A simulation method and system for stress deformation of laser powder bed fusion based on a particle-spring model
By discretizing the laser powder bed fusion forming process into a hexahedral mesh using a mass-spring model and combining thermal strain and material elastic-plasticity constitutive properties, the problems of low computational efficiency and poor convergence in the prior art are solved, and rapid and accurate stress and deformation prediction of the LPBF forming process is realized.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HUAZHONG UNIV OF SCI & TECH
- Filing Date
- 2026-04-13
- Publication Date
- 2026-06-09
AI Technical Summary
Existing technologies for laser powder bed melting and forming suffer from low computational efficiency, poor convergence, and complex models, making it difficult to accurately predict stress and deformation. In particular, they lack systematic modeling of thermo-mechanical coupling behavior when forming large parts.
The three-dimensional model is divided into multiple hexahedral mesh models using a mass-spring model. Each hexahedral mesh is equivalent to a coupled system of three types of springs. By calculating the force and displacement of each vertex, and combining thermal strain and material elastoplastic constitutive model, iterative solution is performed to simulate stress and deformation.
It significantly improves computational efficiency and stability, enabling rapid and accurate prediction of stress and deformation during LPBF forming, and is suitable for complex thermo-mechanical coupling and plastic deformation processes, simplifying the model building process.
Smart Images
Figure CN122174501A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of additive manufacturing technology, and more specifically, relates to a simulation method and system for stress deformation in laser powder bed melting forming based on a mass-spring model. Background Technology
[0002] Laser powder bed fusion (LPBF) technology has been widely used in aerospace, biomedicine, and other fields due to its ability to achieve near-net-shape forming of complex parts. However, the intense and non-uniform thermal cycling during LPBF forming can easily lead to large residual stresses inside the parts, resulting in defects such as warping and cracking, which seriously affect the forming quality. Therefore, rapid and accurate prediction of stress and deformation during the forming process is crucial for optimizing process parameters and predicting defects during the process development stage.
[0003] Currently, macroscopic-scale numerical simulations of the LPBF forming process mainly rely on the finite element method (FEM). The FEM can handle complex geometric models and nonlinear constitutive relations, and has high computational accuracy. However, when applied to workpiece-scale LPBF layer-by-layer forming simulations, this method faces the following technical bottlenecks: (1) Low computational efficiency: The LPBF forming process involves a large number of time steps and complex nonlinear solutions. The finite element method requires solving a large sparse linear system of equations with a huge degree of freedom, resulting in extremely long computation time and making it difficult to meet the needs of rapid iteration in engineering.
[0004] (2) Poor convergence: During the simulation of material melting and cooling, due to the drastic changes in material properties and complex contact nonlinearity, the finite element model often faces the problem of convergence difficulty or even solution failure.
[0005] (3) Complex model construction: The preprocessing work based on the finite element method, such as layer-by-layer activation and application of complex boundary conditions, is cumbersome and requires a high level of professional experience from the user.
[0006] In recent years, some studies have attempted to use the Mass-Spring System (MSS) for rapid deformation simulation. MSS discretizes the continuum into a network of masses and springs, obtaining the displacement field by solving for the force equilibrium of the masses. Compared to the finite element method, the MSS model is simpler to construct, has lower degrees of freedom, and offers stable iterative solutions, leading to successful applications in fields such as computer graphics and biomechanics. However, existing MSS methods are mostly designed for simple elastic bodies and lack systematic modeling of the complex thermo-mechanical coupling behaviors (such as thermal strain and elastoplastic constitutive models) in metal additive manufacturing, making it difficult to directly apply to the accurate prediction of forming stress and deformation in LPBF (Limited Particulate Air Forming).
[0007] As laser powder bed fusion technology matures and becomes more widely used, the size of formed parts is increasing. There is an urgent need to develop a fast simulation method that balances computational efficiency and simulation accuracy to solve the problems of long calculation time and poor convergence in the existing finite element method for predicting stress and deformation of workpiece-scale LPBF. Furthermore, it should be able to handle the complex thermodynamic behavior and elastoplastic behavior of materials during LPBF forming. Summary of the Invention
[0008] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a simulation method and system for stress and deformation in laser powder bed fusion forming based on a mass-spring model, solving problems such as low computational efficiency, poor convergence, and complex models in LPBF forming stress and deformation simulation.
