Termination criterion: Dual gap If the mesh safety factor changes by less than 0.5% for two consecutive rounds, stop the adaptive loop; output the adaptive mesh, plastic zone, and safety factor.

[0054] Extended operating conditions: For cohesive sandy soils, the initial densification threshold is simultaneously lowered to [value missing]. .

[0055] (III) Technical Points

[0056] 1) SDP complementary relaxation + plastic dissipation dual coupling adaptive criterion

[0057] This is the first time that the optimal complementary relaxation condition of semidefinite programming has been introduced into the field of adaptive finite element mesh in geotechnical engineering. From the perspective of convex optimization optimality, the mathematical distance between the stress point and the Mohr-Coulomb yield cone is quantitatively characterized. The degree of cumulative shear failure of the unit is quantified from the dimension of plastic dissipation energy; the dual criteria of geometry and energy are used to jointly determine the unit mesh refinement requirements, which is different from the traditional single strain index. The theory is rigorous and the accuracy of slip zone identification is greatly improved.

[0058] 2) Two-way adaptive mesh control (refinement + automatic coarsening)

[0059] Simultaneously setting the encryption threshold and coarsening threshold, local encryption is applied to plastic critical elements, while deep elastic elements with low complementary relaxation and low plastic dissipation across the entire domain are automatically merged and coarsened, avoiding continuous expansion of the mesh number. Under the same accuracy, the total number of elements is reduced by 35% to 50%, significantly shortening the solution time of the 3D model.

[0060] 3) Adaptive Strategy for Dynamic Thresholds Near the Limit of Instability

[0061] set up The threshold for determining the dual gap control parameter is... When a slope is nearing instability, the densification threshold is automatically reduced, and the mesh refinement of the slip zone is enhanced, solving the industry pain points of large stress gradient and insufficient mesh accuracy in the ultimate state.

[0062] 4) Complete interpolation mapping mechanism for SDP variables

[0063] Mesh update of 3D stress tensor Dual positive semidefinite matrix , Second-order interpolation propagation ensures the continuity of SDP constraints between the old and new grids. After interpolation, the complementary relaxation residuals of all integration points are recalculated, and the adaptive criterion has no data discontinuity throughout the process.

[0064] (iv) Implementation effect verification and comparison

[0065] Testing of strongly pathological, cohesive slopes. .

[0066] 1) Traditional equivalent plastic strain single adaptive: 20% more mesh elements, 8% safety factor error, sparse mesh in slip zone;

[0067] 2) SDP complementary relaxation + plastic dissipation dual criterion adaptive: the number of elements is reduced by 16%, the safety relative error is 0.7%, the slip zone is automatically densified, and the deep elastic zone is significantly coarsened;

[0068] 3) As the plastic zone expands during iteration, the mesh is dynamically refined in sync, achieving full automation without human intervention.

[0069] (V) The relevant mathematical derivations involved in this invention

[0070] i) Basic three-dimensional Mohr-Coulomb SDP model

[0071] The problem of three-dimensional slope stability limit analysis can be handled as the following optimization problem:

[0072]

[0073] Among them, scalar It is the load multiplier. It is a discrete equilibrium operator. and These are vectors representing variable load and constant load, respectively. It is stress, constraint This can be interpreted as the tensile cutoff yield criterion.

[0074] The dual problem of the above optimization problem can be expressed as:

[0075]

[0076] The physical principle of the dual problem is as follows: According to the upper bound theorem, under the condition that the external power is constant, the relationship between the displacement rate u and the strain rate e is minimized, and the internal power (including the external load) is also minimized.

[0077] Now consider a solution that satisfies all the constraints of the original problem. , If a solution (u, e) satisfies all constraints in the dual problem, then the dual gap is...

[0078]

[0079] If we constrain the original problem mentioned above Expand into a cone ,in If the product of multiple subcones is a direct product, then the dual problem becomes:

[0080]

[0081] in for Dual cone: .

[0082] The same result applies to the extended dual difference:

[0083]

[0084] The Mohr-Coulomb criterion is one of the most commonly used yield criteria in rock and soil mechanics. It describes the stress condition of a material at shear failure. In the three-dimensional principal stress space, the criterion can be expressed as:

[0085]

[0086] in, These are material parameters; 'c' represents cohesion. It is the internal friction angle. It is the principal stress.

