Steel structure weld finite element model modeling method and system
Patent Information
- Application Number
- CN202610951761.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-06-29
- Publication Date
- 2026-10-20
Smart Images

Figure FT_1 
Figure FT_2 
Figure SMS_1
Abstract
Description
Technical Field
[0001] This invention relates to the field of computer-aided design technology, specifically to a finite element modeling method and system for steel structure welds. Background Technology
[0002] Currently, finite element modeling methods and systems for steel structure welds are developing towards integration, automation, and high-fidelity multiphysics coupling. The mainstream approach still relies on domain-specific modeling of the base material, weld, and heat-affected zone. However, key aspects such as automatic generation of weld paths and sections, consistency processing from global to local coordinates, and mesh adaptation and error-driven control remain challenging. Parameter integration and topology identification due to diverse data sources require more efficient automation technologies.
[0003] In the existing technology, in the traditional finite element modeling of steel structure welds, the base material, weld, heat-affected zone and other regions are often modeled separately and coupled analysis is performed. Welding heat input, heat diffusion, material nonlinearity and phase transformation behavior are usually performed in a simplified thermo-mechanical coupling or step-by-step processing method. The coupling restoration of temperature field, stress field and phase transformation evolution during the welding process is low, and it is difficult to accurately predict residual stress, deformation and defect tendency. In addition, existing methods have significant shortcomings in parameter integration, coordinate unification, mesh adaptation, and result error control. Most of the structural and weld parameters and working conditions come from different sources and require manual alignment. There is a lack of automated transformation from the global coordinate system to the local coordinate system and topological relationship recognition. The generation of weld paths and cross-sectional profiles largely depends on manual operation. The mesh is usually static or uniformly refined, and the mesh elements are difficult to adaptively optimize, thereby reducing the prediction accuracy of the finite element model.
[0004] Therefore, it is necessary to provide a finite element modeling method and system for steel structure welds to solve the aforementioned problem.
[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention
[0006] The purpose of this invention is to provide a finite element modeling method and system for steel structure welds to solve the problems mentioned in the background art.
[0007] To achieve the above objectives, the present invention provides the following technical solution: A finite element modeling method and system for steel structure welds, comprising the following steps: Step 1: Obtain the geometric parameters of the weld, define the area to be modeled based on the geometric parameters of the weld, and construct the base material basic model of the area to be modeled. Construct the weld geometry at the connection part of the base material according to the geometric parameters of the weld, mark the weld extension path and cross-sectional profile, and perform Boolean merging processing on the base material basic model and the weld geometry to form a solid geometric model containing the base material and weld area. Step 2: Divide the solid geometry model into regions according to the weld extension path and cross-sectional profile, defining the base material region, the weld region, and the heat-affected zone between the base material region and the weld region. Step 3: Construct a welding phase transformation thermo-mechanical coupling model, solve for the phase transformation rate and latent heat of phase transformation in the heat-affected zone, introduce the latent heat of phase transformation into the heat conduction equation for coupling solution, and calculate the temperature field distribution in the heat-affected zone; Step 4: Divide the heat-affected zone into finite element model meshes, and construct stress risk factors based on the phase change rate and temperature field distribution of each mesh. Traverse all meshes within the heat-affected zone and screen out meshes whose stress risk factors exceed the risk threshold. Step 5: Extract the temperature gradient and stress gradient of each screened mesh element, calculate the local error value of each mesh element based on the volume of each mesh element, compare the local error value of each mesh element with the error threshold, determine the density of each mesh element, and perform corresponding finite element model mesh element optimization.
[0008] Furthermore, the region to be modeled is defined based on the geometric parameters of the weld, and a base material model of the region to be modeled is constructed. The method used is as follows: Collect the geometric parameters of the weld, including weld width, weld height, weld length, weld bevel angle, and base metal thickness; The formula used to determine the radius of the heat-affected zone of the weld based on the weld height is: in, The radius of the heat-affected zone of the weld. For weld height, It is an empirical coefficient for welding conditions. The value range is from 1 to 3; Set the coordinates of the weld start point in the global coordinate system as follows: , Let x, y, and y be the x, y, and y coordinates of the weld start point, respectively. Combined with the weld length, the coordinates of the weld end point are determined as follows: ,in Indicates the weld length; Based on weld width weld height and the radius of the heat-affected zone Define the spatial boundaries of the area to be modeled, and enclose it to form a rectangular bounding box to be modeled; The spatial extent of the rectangular bounding box in the global coordinate system is as follows: Xiangwei ; Xiangwei ; Xiangwei ; Based on the coordinates of the rectangular bounding box and the boundary constraints, a basic model of the base material of the area to be modeled is constructed in the 3D modeling software, and the weld geometry is constructed by matching the parameters of the connection part of the base material.
[0009] Furthermore, the weld extension path and cross-sectional profile are calibrated, and the base metal model and weld geometry are Boolean merged to form a solid geometric model containing both the base metal and weld regions. The method used is as follows: Based on the weld bevel angle weld width weld height The standard cross-sectional profile parameters of the weld are calibrated. The weld is a trapezoidal groove weld for steel structure butt joints, and the cross-section of the weld is an axisymmetric isosceles trapezoid. The cross-sectional dimensions satisfy the following geometric constraint formula: in, This refers to the bottom butt joint width of the weld section; The linear weld extension path is calibrated based on a global coordinate system. The weld extension path is the central axis from the weld start point to the weld end point. The spatial parameter equation of the extension path is: in, This represents the x-coordinate of any sampling point along the extension path of the weld center in the global coordinate system, which varies with the path coefficient. Linear change, Let represent the longitudinal coordinates of all points along the extended path from the weld center in the global coordinate system. The vertical coordinates of all points along the extended path from the weld center in the global coordinate system; The calibrated weld section profile is scanned and stretched along the weld extension path to generate an integrated weld geometry at the base material butt joint. The base material basic model and the weld geometry are selected to perform solid summation Boolean merging operations, that is, to remove redundant overlapping surfaces at the contact point between the base material and the weld geometry, close the internal cavity, and retain the original geometric boundaries of the base material boundary and the weld outer contour. The integrated molding results in a solid geometric model containing the base material region and the weld region.