[0009] To achieve the above objectives, according to one aspect of the present invention, a method for simulating stress and deformation in laser powder bed melting forming based on a mass-spring model is provided, the method comprising the following steps: S1 divides the three-dimensional model of the substrate and the part to be formed in laser powder bed melting into multiple hexahedral mesh models. Each hexahedral mesh model is equivalent to a coupling system of three types of springs, including edge springs, angle springs and volume springs. S2 calculates the force on each vertex of the hexahedron under the current temperature field using the three types of springs equivalent to each hexahedron mesh model, and calculates the displacement of each vertex under the force, and updates the coordinates of each vertex using the displacement. S3 determines whether the displacement increment of each vertex relative to the previous moment is greater than a preset threshold. If it is greater than the preset threshold, return to step S2 until the displacement increment of all vertices is less than the preset threshold. Otherwise, output the current coordinates of each vertex and calculate the current stress and strain of each vertex. S4 Repeat steps S2 to S3 until the coordinates, stress, and strain of each vertex under the temperature field at all times are obtained.
[0010] More preferably, the hexahedral mesh model is equivalent to a coupling system of three types of springs in the following manner: Each edge of a hexahedral mesh is equivalent to an edge spring; any two edges at each vertex form an angle spring; the hexahedral mesh as a whole is a volume spring.
[0011] More preferably, the formula for calculating the force on each vertex is as follows:
[0012] in, The resultant force of the spring force acting on the vertex. Let be the resultant force exerted on the vertex by all the edge springs acting on that vertex. The resultant force of all angular springs acting on the vertex is the force acting on the vertex. The resultant force of all volume springs acting on the vertex is the force acting on the vertex.
[0013] More preferably, the formula for calculating the force at the two vertices of the side spring is as follows:
[0014]
[0015] in, , These are the two vertices of the side spring. , The force exerted by the spring on that side Let be the stiffness of the edge spring. This refers to the elastic deformation of the edge spring. From the vertex Pointing to the vertex The unit vector.
[0016] More preferably, the formula for calculating the elastic deformation of the side spring is as follows:
[0017] in, For , The elastic deformation of the edge spring at the vertex. The equivalent elastic strain of the edge spring. The initial length of the side spring is given.
[0018] More preferably, the formula for calculating the force at each vertex of the angle spring is as follows:
[0019]
[0020]
[0021] in, , , For As the vertex, , The angle of the spring at the endpoint relative to the vertex , , The force, This is the current angle of the angle spring. Let this be the stiffness of the spring at that angle. The elastic angular deformation of the angle spring. , , The coordinates are , , , , .
[0022] More preferably, the formula for calculating the elastic deformation of the angle spring is as follows:
[0023] in, For As the vertex, , The elastic angular deformation of the spring is the angle at the endpoint. The equivalent elastic strain of the angle spring is... This is the initial angle of the angle spring.
[0024] More preferably, the formula for calculating the force at any vertex of the volume spring is as follows:
[0025] in, For a volume spring about any vertex The force, Let the stiffness of the spring be the volume. This refers to the elastic deformation of a volume spring. As vertex Location coordinates, It is the volume of the spring.
[0026] More preferably, the formula for calculating the elastic deformation of the volume spring is as follows:
[0027] in, This represents the elastic deformation of the spring of this volume. This refers to the mechanical deformation of the spring of this volume.
[0028] According to another aspect of the present invention, a simulation system for stress deformation in laser powder bed fusion forming based on a mass-spring model is provided. The system includes an actuator for performing the above-described simulation method for stress deformation in laser powder bed fusion forming based on a mass-spring model.
[0029] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art: 1. This invention divides the 3D model into multiple hexahedral mesh models using a mass-spring model, and each hexahedral mesh model is equivalent to a coupled system of three types of springs. Each vertex of the hexahedral mesh undergoes independent nonlinear iteration based on mechanical equilibrium. Traditional finite element methods require solving a large set of equations, which is slow, prone to divergence, and requires continuous expansion of the equation set for the LPBF layer-by-layer scanning process, making it complex. Compared with the method of solving a set of equations, this invention has a faster solution speed, lower coupling, better convergence, and is easy to add nodes to the discrete system, making it suitable for the process characteristics of adding nodes in LPBF layer-by-layer scanning.
[0030] 2. When calculating the forces acting on each vertex of a hexahedron, this invention calculates the forces acting on each spring separately. It incorporates thermal strain and the material's elastoplastic constitutive model into the solution of elastic deformation, thus improving upon the shortcomings of the traditional mass-spring model, which is difficult to balance thermal coupling and material elastoplasticity. By introducing the vertex-spring model, it makes it suitable for LPBF forming, a forming process with high thermal coupling and prone to plastic deformation.