[0087] set up If it is a symmetric stress tensor, then It is its characteristic value.

[0088] Introducing auxiliary scalars The Mohr-Coulomb criterion can be expressed as two sets of third-order positive semidefinite constraints:

[0089]

[0090] in, It is an identity matrix.

[0091] Let the two positive semi-definite matrices corresponding to Mohr's Coulomb be denoted as follows:

[0092]

[0093] The original constraint is equivalent to: .

[0094] The original semidefinite program is:

[0095]

[0096] The dual semidefinite program is:

[0097]

[0098] SDP dual gap: .

[0099] ii) SDP complementary relaxation residuals Derivation

[0100] The optimal complementary relaxation condition for a semi-definite cone: The feasible optimal solution satisfies that the complementary relaxation residuals take the maximum value of two sets of traces, characterizing the degree of deviation of the current stress from the optimal surface of the yield cone.

[0101]

[0102] The larger the value, the more severe the deviation of the stress at the Gaussian point from the Mohr-Coulomb yield cone, and the more refined the mesh needs to be. Approaching 0, the stress-yield surface is fully elastic and can be coarsened.

[0103] iii) Elemental plastic dissipation integral Derivation

[0104] The plastic dissipation density is a linear combination of the traces of the dual variables. The total cumulative plastic energy of the element is obtained by integrating over the entire element:

[0105]

[0106] Discrete Gaussian weighted summation form:

[0107]

[0108] The weights are Gaussian integrals. The larger the value, the higher the accumulation of plastic shear energy in the element, which belongs to the potential slip zone, and the mesh should be locally refined.

[0109] This invention has the following characteristics:

[0110] 1) The SDP theory of cross-convex optimization and the finite element method of soil and rock innovatively use the complementary relaxation optimal condition as the standard for mesh refinement and quantification, breaking through the limitations of traditional pure deformation empirical criteria;

[0111] 2) Geometric distance and plastic energy are used for dual-dimensional collaborative control of densification / coarsening to achieve bidirectional self-adaptation;

[0112] 3) Coupled iterative dynamic mesh updates, and automatic optimization of slip zone mesh accuracy when approaching the limit state.

[0113] The mathematical symbols used in the formulas and expressions of this invention are as follows:

[0114] Symmetric three-dimensional stress tensor;

[0115] : eigenvalues, Principal stresses;

[0116] : Identity matrix;

[0117] c: Soil-rock cohesion;

[0118] Φ: Angle of internal friction between rock and soil;

[0119] : Unit plastic dissipation integral;

[0120] :represent , It is a symmetric positive semi-definite matrix (i.e., its eigenvalues ​​are not less than 0);

[0121] Y is a 3rd order symmetric positive semi-definite matrix, Y = vec( ) is a symmetric matrix vectorization operator, i.e., vec( )= ;

[0122] Complementary relaxation residuals of semidefinite programming;

[0123] , Preset mesh refinement and Threshold;

[0124] , Preset mesh coarsening and Threshold.

Claims

1. A three-dimensional slope finite element adaptive meshing method, comprising the following steps: S1. Basic SDP Model Construction: Based on the three-dimensional slope geometry model, an initial finite element mesh is generated using a coarse mesh, and the global discrete equilibrium operator is extracted. Three-dimensional symmetric stress tensor A three-dimensional Mohr-Coulomb primitive-dual positive semidefinite programming model for SSR intensity reduction is established, defining two sets of positive semidefinite cones: , Dual positive semidefinite variables: , ; S2. SDP Dual Quantization Adaptive Criterion Global Calculation: Traversing all Gaussian integration points and solving for complementary relaxation residuals at all finite element Gaussian integration points. ; By iterating through all the integration weights of the three-dimensional elements, the integral is obtained as the element plastic dissipation integral. ; S3. Finite element classification label: preset encryption threshold and and coarsening threshold and The cell partitioning is completed based on the dual coupling criterion, and any Gaussian point within the cell satisfies... Or the integral of unit plastic dissipation Marked as an encrypted unit; all integration points of the unit and If the above conditions are not met, the element is marked as a coarsened element; if the above conditions are not met, the element is marked as a retained element or not marked. S4. Adaptive re-meshment of 3D mesh: Tetrahedral / hexahedral local mesh refinement is performed in the region where the refinement element is located, and mesh sparsity is achieved by merging elements in the region where the coarsening element is located; Complete the stress tensor between the old and new meshes Dual variables , Interpolation mapping generates an updated global finite element mesh; S5. Results Output: Outputs adaptive mesh, 3D plastic slip zone distribution, slope ultimate safety factor, and global stress field visualization results.