[0010] Furthermore, in step S2, the base material region, weld region, and heat-affected region are defined respectively, based on the following method: The heat-affected zone is the transitional solid area between the weld area and the base metal area. Using the weld center axis as the path and the isosceles trapezoid as the cross-sectional profile, the outer contour boundary of the weld is determined, and the weld area is enclosed. This area strictly follows the constraints of the weld cross-sectional dimensions and the center path coordinates. Using the weld centerline as a reference, the isosceles trapezoidal weld section is divided according to the radius of the heat-affected zone. The heat-affected zone (HAZ) cross-sectional profile is obtained by equidistant expansion, with the expansion distance on one side equal to the radius of the HAZ. ; The cross-sectional profile is scanned and stretched along the weld extension path to form a three-dimensional heat-affected zone. The inner side of this zone is attached to the outer contour of the weld zone, and the outer side is connected to the inner boundary of the base material zone. The overall base area is determined by the rectangular boundary to be modeled. The weld area and heat-affected area within the range are removed, and the remaining solid is the base material area. The three regions satisfy the volume conservation relationship: ,in, The total volume of the solid geometric model. For the volume of the parent material region, For the volume of the weld area, The volume of the heat-affected zone.
[0011] Furthermore, the phase change rate and latent heat of phase change within the heat-affected region are solved. The latent heat of phase change is then incorporated into the heat conduction equation for coupled solution, and the temperature field distribution within the heat-affected region is calculated. The method used is as follows: A two-way coupled solid-state phase transformation-thermodynamic model is constructed for the defined heat-affected zone. The real-time phase transformation rate of the heat-affected zone is solved based on the phase transformation kinetic equation. The formula for calculating the phase transformation rate is as follows: in, This indicates the real-time phase transformation rate of the steel structure in the heat-affected zone. The volume fraction of the instantaneous phase transition. This refers to the phase transformation morphology index of welded steel. The value range is 1.2-2.0. These are temperature-dependent phase transition kinetic coefficients. The instantaneous temperature of a single grid cell in the heat-affected zone; The instantaneous latent heat of phase change per unit volume of a single grid cell in the heat-affected zone is calculated by combining the real-time phase change rate. The formula for calculating the instantaneous latent heat of phase change per unit volume is as follows: in, The instantaneous latent heat of phase transition per unit volume of a single grid cell. Density of the base steel structure. The enthalpy of phase transformation per unit mass of steel; By introducing the latent heat of instantaneous phase change as an internal heat source term into the classical transient heat conduction equation, a phase change-thermodynamic coupled heat conduction governing equation is constructed. The formula on which this equation is based is: in, For the specific heat capacity of steel structures, For welding simulation duration, The thermal conductivity of the base material For the temperature Laplace operator, To input heat from an external heat source for welding; Based on the finite element boundary conditions and the spatial boundary of the heat-affected zone, the coupled modified heat conduction equation is solved iteratively, and the three-dimensional instantaneous temperature field distribution data of the entire heat-affected zone is output.
[0012] Furthermore, a stress risk factor is constructed based on the real-time phase change rate and temperature field distribution within the heat-affected zone. The method used is as follows: The stress risk factor for each mesh element is extracted based on the real-time phase transition rate and instantaneous temperature coupling. The formula used is as follows: in, The stress risk factor for the mesh element. The maximum phase transition rate in the heat-affected zone. The peak temperature of the entire heat-affected zone. , These are the dimensionless weighting coefficients corresponding to the phase change rate term and the temperature term, respectively. On this basis, let ; Based on the above formula for calculating stress risk factors, the stress risk factors of all mesh elements are calculated by traversing all mesh elements. Filter grid cells whose stress risk factor is greater than the preset risk threshold.
[0013] Furthermore, the local error value of each selected grid cell is calculated using the following formula: in, This represents the local error value of the selected grid cells. For temperature gradient, For stress gradient, The volume of the grid cell; Based on the formula for calculating local error values mentioned above, all selected mesh cells are traversed, and the local error values of all selected mesh cells are calculated.
[0014] Furthermore, the local error values of each selected mesh element are compared with the error threshold to determine the density of each mesh element, and the corresponding finite element model mesh element optimization is performed, as follows: When the local error value of a mesh element is less than or equal to the error threshold, it is determined that the discretization simulation error of the mesh element meets the accuracy requirements of welding thermo-coupling calculation, and the original hexahedral mesh element structure and mesh size are retained without modification. When the local error value of a mesh element is greater than the error threshold, it is determined that the discretization simulation error of the mesh element does not meet the accuracy requirements of welding thermo-coupling calculation. The mesh element is then densified to reduce the volume of a single mesh element. After all mesh elements are optimized, the global mesh model of the heat-affected zone is updated to complete the mesh element optimization of the weld finite element model.
[0015] The present invention also provides a finite element modeling system for steel structure welds, the system being used to execute the above-described finite element modeling method for steel structure welds, comprising: The parameter collection module is used to obtain the geometric parameters of the weld, delineate the area to be modeled based on the geometric parameters of the weld, construct the base material basic model of the area to be modeled, construct the weld geometry at the connection part of the base material according to the geometric parameters of the weld, calibrate the weld extension path and cross-sectional contour, and perform Boolean merging processing on the base material basic model and the weld geometry to form a solid geometric model containing the base material and weld area. The region division module is used to divide the solid geometry model into regions based on the weld extension path and cross-sectional profile, defining the base material region, the weld region, and the heat-affected zone located between the base material region and the weld region. The coupled model construction module is used to construct a welding phase change thermo-mechanical coupled model, solve the phase change rate and latent heat of phase change in the heat-affected region, introduce the latent heat of phase change into the heat conduction equation for coupled solution, and calculate the temperature field distribution in the heat-affected region. The region filtering module is used to divide the heat-affected zone into finite element model mesh elements, and construct stress risk factors based on the phase change rate and temperature field distribution of each mesh element. It traverses all initial mesh elements in the heat-affected zone and filters out mesh elements whose stress risk factors exceed the risk threshold. The mesh optimization module is used to extract the temperature gradient and stress gradient of each screened mesh element, calculate the local error value of each mesh element in combination with the volume of each mesh element, compare the local error value of each mesh element with the error threshold, determine the density of each mesh element, and perform corresponding finite element model mesh element optimization.