[0031] 3. The simulation method provided by the present invention discretizes the continuum into an equivalent mass-spring system and introduces equivalent thermal strain and elastoplastic constitutive model into the discretized system, thereby significantly improving the computational efficiency and stability while ensuring the accuracy of stress deformation simulation calculation in the LPBF forming process. Attached Figure Description
[0032] Figure 1 This is a flowchart of the iterative solution algorithm in the embodiments of the present invention.
[0033] Figure 2 This is a schematic diagram of the discrete model of hexahedral mesh particles-spring in an embodiment of the present invention.
[0034] Figure 3 This is a schematic diagram illustrating the material rheological curves and plastic strain calculations at different temperatures in an embodiment of the present invention. Detailed Implementation
[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.
[0036] A simulation method for stress deformation in laser powder bed melting forming based on a mass-spring model, comprising the following steps: S1 represents the discretized hexahedral mesh of the 3D solid model as a coupled system composed of three types of springs: edge springs, angle springs, and volume springs. Based on the energy consistency principle of the continuum mechanics that the strain energy is equal to the potential energy of the discrete springs, the stiffness expressions of the edge springs, angle springs, and volume springs are obtained, and the force exerted by each spring on the nodes is obtained according to the potential energy gradient principle.
[0037] (1) Construction of discrete model of mass-spring Read the hexahedral mesh model of the laser powder bed fusion printed part and the substrate generated by the ray method or other mesh generation algorithm, and then convert each hexahedral mesh into a coupled system of three types of springs (edge springs, angle springs, and volume springs) and discrete particles to construct a discrete particle-spring model.
[0038] Edge springs: These are placed along each edge of a hexahedron to characterize the axial tensile and compressive effects of the material.
[0039] Angle spring: At each node, any two adjacent edges with that node as the vertex constitute an angle spring, used to characterize the shear deformation effect of the material.
[0040] Volume spring: A volume spring is placed inside each hexahedral unit to characterize the volume change effect of the material.
[0041] like Figure 2 As shown, each hexahedral element is discretized into 12 edge springs, 24 angle springs (3 groups per vertex), and 1 volume spring. Discrete particles are all nodes of the hexahedral mesh, and these particles interact with each other through edge springs, angle springs, and volume springs.
[0042] (2) Spring stiffness setting and force calculation formula The equivalent stiffness of each spring is calculated according to the principle of energy consistency. A mapping relationship is established between the stiffness of the discrete spring and the actual mechanical properties of the material (such as shear modulus G(T), bulk modulus K(T), Lamé constant λ(T)) and mesh size, so that the discrete model can accurately reflect the macroscopic mechanical behavior of the material. Taking a cubic hexahedral mesh as an example, with a mesh side length of h, the conclusions are consistent for irregular hexahedral meshes. The stiffnesses of the three types of springs are as follows: (1) Side spring stiffness: (1) (2) Angular spring stiffness: (2) (3) Volume spring stiffness: (3) Then, using the principle of potential energy gradient, we can obtain the forces exerted by various types of springs on the nodes: (1) Axial internal force of the side spring: For the side spring formed by nodes i and j, Let be the unit vector pointing from node i to node j. Then the relationship between the axial force of the side spring on both nodes and the axial elastic deformation of the side spring is as follows: (4) (5) (2) Shear force of the angle spring: For the angle spring composed of nodes u, v, and w, u is the vertex, and the coordinates of nodes u, v, and w are respectively , , Let vector , The included angle is The relationship between the force exerted by the angle spring on the three nodes and the elastic deformation of the angle spring is as follows: (6) (7) (8) (3) Volumetric spring internal force: For any node p of the elements constituting the hexahedron, the coordinates are The force exerted by the volume spring is: (9) in As the initial reference volume, the volume of a hexahedron is decomposed into several tetrahedrons for solution. , , , The volume of the tetrahedron formed by these tetrahedrons is expressed as: (10) It can be obtained by taking the partial derivatives of the volumes of each decomposed tetrahedron with respect to the coordinates of node p and adding them together.
[0043] S2 applies the effect of thermal deformation to the side spring and volume spring obtained by discretization in (1) through the coefficient of thermal expansion, and applies the effect of the elastic-plastic constitutive model of J2 to the side spring and angle spring obtained by discretization in (1).