2. The three-dimensional slope finite element adaptive meshing method according to claim 1, characterized in that... In step S2, the complementary relaxation residuals are solved based on the following formula. : ； in, , , , To correspond to the dual positive semidefinite matrix, For matrix trace operations; The element plastic dissipation integral is obtained by integrating the following formula. : ； in, Let e ​​be the integration domain of the three-dimensional finite element, and the integration is implemented by Gaussian weighted summation discretization.

3. The three-dimensional slope finite element adaptive meshing method according to claim 1, characterized in that... The coefficients are calculated based on the following formula. , : ； The three-dimensional slope finite element adaptive meshing method according to claim 1 is characterized in that... The original positive semidefinite programming expression, Primal-SDP, is as follows: The expression for the dual semidefinite programming method (Dual-SDP) is as follows: The duality gap is: .

4. The three-dimensional slope finite element adaptive meshing method according to claim 1, characterized in that... In step S3, the threshold configuration rule is: encryption threshold , Take 0.6 to 0.8 times the average plastic dissipation of the global element; coarsening threshold. , Take 0.1 to 0.3 times the average value of plastic dissipation of the global element.

5. The three-dimensional slope finite element adaptive meshing method according to claim 5, characterized in that... For sandy slopes with high internal friction and no cohesion, the densification threshold should be lowered simultaneously. and .

6. The three-dimensional slope finite element adaptive meshing method according to claim 1, characterized in that... In step S4, the interpolation method for the new and old mesh variables is: stress tensor and dual matrix , Second-order Lagrange form interpolation is used for propagation, and the complementary relaxation residuals at all integration points are recalculated after interpolation. .

7. The three-dimensional slope finite element adaptive meshing method according to any one of claims 1 to 7, characterized in that... The adaptive loop termination condition is: dual gap If the relative change in the safety factor is less than 0.5% after two consecutive rounds of mesh partitioning, the adaptive iteration is stopped.

8. A three-dimensional slope finite element adaptive subdivision device, characterized in that... The method for implementing the three-dimensional slope finite element adaptive meshing method according to any one of claims 1 to 8 includes: The basic SDP model building module is used to generate initial finite element meshes based on a 3D slope geometry model using a coarse mesh, and extract global discrete equilibrium operators. Three-dimensional symmetric stress tensor A three-dimensional Mohr-Coulomb primitive-dual positive semidefinite programming model for SSR intensity reduction is established, defining two sets of positive semidefinite cones: , Dual positive semidefinite variables: , ; The SDP dual-quantization adaptive criterion global calculation module is used to traverse all Gaussian integration points and solve for complementary relaxation residuals at all finite element Gaussian integration points. ; Traverse all the three-dimensional element integration weights and integrate to obtain the element plastic dissipation integral. ; Finite element element classification and labeling module: used to load encryption thresholds and and coarsening threshold and The cell partitioning is completed based on the dual coupling criterion, and any Gaussian point within the cell satisfies... Or the integral of unit plastic dissipation Marked as an encrypted unit; all integration points of the unit and If the above conditions are not met, the element is marked as a coarsened element; if the above conditions are not met, the element is marked as a retained element or not marked. The 3D adaptive re-mesh module is used to perform tetrahedral / hexahedral local mesh refinement in the region containing refined elements, and to achieve mesh sparsity processing in the region containing coarsened elements by merging elements; it also completes the stress tensor between the old and new meshes. Dual variables , Interpolation mapping generates an updated global finite element mesh; Results output module: Used to output the adaptive network, as well as the three-dimensional plastic slip zone distribution, slope ultimate safety factor, and global stress field visualization results.

9. A computer-readable storage medium, characterized in that... The device contains a computer program that, when executed by a processor, implements the three-dimensional slope finite element adaptive subdivision method according to any one of claims 1 to 8.

Images