[0016] Compared with the prior art, the beneficial effects of the present invention are: To address the issues of weak zonal coupling in traditional finite element modeling of steel structure welds, simplified step-by-step processing of phase transformation and thermodynamic processes, and low fidelity of multi-physics coupling, this invention utilizes a unified coordinate system to complete quantitative geometric modeling and Boolean merging, achieving precise and seamless division of the base material, weld, and heat-affected zone. Furthermore, it incorporates the latent heat of phase transformation into the heat conduction equation to construct a phase transformation thermodynamic coupling model, fully reproducing the bidirectional interaction mechanism between the welding temperature field and solid-state phase transformation, effectively improving the prediction accuracy of residual stress, deformation, and defect tendency. This invention uses standardized parameters to drive the entire modeling process. It targets and locks down mesh cells whose stress risk factors exceed the risk threshold based on stress risk factors, obtains the local error value of each mesh cell, compares the local error value of each mesh cell with the error threshold, determines the density of each mesh cell, and performs corresponding adaptive optimization of the finite element model mesh cells, thereby controlling the computational load while ensuring the simulation accuracy of key areas. Attached Figure Description
[0017] Figure 1 This is a schematic diagram of the overall method flow of the present invention.
[0018] Figure 2 This is a block diagram of the system modules of the present invention. Detailed Implementation
[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.
[0020] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.
[0021] Example: Please see Figure 1 A finite element modeling method for steel structure welds, comprising the following steps: Step 1: Obtain the geometric parameters of the weld, define the area to be modeled based on the geometric parameters of the weld, and construct the base material basic model of the area to be modeled. Construct the weld geometry at the connection part of the base material according to the geometric parameters of the weld, calibrate the weld extension path and cross-sectional profile, and perform Boolean merging processing on the base material basic model and the weld geometry to form a solid geometric model containing the base material and weld area.
[0022] In a specific embodiment of the present invention, this step is to construct a solid geometric model with parameter quantification, step-by-step modeling and overall integration as the core design ideas. First, core geometric parameters such as weld width, weld height, weld length, weld bevel angle and base metal thickness are collected in a comprehensive manner and used as the basis for modeling. Then, the radius of the heat-affected zone is calculated by formula quantification, and the start and end coordinates of the weld and the rectangular bounding box to be modeled are solved by relying on a unified global coordinate system to delineate the modeling range, thus abandoning the traditional mode of arbitrarily delineating the area based on manual experience. Based on this, a base material model is first built, and then the cross-sectional dimensions of the trapezoidal groove weld are determined by using geometric constraint formulas in combination with weld geometric parameters. At the same time, the extension path of the weld center is calibrated by spatial parameter equations, and the weld geometry is generated by scanning and stretching the cross-sectional profile along the path to accurately restore the actual spatial shape of the weld. Finally, a solid summation Boolean merge operation is performed on the base material model and the weld geometry to eliminate geometric defects at the model joint, and merge the two parts of the structure into a complete and continuous solid model, completing the preliminary geometric modeling work and providing a compliant and complete geometric carrier for subsequent processes such as model region division and phase change thermo-mechanical coupling solution.
[0023] Furthermore, the region to be modeled is defined based on the geometric parameters of the weld, and a base material model of the region to be modeled is constructed. The method used is as follows: Collect the geometric parameters of the weld, including weld width, weld height, weld length, weld bevel angle, and base metal thickness; The above geometric parameters are all measured in millimeters, where: weld width The maximum transverse width of the weld top surface, and the weld height. The vertical height of the weld bead above the base material surface, the weld length The weld bevel angle is the total length of the weld along its extension direction. The bevel angle of the base material butt joint is the angle between the bevels, and the thickness of the base material is the vertical thickness of the weld base plate. All geometric parameters were obtained through engineering measurements, welding drawing annotations, or 3D scanning. The formula used to determine the radius of the heat-affected zone of the weld based on the weld height is: in, The radius of the heat-affected zone of the weld. For weld height, It is an empirical coefficient for welding conditions. The value ranges from 1 to 3. In the above formula, the empirical coefficient for welding conditions is... The selection rule is as follows: when using manual arc welding and with a large heat input, take... When using medium heat input welding processes such as gas shielded welding and submerged arc welding, take... When using low heat input welding processes such as pulse welding and cold welding, take... ; Set the coordinates of the weld start point in the global coordinate system as follows: , Let x, y, and y be the x, y, and y coordinates of the weld start point, respectively. Combined with the weld length, the coordinates of the weld end point are determined as follows: ,in Indicates the weld length; It should be noted that this scheme uniformly adopts a three-dimensional Cartesian global rectangular coordinate system. The origin of the coordinate system is selected at any position outside the modeling area where there is no structural interference. The following rules apply: The axis is parallel to the direction of weld extension. The shaft is arranged transversely to the base material and perpendicular to the weld extension direction. The axis is the vertical height direction. This scheme is for modeling straight butt welds, including all points along the entire weld. , The coordinates remain constant; Selecting formula The technical basis for determining the radius of the heat-affected zone (HAZ) is as follows: the extent of the weld HAZ is essentially determined by both the welding heat input and the heat transfer characteristics of the base metal; in engineering, the weld height is significantly positively correlated with the welding heat input. The greater the heat input, the more weld deposits and the higher the weld height, the wider the HAZ formed by the heat diffusion to the base metal. Moreover, this formula belongs to the classic empirical estimation paradigm in the field of welding engineering and falls within the scope of existing technology. Public information and engineering manuals in the welding industry generally recognize the rule that "the size of the HAZ is positively correlated with the weld geometry and the welding heat input." There are a large number of similar empirical formulas and engineering methods that estimate the HAZ range based on weld size, heat input, and empirical coefficients.