[0044] like Figure 1 As shown, for the temperature field at each time step, the temperature field of that time step is first loaded into the discrete mass-spring model. Due to the change in the temperature field, the force equilibrium positions of all discrete particles at the previous moment are no longer in equilibrium. It is necessary to solve for the new force equilibrium positions of each discrete particle, which is solved through the following iterative process: (1) Solve for the total axial deformation of each side spring, the total angular deformation of each angle spring, and the total volume deformation of each volume spring based on the position of the current discrete mass point.
[0045] Among them, the total axial deformation of the side spring composed of discrete mass points i and j Solution: First, let's consider the current coordinates of discrete particles i and j. Find the current length of the side spring The initial length of the spring is determined by the initial coordinates of discrete mass points i and j. Calculate the initial length The total axial deformation of the side spring is then... .
[0046] For discrete particles For the vertex and two other discrete particles , Solve for the total angular deformation of the spring at the endpoints: Firstly, when discrete particles... , , Current coordinates , , Calculate the current included angle , by discrete particles , , Calculate the initial angle from the initial coordinates. Then the total angular deformation of the angle spring .
[0047] For by — A volume spring composed of eight discrete particles, with one point taken within a hexahedron. Then take three points within the same plane, such as... To form a tetrahedron Therefore, the volume of the hexahedron can be decomposed into the sum of the volumes of eight tetrahedrons. Based on the coordinates of the current eight discrete particles and the initial eight discrete particles, the volumes of the hexahedrons can be calculated respectively. and The total volumetric deformation of the volume spring is...
[0048] (2) Solve for the axial thermal deformation of each side spring and the volumetric thermal deformation of each volume spring caused by the temperature change using the temperature change and the coefficient of thermal expansion. Subtract the corresponding total thermal deformation from the total deformation of each side spring and volume spring to obtain the total mechanical deformation (the sum of elastic deformation and plastic deformation). Angular springs have no thermal deformation, and the mechanical deformation of each angular spring is equal to its total deformation.
[0049] Thermal deformation in discrete systems only affects the edge springs and volume springs. Since thermal deformation is a uniform expansion in all directions, no angular deformation occurs. The effect of thermal strain is demonstrated through the thermal deformation of each edge spring and volume spring. The following discussion explores how to solve for the thermal deformation of each edge spring and volume spring using unidirectional thermal strain. For discrete point masses... The thermal deformation of the edge spring at the endpoint can be expressed as equation (11).
[0050]
[0051] in For discrete particles The initial length of the edge spring at the endpoint is . The current equivalent temperature of the spring on this side is defined as the current temperature at both ends. and The average value.
[0052] For a spring of a certain volume, its thermal deformation It can be approximated as equation (12).
[0053]
[0054] in, Let this be the initial volume of the spring. The equivalent temperature of the volumetric spring is defined as the average of the current temperatures of the eight nodes of the hexahedral mesh containing the volumetric spring.
[0055] Solve and Then, the total deformation of each side spring, angle spring, and volume spring minus their respective thermal deformation is the mechanical deformation, as shown in equation (13).
[0056]
[0057] (13)
[0058] (3) Using J2 elastic-plastic theory, such as Figure 3 As shown, the mechanical deformation of each side spring and angle spring is decomposed into elastic deformation and plastic deformation. For volume springs, elasticity and plasticity are not considered; that is, only elastic deformation exists, which is equal to the mechanical deformation.
[0059] This invention employs J2 elastoplasticity for the treatment of elastoplasticity, where plastic strain gradually accumulates. The material's rheological curve describes the relationship between equivalent plastic strain and stress at the current temperature. When mechanical strain is input... (The sum of elastic strain and plastic strain) and the accumulated plastic strain At that time, mechanical strain can be decomposed into elastic strain using rheological curves. and plastic strain The decomposition method first requires the assumption that the accumulated plastic strain has not increased, that is, the plastic strain under this stress state is... Then the elastic strain at this time (Trial calculation of elastic strain) and stress (Trial stress) can be expressed as equation (14) and equation (15).
[0060]
[0061] in, This is the elastic modulus at the current temperature. If we calculate the stress... Less than or equal to the current plastic strain Corresponding yield strength This indicates that the assumption is correct, and the plastic strain has not increased. Therefore, the elastic strain after decomposition is... and plastic strain As shown in equations (16) and (17) respectively.