[0024] Based on weld width weld height and the radius of the heat-affected zone The spatial boundary of the area to be modeled is enclosed to form a rectangular bounding box for modeling; The spatial extent of the rectangular bounding box in the global coordinate system is as follows: Towards: Towards: Towards: The three sets of boundaries are centered on the weld body contour and are defined along the length, width, and height dimensions according to the radius of the heat-affected zone. The entire area is expanded outward to form a rectangular boundary frame; this ensures that the entire weld body is included and the surrounding heat-affected zone is fully incorporated. Based on the coordinates of the rectangular boundary frame and the boundary constraints, the base material model of the area to be modeled is constructed in the 3D modeling software, and the weld geometry is constructed by matching the parameters of the connection part with the base material.
[0025] It should be noted that: In this plan The shaft is arranged along the extension direction of the weld, and the weld body is in To the interval is To incorporate the heat-affected zones at both ends of the weld, along Radius of the heat-affected zone expanding outwards at both ends ,get To the entire region ; The axis is along the width of the weld, and the weld is centered on the centerline. Symmetrical distribution, body width range is Expand outwards to both sides by a distance, i.e., radius After that, I received Towards the boundary range ; The axis is the vertical height direction. In this scheme, the heat-affected zone is divided equally along the vertical direction, with the upper and lower sides extending outwards by a distance of [missing information]. The lower limit of the interval is shifted downward from the reference height. We have obtained that the upper limit of the interval includes the overall height of the weld. And shift upwards .
[0026] This embodiment uses mainstream industrial 3D solid modeling software, including any one of SolidWorks, UG-NX, and AutoCAD-3D. Before modeling, the software unit is uniformly set to millimeters, and the global tolerance for modeling is set to 0.01mm. When constructing the base material model, the solid structure is created strictly according to the rectangular boundary frame range. The thickness of the base material is consistent with the base material parameters collected in the early stage. The mating surface of the base material is a flat and fitting surface to ensure accurate assembly with the weld geometry in the later stage.
[0027] Furthermore, the weld extension path and cross-sectional profile are calibrated, and the base metal model and weld geometry are Boolean merged to form a solid geometric model containing both the base metal and weld regions. The method used is as follows: Based on the weld bevel angle Weld width (width at the top of the weld cross-section) weld height Complete the calibration of the standard cross-sectional profile parameters of the weld; The modeling object of this invention is a trapezoidal groove weld in a steel structure, with a cross-section that is axisymmetric and isosceles trapezoidal. The cross-sectional dimensions satisfy the following geometric constraint formula: in, This refers to the bottom butt joint width of the weld section; It should be noted that this solution uses a double-sided symmetrical welding bevel, and the bevel angle... The angle between the bevel slope and the vertical direction; in the isosceles trapezoidal section, the upper base corresponds to the top surface of the weld, and the lower base corresponds to the bottom surface where the weld and the base material fit together. The entire section is symmetrical about the central axis of the weld.
[0028] The linear weld extension path is calibrated based on a global coordinate system. The weld extension path is the central axis from the weld start point to the weld end point. The spatial parameter equation of the extension path is: in, This represents the x-coordinate of any sampling point along the extension path of the weld center in the global coordinate system, which varies with the path coefficient. Linear change, Let represent the longitudinal coordinates of all points along the extended path from the weld center in the global coordinate system. Let be the vertical coordinates of all points along the extended path from the weld center in the global coordinate system; in the above formula, the path coefficient... For normalized position coefficients, when When, it corresponds to the start of the weld; when When, it corresponds to the end point of the weld; when At that time, it corresponds to the midpoint on the weld extension path; The calibrated weld section profile is scanned and stretched along the weld extension path to generate an integrated weld geometry at the base material butt joint. The base material basic model and the weld geometry are selected to perform solid summation Boolean merging operations, that is, to remove redundant overlapping surfaces at the contact point between the base material and the weld geometry, close the internal cavity, and retain the original geometric boundaries of the base material boundary and the weld outer contour. The integrated molding results in a solid geometric model containing the base material region and the weld region.
[0029] Step 2: Divide the solid geometry model into regions according to the weld extension path and cross-sectional profile, defining the base material region, the weld region, and the heat-affected zone located between the base material region and the weld region.
[0030] In a specific embodiment of the present invention, this part uses the method of "equidistant outward expansion of weld section + scanning and stretching along the path" to generate the heat-affected zone, so that the heat-affected zone completely covers the outer periphery of the weld. The shape is highly matched with the spatial shape of the actual heat-affected zone formed by heat diffusion and microstructure transformation during the welding process of steel structure, which conforms to the physical laws of welding heat transfer and solid phase transformation. Furthermore, through the boundary design of inner fitting and outer connection, the weld area, heat-affected zone and base material area are seamlessly connected. At the same time, the volume conservation formula is used to verify the partitioning results, and the three major areas are forcibly constrained to have no overlap, no gaps, and no solid missing parts, which effectively avoids problems such as interruption of temperature field and stress field transmission and calculation distortion caused by area intersection, voids, and misalignment. The heat-affected zone, as the transition area between the weld and the base material, is independently divided to form a dedicated computational domain. This domain can accurately meet the requirements of the phase transformation thermo-mechanical coupling solution in step 3. Phase transformation and heat conduction calculation conditions can be applied to the heat-affected zone separately. The partition boundaries are clear and the computational domain is independent, which greatly improves the relevance and calculation accuracy of subsequent multiphysics simulations.
[0031] Furthermore, in step S2, the base material region, weld region, and heat-affected region are defined respectively, based on the following method: The heat-affected zone is the transitional solid area between the weld area and the base metal area. Using the weld center axis as the path and the isosceles trapezoid as the cross-sectional profile, the outer contour boundary of the weld is determined, and the weld area is enclosed. This area strictly follows the constraints of the weld cross-sectional dimensions and the center path coordinates. Using the weld centerline as a reference, the isosceles trapezoidal weld section is divided according to the radius of the heat-affected zone. The heat-affected zone (HAZ) cross-sectional profile is obtained by equidistant expansion, with the expansion distance on one side equal to the radius of the HAZ. ; The cross-sectional profile is scanned and stretched along the weld extension path to form a three-dimensional heat-affected zone. The inner side of this zone is attached to the outer contour of the weld zone, and the outer side is connected to the inner boundary of the base material zone. The overall base area is determined by the rectangular boundary to be modeled. The weld area and heat-affected area within the range are removed, and the remaining solid is the base material area. The three regions satisfy the volume conservation relationship: ,in, The total volume of the solid geometric model. For the volume of the parent material region, For the volume of the weld area, The volume of the heat-affected zone.
[0032] Step 3: Construct a welding phase transformation thermo-mechanical coupling model, solve for the phase transformation rate and latent heat of phase transformation in the heat-affected zone, introduce the latent heat of phase transformation into the heat conduction equation for coupling solution, and calculate the temperature field distribution in the heat-affected zone.
[0033] In a specific embodiment of the present invention, this step constructs a two-way coupled model of solid-state phase transformation and thermodynamics for the heat-affected zone. The phase transformation rate of the unit is calculated based on the phase transformation kinetic equation, and the latent heat of phase transformation is solved in combination with the phase transformation rate. The latent heat of phase transformation is introduced as an internal heat source into the transient heat conduction equation to complete the coupled solution. This completely makes up for the shortcomings of traditional welding temperature field simulation, which only uses pure heat conduction equation and ignores the heat release effect of solid-state phase transformation and latent heat of phase transformation of steel. It fully restores the real physical process of the interaction between temperature field and solid-state phase transformation during welding, greatly improves the calculation accuracy and realism of three-dimensional instantaneous temperature field of heat-affected zone, and provides accurate and reliable field quantity basic data for subsequent stress risk factor construction, mesh local error calculation and mesh adaptive optimization. Furthermore, the phase change rate and latent heat of phase change within the heat-affected region are solved. The latent heat of phase change is then incorporated into the heat conduction equation for coupled solution, and the temperature field distribution within the heat-affected region is calculated. The method used is as follows: All physical quantities in this step adopt the International System of Units (SI): the unit for temperature is... The unit of length is The density unit is The units for heat and enthalpy are: ; A two-way coupled solid-state phase transformation-thermodynamic model is constructed for the defined heat-affected zone. Based on the phase transformation kinetic equation, the real-time phase transformation rate of the heat-affected zone is solved. The formula for calculating the phase transformation rate is as follows: in, This indicates the real-time phase transformation rate of the steel structure in the heat-affected zone. The volume fraction of the instantaneous phase transition. This refers to the phase transformation morphology index of welded steel. The value range is 1.2-2.0. These are temperature-dependent phase transition kinetic coefficients. The instantaneous temperature of a single grid cell in the heat-affected zone; In the above formula, take The range of values always satisfies For ferrite phase transformation Targeting the phase transition of pearlite ; The curve was obtained by fitting the transformation curve of the steel under continuous cooling, and it varies with the instantaneous temperature of the mesh elements. Dynamic changes; The phase transformation rate calculation formula used in this invention is essentially a differential form of the phase transformation kinetic equation, which belongs to the classic existing technology in the field of material phase transformation kinetics. Using this formula, the nucleation-growth kinetics of diffusion-type solid phase transformation such as ferrite and pearlite in the heat-affected zone of steel structure welding can be accurately described. It can characterize the coupled influence of temperature and phase transformation fraction on the phase transformation rate and is highly consistent with the working conditions of non-isothermal and continuous phase transformation in welding.
[0034] The instantaneous latent heat of phase change per unit volume of a single grid cell in the heat-affected zone is calculated by combining the real-time phase change rate. The formula for calculating the instantaneous latent heat of phase change per unit volume is as follows: in, The instantaneous latent heat of phase transition per unit volume of a single grid cell. Density of the base steel structure. The enthalpy of phase transition per unit mass of steel is given. The range of values for the enthalpy of phase transition per unit mass of conventional welded steel is as follows: This formula belongs to the well-known existing technology in the field of materials heat transfer and welding numerical simulation. It is the standard instantaneous calculation form of the latent heat of phase change "internal heat source method (source term method)". Its derivation logic is based on the basic principle of energy conservation and has been widely used in welding thermal process simulation and solid-state phase change simulation of materials.
[0035] By introducing the latent heat of instantaneous phase change as an internal heat source term into the classical transient heat conduction equation, a phase change-thermodynamic coupled heat conduction governing equation is constructed. The formula on which this equation is based is: in, For the specific heat capacity of steel structures, For welding simulation duration, The thermal conductivity of the base material For the temperature Laplace operator, To input heat from the external heat source for welding, this embodiment uses a general double ellipsoidal volume heat source model for welding simulation. The heat source loading position coincides with the central axis of the weld, and the loading time is consistent with the actual welding operation time. The main framework of this phase change-thermal coupled heat conduction governing equation is derived from the classical transient heat conduction equation, which is a well-known existing technology in the field of heat transfer; an external heat source for welding is introduced on the basis of the classical equation. With latent heat of phase change internal heat source The dual-source coupling form is also a common and mature technical solution in the field of welding thermo-mechanical coupling simulation; for the thermal conductivity of the base material The specific determination method is as follows: Based on the specific grade of the base material, consult the corresponding material thermophysical property handbook and the parameter library for the continuous cooling transformation curve of steel to obtain the measured values of thermal conductivity at multiple temperature nodes; for low-carbon steel and low-alloy steel base materials, take the average equivalent thermal conductivity from room temperature to the welding medium temperature range. The range of values is Among them, ordinary low-carbon steels such as Q235 and Q355 are used. Low alloy high strength steel is taken Furthermore, priority should be given to using the "Handbook of Thermophysical Properties of Metallic Materials", the nominal parameters of national steel standards, or publicly available test data of the same grade of steel.
[0036] The initial temperature of the entire simulation domain is uniformly set to room temperature. Thermal boundary conditions were set for the model: the outer surface of the base material and the top surface of the weld adopted a combined convection and thermal radiation boundary, and the ambient temperature was [temperature value missing]. The surface emissivity of the steel is set to 0.8; the bottom and far-end sides of the model are set as thermally insulating boundaries. Based on the above-mentioned finite element initial conditions, thermal boundary conditions, and spatial boundary of the thermally affected region, iterative calculations are carried out using a finite element transient solver. The control parameters for solving the problem are set as follows: the transient time step is taken as... The maximum number of iterations is set to 1000, and the temperature convergence tolerance is set to... When the calculation results meet the convergence tolerance, the iteration is considered complete, and the final output is the three-dimensional instantaneous temperature field distribution data of the global thermally affected area.