[0062]
[0063] If the stress is calculated Greater than the current plastic strain Corresponding rheological stress If the result is negative, it means the assumption is invalid and the plastic strain increases. In this case, it is necessary to solve for the intersection of the two curves represented by equations (18) and (19), where the horizontal and vertical axes are the equivalent plastic strains. and stress ,like Figure 3 As shown, equation (19) represents the rheological curve of the material. In the solution process, the piecewise linear method is often used. Therefore, this problem can be simplified to the problem of finding the intersection of a straight line and a piecewise linear function.
[0064]
[0065] The x-coordinate of the intersection point obtained by solving is the plastic strain value after the plastic strain increases. The elastic strain value obtained from the decomposition is... .
[0066] According to the rheological curve, after inputting mechanical strain and accumulated plastic strain, the total strain can be decomposed into elastic strain and plastic strain. However, the three types of spring models used cannot directly characterize strain, but can only describe the deformation of the spring. Therefore, it is necessary to first convert the deformation of the three types of springs into equivalent strains, then separate the elastic strain and plastic strain according to the above method, and finally inversely map the elastic strain and plastic strain into the corresponding elastic deformation and plastic deformation of the spring. Due to the mechanical deformation of the volume spring... Excluding plastic deformation Therefore, the mechanical deformation of the volume spring does not need to be decomposed, and its elastic deformation... Equal to mechanical deformation, that is .
[0067] For discrete particles Mechanical deformation of the edge spring at the endpoint The decomposition of is shown in Equation (20) for the equivalent mechanical strain calculation.
[0068]
[0069] in For discrete particles The initial length of the end spring is given. An equivalent cumulative plastic strain is maintained in each end spring structure. The variable is the equivalent mechanical strain of the side spring. and equivalent cumulative plastic strain Substituting the method described above, the equivalent elastic strain of the side spring can be obtained. and equivalent plastic strain and will The plastic strain is stored in the equivalent cumulative plastic strain maintained within the side spring structure. In the variables, the spring on that side is decomposed to obtain elastic deformation. .
[0070] Since the deformations in this study are all small, the shear strain can be characterized by changes in angle. For discrete particles... For the vertex and two other discrete particles Mechanical deformation of the spring at the end point The decomposition of is shown in Equation (21) for the equivalent mechanical strain calculation.
[0071]
[0072] in For discrete particles For the vertex and two other discrete particles The initial included angle of the spring at the endpoint. An equivalent cumulative plastic strain is maintained in each spring structure. The variable is the equivalent mechanical strain of the angle spring. and equivalent cumulative plastic strain Substituting the method described above, the equivalent elastic strain of the angle spring can be obtained. and equivalent plastic strain and will The plastic strain is stored in the equivalent cumulative plastic strain maintained within the side spring structure. In the variables, the elastic deformation of the spring at that angle is obtained by decomposition. .
[0073] S3 calculates the position of all nodes based on force balance iteration for the temperature field at each time step, and then calculates physical quantities such as displacement, strain, and stress through the node positions, thereby completely simulating the stress and strain evolution of the entire LPBF forming process from scanning and cooling to the end of forming, as well as the residual stress and deformation distribution in the final state.
[0074] Using the formula given in the second stage for calculating the force on discrete particles from the elastic deformation of each spring, the force exerted by each spring on its related discrete particles is calculated, and then the resultant force of the spring action on each discrete particle is solved.
[0075] To achieve mechanical equilibrium for all discrete particles, each discrete particle moves a small step along the direction of the resultant force acting on it. (in For elastic modulus, Let be the grid side length. For iteration coefficients, The net force of the spring on this discrete particle. The iteration coefficients (typically 0.05-0.1) are used to update the coordinates. .
[0076] Check if the iteration has ended: when the maximum coordinate change of all nodes... When the temperature field is less than the set threshold (e.g., 1e-6mm), the iteration of the temperature field at the current time step ends, and it is assumed that the position of each discrete particle is the force equilibrium position under the temperature field conditions at the current time step. If the temperature field is not less than the set threshold, the operation of steps (1)-(5) needs to be repeated to continue iterating the position of the node.
[0077] After obtaining the force equilibrium positions of all discrete particles under the temperature field conditions at the current time step through iterative solution, the deformation field, strain field, and stress field of the continuum under the current temperature field conditions can be obtained in one step using mature finite element or finite difference algorithms.