[0037] Step 4: Divide the heat-affected zone into finite element model meshes, and construct stress risk factors based on the phase change rate and temperature field distribution of each mesh element. Traverse all mesh elements within the heat-affected zone and screen out mesh elements whose stress risk factors exceed the risk threshold.
[0038] In this specific embodiment of the invention, this step continues the previous three-dimensional modeling and finite element solution software environment, and uniformly adopts a global modeling tolerance of 0.01mm and international standard physical measurement units to adapt to the straight weld seam conditions of carbon steel and low alloy steel flat plates. First, the independently divided heat-affected zone is structured and meshed. The entire region is initially meshed using regular hexahedral solid mesh elements. The mesh elements have regular shapes, no distorted sharp angles, and no degenerate meshes. The initial mesh size of the heat-affected zone is uniformly set, and the mesh nodes are coupled at the interface of the three zones to ensure continuous transmission of field data across regions. After the meshing is completed, the simulation results that have converged in step 3 are retrieved, and the real-time phase transition rate corresponding to each hexahedral mesh element in the heat-affected zone is extracted. Instantaneous temperature of a single grid cell in the heat-affected zone ; Furthermore, a stress risk factor is constructed based on the phase change rate and temperature field distribution within the thermally affected region. The method used is as follows: The stress risk factor for each mesh element is extracted based on the real-time phase transition rate and instantaneous temperature coupling. The formula used is as follows: in, The stress risk factor for the mesh element; In the formula for calculating the stress risk factor in the design, , All designed to be compatible with The reason for the linear positive correlation is that the essence of welding stress risk is the superposition of the intensity of thermal effect and phase transformation effect: the higher the temperature, the more intense the local thermal expansion and contraction, and the greater the thermal stress; the faster the phase transformation rate, the more significant the volumetric abrupt change of the microstructure, and the greater the microstructure stress. The higher the intensity of the two types of inducing factors, the higher the risk of stress failure. The two are naturally positively correlated, and the linear form is the most direct and essential mathematical expression of this positive correlation law. During the welding cooling process, the steel in the heat-affected zone undergoes a solid-state phase transformation, accompanied by changes in specific volume and volume. The faster the phase transformation rate, the more drastic the abrupt change in microstructure volume per unit time, resulting in greater microstructural stress. Furthermore, the stronger the phase transformation inhomogeneity, the easier it is to induce localized stress concentration and microcracks, thus increasing the risk of weld cracking and deformation failure. The larger, The larger it is, the bigger it becomes; Localized high-temperature heating during welding, followed by uneven cooling, causes differentiated thermal expansion and contraction in the material, which is the core source of welding thermal stress. The higher the temperature of the affected area, the greater the temperature difference with the surrounding lower-temperature areas, resulting in stronger constraint of thermal deformation by the surrounding base material and a higher level of thermal stress. Simultaneously, the yield strength of steel decreases at high temperatures, making it more prone to plastic deformation and residual stress accumulation, significantly increasing the risk of stress failure and structural damage. The larger, The larger it is, the bigger it becomes; The maximum phase transition rate in the heat-affected zone. The peak temperature of the entire heat-affected zone. , These are the dimensionless weighting coefficients corresponding to the phase change rate term and the temperature term, respectively. On this basis, let ; In the formula for the stress risk factor of the above-mentioned mesh element generation, combined with the stress generation mechanism of steel structure welding, welding thermal stress is the dominant cause of regional stress cracking, and microstructure phase transformation stress is the secondary cause. Therefore, the weighting coefficient of the temperature term is limited. The weighting coefficient of the phase transition rate term is greater than ; Based on the above formula for calculating stress risk factors, a mesh traversal operation logic was written to automatically traverse all the divided hexahedral mesh elements within the heat-affected zone, batch normalize the two physical parameters of phase change rate and temperature, and simultaneously calculate the dimensionless stress risk factors corresponding to all mesh elements. The risk threshold of this invention is obtained by improving and calibrating the industry standard for stress failure in the weld heat-affected zone and phase transformation stress test data, and a preset risk threshold is established. Each unit risk factor is compared and judged against the risk threshold, and those that meet the criteria are selected. Grid cells.
[0039] Step 5: Extract the temperature gradient and stress gradient of each screened mesh element, calculate the local error value of each mesh element based on the volume of each mesh element, compare the local error value of each mesh element with the error threshold, determine the density of each mesh element, and perform corresponding finite element model mesh element optimization.
[0040] In a specific embodiment of the present invention, the finite element solution post-processing module is called to extract field parameters from all selected hexahedral mesh elements. The average temperature gradient of a single mesh element, the equivalent Mises stress gradient of the element, and the solid volume of the mesh element are extracted in a unified manner. The field parameter extraction nodes correspond one-to-one with the mesh nodes in step 4 to ensure that the gradient data and volume data are from the same source and to prevent data misalignment and deviation.
[0041] Furthermore, the local error value of each grid cell is calculated using the following formula: in, This represents the local error value of the mesh element. For temperature gradient, For stress gradient, The volume of the grid cell; In the above calculation formula, the local error value is calculated based on the fundamental theoretical basis of finite element posterior error. The core error of finite element mesh discretization simulation is determined by two core factors: the degree of abrupt change in the gradient of field variables and the size of mesh elements. The larger the physical field gradient and the larger the mesh element volume size, the greater the mesh interpolation fitting deviation and the higher the simulation discretization error. This is the core underlying theoretical support of this formula. In addition, based on the specific engineering basis of welding thermo-coupling simulation, the heat-affected zone of steel structure welds has the dual field strength abrupt change characteristics of temperature field and residual stress field. A single temperature gradient or a single stress gradient cannot characterize the real error of coupling simulation. Euclidean norm is used to couple and merge temperature gradient and stress gradient to accurately match the error evaluation requirements of phase change-thermal bidirectional coupling simulation of this invention. The mesh size correction mechanism in the formula is based on the cube root of the mesh element volume. Size correction is performed to conform to the industry standard for volume error correction of 3D solid hexahedral meshes, eliminate interference from mesh length, width and shape, and unify the standard for 3D mesh size error correction. Based on the formula for calculating local error values mentioned above, traverse all mesh cells and calculate the local error values for all mesh cells.
[0042] It should be noted that the error threshold is calculated based on the improved calculation of the mean parameters of the global grid cells obtained through screening. The formula for calculating the error threshold is: ,in To obtain a globally uniform error threshold through adaptive solution, This represents the arithmetic mean of the temperature gradients of all grid cells. The arithmetic mean of the stress gradients of all mesh elements; The arithmetic mean of the volumes of all grid cells; The existing common correction coefficient for welding thermo-coupling simulation is 0.8, which is taken as the steel working condition in this invention. This coefficient is a publicly available fixed working condition parameter in the industry. Furthermore, the local error values of each selected mesh element are compared with the error threshold to determine the density of each mesh element, and the corresponding finite element model mesh element optimization is performed, as follows: When the local error value of a mesh element is less than or equal to the error threshold, it is determined that the discretization simulation error of the mesh element meets the accuracy requirements of welding thermo-coupling calculation, and the original hexahedral mesh element structure and mesh size are retained without modification. When the local error value of a mesh element is greater than the error threshold, it is determined that the discretization simulation error of the mesh element does not meet the accuracy requirements of welding thermo-coupling calculation. The mesh element is then densified to reduce the volume of a single mesh element. After all mesh elements are optimized, the global mesh model of the heat-affected zone is updated to complete the mesh element optimization of the weld finite element model.
[0043] Please see Figure 2 The present invention also provides a finite element modeling system for steel structure welds, the system being used to execute the above-described finite element modeling method for steel structure welds, comprising: The parameter collection module is used to obtain the geometric parameters of the weld, delineate the area to be modeled based on the geometric parameters of the weld, construct the base material basic model of the area to be modeled, construct the weld geometry at the connection part of the base material according to the geometric parameters of the weld, calibrate the weld extension path and cross-sectional contour, and perform Boolean merging processing on the base material basic model and the weld geometry to form a solid geometric model containing the base material and weld area. The region division module is used to divide the solid geometry model into regions based on the weld extension path and cross-sectional profile, defining the base material region, the weld region, and the heat-affected zone located between the base material region and the weld region. The coupled model construction module is used to construct a welding phase change thermo-mechanical coupled model, solve the phase change rate and latent heat of phase change in the heat-affected region, introduce the latent heat of phase change into the heat conduction equation for coupled solution, and calculate the temperature field distribution in the heat-affected region. The region filtering module is used to divide the heat-affected zone into finite element model mesh elements, and construct stress risk factors based on the phase change rate and temperature field distribution of each mesh element. It traverses all initial mesh elements in the heat-affected zone and filters out mesh elements whose stress risk factors exceed the risk threshold. The mesh optimization module is used to extract the temperature gradient and stress gradient of each screened mesh element, calculate the local error value of each mesh element in combination with the volume of each mesh element, compare the local error value of each mesh element with the error threshold, determine the density of each mesh element, and perform corresponding finite element model mesh element optimization.
[0044] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.
[0045] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.
[0046] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.
[0047] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.
Claims
1. A finite element modeling method for steel structure welds, characterized in that, The specific steps include: Step 1: Obtain the geometric parameters of the weld, define the area to be modeled based on the geometric parameters of the weld, and construct the base material basic model of the area to be modeled. Construct the weld geometry at the connection part of the base material according to the geometric parameters of the weld, mark the weld extension path and cross-sectional profile, and perform Boolean merging processing on the base material basic model and the weld geometry to form a solid geometric model containing the base material and weld area. Step 2: Divide the solid geometry model into regions according to the weld extension path and cross-sectional profile, defining the base material region, the weld region, and the heat-affected zone between the base material region and the weld region. Step 3: Construct a welding phase transformation thermo-mechanical coupling model, solve for the phase transformation rate and latent heat of phase transformation in the heat-affected zone, introduce the latent heat of phase transformation into the heat conduction equation for coupling solution, and calculate the temperature field distribution in the heat-affected zone; Step 4: Divide the heat-affected zone into finite element model meshes, and construct stress risk factors based on the phase change rate and temperature field distribution of each mesh. Traverse all meshes within the heat-affected zone and screen out meshes whose stress risk factors exceed the risk threshold. Step 5: Extract the temperature gradient and stress gradient of each screened mesh element, calculate the local error value of each mesh element based on the volume of each mesh element, compare the local error value of each mesh element with the error threshold, determine the density of each mesh element, and perform corresponding finite element model mesh element optimization.
2. The finite element modeling method for steel structure welds according to claim 1, characterized in that, The method used to define the region to be modeled based on the geometric parameters of the weld and to construct the base material model of the region to be modeled is as follows: Collect the geometric parameters of the weld, including weld width, weld height, weld length, weld bevel angle, and base metal thickness; The radius of the heat-affected zone of the weld is determined based on the weld height. Set the coordinates of the weld start point in the global coordinate system as follows: , Let x, y, and y be the x, y, and y coordinates of the weld start point, respectively. Combined with the weld length, the coordinates of the weld end point are determined as follows: ,in Indicates the weld length; Based on weld width weld height and the radius of the heat-affected zone Define the spatial boundaries of the area to be modeled, and enclose it to form a rectangular bounding box to be modeled; The spatial extent of the rectangular bounding box in the global coordinate system is as follows: Xiangwei ; Xiangwei ; Xiangwei ; Based on the coordinates of the rectangular bounding box and the boundary constraints, a basic model of the base material of the area to be modeled is constructed in the 3D modeling software, and the weld geometry is constructed by matching the parameters of the connection part of the base material.