[0078] S4 Repeat the above process, load the temperature field data for all time steps and calculate the deformation stress and strain field data under the temperature field conditions at that time step, thereby realizing the simulation of deformation stress and strain of the entire process of laser powder bed melting from scanning to cooling.
[0079] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for simulating stress and deformation in laser powder bed melting forming based on a mass-spring model, characterized in that, The method includes the following steps: S1 divides the three-dimensional model of the substrate and the part to be formed in laser powder bed melting into multiple hexahedral mesh models. Each hexahedral mesh model is equivalent to a coupling system of three types of springs, including edge springs, angle springs and volume springs. S2 calculates the force on each vertex of the hexahedron under the current temperature field using the three types of springs equivalent to each hexahedron mesh model, and calculates the displacement of each vertex under the force, and updates the coordinates of each vertex using the displacement. S3 determines whether the displacement increment of each vertex relative to the previous moment is greater than a preset threshold. If it is greater than the preset threshold, return to step S2 until the displacement increment of all vertices is less than the preset threshold. Otherwise, output the current coordinates of each vertex and calculate the current stress and strain of each vertex. S4 Repeat steps S2 to S3 until the coordinates, stress, and strain of each vertex under the temperature field at all times are obtained.
2. The method for simulating stress and deformation in laser powder bed melting forming based on a mass-spring model as described in claim 1, characterized in that, The hexahedral mesh model is equivalent to a coupling system of three types of springs, as follows: Each edge of a hexahedral mesh is equivalent to an edge spring; any two edges at each vertex form an angle spring; the hexahedral mesh as a whole is a volume spring.
3. The method for simulating stress and deformation in laser powder bed melting forming based on a mass-spring model as described in claim 1, characterized in that, The formulas for calculating the forces acting on each vertex are as follows: in, The resultant force of the spring force acting on the vertex. Let be the resultant force exerted on the vertex by all the edge springs acting on that vertex. The resultant force of all angular springs acting on the vertex is the force acting on the vertex. The resultant force of all volume springs acting on the vertex is the force acting on the vertex.
4. The method for simulating stress and deformation in laser powder bed melting forming based on a mass-spring model as described in claim 1, characterized in that, The formula for calculating the force on the two vertices of the side spring is as follows: in, , These are the two vertices of the side spring. , The force exerted by the spring on that side Let be the stiffness of the edge spring. This refers to the elastic deformation of the edge spring. From the vertex Pointing to the vertex The unit vector.
5. The method for simulating stress and deformation in laser powder bed melting forming based on a mass-spring model as described in claim 4, characterized in that, The formula for calculating the elastic deformation of the side spring is as follows: in, For , The elastic deformation of the edge spring at the vertex. The equivalent elastic strain of the edge spring. The initial length of the side spring is given.
6. A method for simulating stress and deformation in laser powder bed melting forming based on a mass-spring model as described in claim 1 or 5, characterized in that, The formulas for calculating the forces acting on each vertex of the angle spring are as follows: in, , , For As the vertex, , The angle of the spring at the endpoint relative to the vertex , , The force, This is the current angle of the angle spring. Let this be the stiffness of the spring at that angle. The elastic angular deformation of the angle spring. , , The coordinates are , , , , .
7. The method for simulating stress and deformation in laser powder bed melting forming based on a mass-spring model as described in claim 6, characterized in that, The formula for calculating the elastic deformation of the angle spring is as follows: in, For As the vertex, , The elastic angular deformation of the spring is the angle at the endpoint. The equivalent elastic strain of the angle spring is... This is the initial angle of the angle spring.
8. A method for simulating stress and deformation in laser powder bed melting forming based on a mass-spring model as described in claim 1 or 7, characterized in that, The formula for calculating the force at any vertex of the volume spring is as follows: in, For a volume spring about any vertex The force, Let the stiffness of the spring be the volume. This refers to the elastic deformation of a volume spring. As vertex Location coordinates, It is the volume of the spring.
9. The method for simulating stress and deformation in laser powder bed melting forming based on a mass-spring model as described in claim 8, characterized in that, The formula for calculating the elastic deformation of the volume spring is as follows: in, This represents the elastic deformation of the spring of this volume. This refers to the mechanical deformation of the spring of this volume.
10. A simulation system for stress and deformation in laser powder bed melting forming based on a mass-spring model, characterized in that, The system includes an actuator for performing a simulation method for stress deformation in laser powder bed melting forming based on a mass-spring model, as described in any one of claims 1-9.