3. The finite element modeling method for steel structure welds according to claim 2, characterized in that, The weld extension path and cross-sectional profile are calibrated, and the base material model and weld geometry are Boolean merged to form a solid geometric model containing the base material and weld regions. The method used is as follows: Based on the weld bevel angle weld width weld height The standard cross-sectional profile parameters of the weld are calibrated. The weld is a trapezoidal groove weld for steel structure butt joint. The cross-section of the weld is an axisymmetric isosceles trapezoid, and the cross-sectional dimensions satisfy the geometric constraint formula. Based on the global coordinate system, the straight weld extension path is calibrated. The weld extension path is the central axis from the weld start point to the weld end point. The spatial parameter equation of the extension path is constructed. The calibrated weld section profile is scanned and stretched along the weld extension path to generate an integrated weld geometry at the base material butt joint. The base material basic model and the weld geometry are selected to perform solid summation Boolean merging operations, that is, to remove redundant overlapping surfaces at the contact point between the base material and the weld geometry, close the internal cavity, and retain the original geometric boundaries of the base material boundary and the weld outer contour. The integrated molding results in a solid geometric model containing the base material region and the weld region.
4. The finite element modeling method for steel structure welds according to claim 3, characterized in that, In step S2, the base material area, weld area, and heat-affected zone are defined respectively, based on the following method: The heat-affected zone is the transitional solid area between the weld area and the base metal area. Using the weld center axis as the path and the isosceles trapezoid as the cross-sectional profile, the outer contour boundary of the weld is determined, and the weld area is enclosed. This area strictly follows the constraints of the weld cross-sectional dimensions and the center path coordinates. Using the weld centerline as a reference, the isosceles trapezoidal weld section is divided according to the radius of the heat-affected zone. The heat-affected zone (HAZ) cross-sectional profile is obtained by equidistant expansion, with the expansion distance on one side equal to the radius of the HAZ. ; The cross-sectional profile is scanned and stretched along the weld extension path to form a three-dimensional heat-affected zone. The inner side of this zone is attached to the outer contour of the weld zone, and the outer side is connected to the inner boundary of the base material zone. The overall base area is determined by the rectangular boundary to be modeled. The weld area and heat-affected area within the range are removed, and the remaining solid is the base material area. The three regions satisfy the volume conservation relationship: ,in, The total volume of the solid geometric model. For the volume of the parent material region, For the volume of the weld area, The volume of the heat-affected zone.
5. The finite element modeling method for steel structure welds according to claim 4, characterized in that, The phase change rate and latent heat of phase change within the heat-affected region are determined by incorporating the latent heat of phase change into the heat conduction equation for coupled solution, thereby calculating the temperature field distribution within the heat-affected region. The method used is as follows: A two-way coupled model of welding solid-state phase transformation and thermodynamics was constructed for the defined heat-affected zone, and the real-time phase transformation rate of the heat-affected zone was solved based on the phase transformation kinetic equation. The instantaneous latent heat of phase change per unit volume of a single grid cell in the thermally affected region is solved by combining the real-time phase change rate. The latent heat of instantaneous phase change is introduced as an internal heat source term into the classical transient heat conduction equation to construct the phase change-thermal coupling heat conduction control equation. Based on the finite element boundary conditions and the spatial boundary of the heat-affected zone, the coupled modified heat conduction equation is solved iteratively, and the three-dimensional instantaneous temperature field distribution data of the entire heat-affected zone is output.
6. The finite element modeling method for steel structure welds according to claim 5, characterized in that, The stress risk factor is constructed based on the real-time phase change rate and temperature field distribution within the heat-affected zone. The method used is as follows: The stress risk factor is constructed by extracting the real-time phase transition rate and instantaneous temperature coupling corresponding to each grid cell. The stress risk factor of all grid cells is calculated by traversing all grid cells. Filter grid cells whose stress risk factor is greater than the preset risk threshold.
7. The finite element modeling method for steel structure welds according to claim 6, characterized in that, Calculate the local error value of each selected grid cell, iterate through all selected grid cells, and calculate the local error value of all selected grid cells.
8. The finite element modeling method for steel structure welds according to claim 7, characterized in that, The local error values of each selected mesh element are compared with the error threshold to determine the density of each mesh element, and the corresponding finite element model mesh element optimization is performed, as follows: When the local error value of a mesh element is less than or equal to the error threshold, it is determined that the discretization simulation error of the mesh element meets the accuracy requirements of welding thermo-coupling calculation, and the original hexahedral mesh element structure and mesh size are retained without modification. When the local error value of a mesh element is greater than the error threshold, it is determined that the discretization simulation error of the mesh element does not meet the accuracy requirements of welding thermo-coupling calculation. The mesh element is then densified to reduce the volume of a single mesh element. After all mesh elements are optimized, the global mesh model of the heat-affected zone is updated to complete the mesh element optimization of the weld finite element model.
9. A finite element modeling system for steel structure welds, characterized in that, The system is used to execute the finite element modeling method for steel structure welds according to any one of claims 1-8, including: The parameter collection module is used to obtain the geometric parameters of the weld, delineate the area to be modeled based on the geometric parameters of the weld, construct the base material basic model of the area to be modeled, construct the weld geometry at the connection part of the base material according to the geometric parameters of the weld, calibrate the weld extension path and cross-sectional contour, and perform Boolean merging processing on the base material basic model and the weld geometry to form a solid geometric model containing the base material and weld area. The region division module is used to divide the solid geometry model into regions based on the weld extension path and cross-sectional profile, defining the base material region, the weld region, and the heat-affected zone located between the base material region and the weld region. The coupled model construction module is used to construct a welding phase change thermo-mechanical coupled model, solve the phase change rate and latent heat of phase change in the heat-affected region, introduce the latent heat of phase change into the heat conduction equation for coupled solution, and calculate the temperature field distribution in the heat-affected region. The region filtering module is used to divide the heat-affected zone into finite element model mesh elements, and construct stress risk factors based on the phase change rate and temperature field distribution of each mesh element. It traverses all initial mesh elements in the heat-affected zone and filters out mesh elements whose stress risk factors exceed the risk threshold. The mesh optimization module is used to extract the temperature gradient and stress gradient of each screened mesh element, calculate the local error value of each mesh element in combination with the volume of each mesh element, compare the local error value of each mesh element with the error threshold, determine the density of each mesh element, and perform corresponding finite element model mesh element optimization.