A thermal coupled multi-scale parallel topology optimization method for additive manufacturing

Abstract

The application relates to the technical field of topology optimization, and discloses a thermal force coupling multi-scale parallel topology optimization method for additive manufacturing, which divides a macroscopic design domain into a plurality of macroscopic sub-design domains through a fuzzy C clustering method, maps macroscopic sub-design domain information on a microscopic side as a constraint condition for microscopic optimization, converts transient temperature load into equivalent static load, introduces the equivalent thermal load into a multi-scale topology optimization model, carries out thermal force coupling finite element analysis of the macroscopic and microscopic sides according to a thermal force coupling control equation, solves a displacement vector matrix by using an HHT-alpha method, analyzes the sensitivity of a macro-microscopic objective function and a constraint condition, and uses a moving asymptote MMA method as a solver for updating the macro-microscopic design variables; the microstructure is filled into the macroscopic configuration to obtain an overall configuration, and a convergence condition is judged; if the convergence condition is met, an optimal material distribution structure and a microscopic optimal configuration are output. The application can better reflect the real working state of a workpiece.

Description

Technical Field

[0001] This invention belongs to the field of topology optimization technology, specifically relating to a thermo-mechanically coupled multi-scale parallel topology optimization method for additive manufacturing. Background Technology

[0002] Many industrial devices, such as rockets and steam turbines, are subjected to mechanical loads and high temperatures during operation. Therefore, structural optimization must consider the temperature and force fields. When the temperature rises above a certain range during operation, the equipment's structure may be unable to effectively dissipate heat, potentially leading to damage due to overheating. Furthermore, the structure must possess sufficient strength to ensure the equipment is not damaged under external loads.

[0003] Currently, there is a considerable amount of research on the optimization design of thermo-mechanical coupling problems, but most of it focuses on steady-state heat conduction. In the flight of rockets, high-speed aircraft, and other vehicles, temperature often exhibits transient effects, causing thermal stress to change over time. Transient heat conduction analysis involves significant computational costs, especially when the time step is very small. Furthermore, increasing the time step leads to fluctuations in the temperature field at different times. Most research on thermo-mechanical coupling considering transient responses in additive manufacturing focuses on macroscopic scales, with very little research on multi-scale design, thus limiting further development of material structure properties. Summary of the Invention

[0004] The purpose of this invention is to provide a thermo-mechanically coupled multi-scale parallel topology optimization method for additive manufacturing, which can reflect the actual working state of the workpiece.

[0005] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution.

[0006] In a first aspect, the present invention provides a thermo-mechanically coupled multi-scale parallel topology optimization method for additive manufacturing, comprising the following steps:

[0007] Step S1: Define the dimensions, material properties, design domain, boundary conditions, and iteration number of the initial macroscopic structure. Divide the macroscopic design domain of the multiphase material structure using the fuzzy C-clustering method. Discretize the design into several macroscopic sub-design domains, and map the information of the macroscopic sub-design domains onto the microscopic level as constraints for microscopic optimization; transform the transient temperature load into an equivalent static value, and introduce the equivalent thermal load to obtain a multi-scale topology optimization model;

[0008] Step S2: Perform finite element analysis on the multi-scale topology optimization model, calculate the objective function and constraints, including solving the equivalent temperature field over a certain time interval, solving the displacement vector matrix, and calculating the volume fractions at the macro and micro levels.

[0009] Step S3: Perform sensitivity analysis on the objective function and constraints, and use the moving asymptote MMA criterion method as the solver for updating macro and micro design variables in the multi-scale topology optimization model to perform iterative calculations and obtain the macro and micro design variables in the last step after iteration.

[0010] Step S4: Fill the macroscopic design variables obtained in the last step into the macroscopic design domain, fill the microscopic design variables obtained in the last step into the macroscopic sub-design domain to obtain the overall configuration, and judge the convergence condition. If the convergence condition is met, output the optimal material distribution structure and the optimal microscopic configuration.

[0011] In conjunction with the first aspect, the thermo-coupling multi-scale parallel topology optimization method of the present invention further includes the step of observing and verifying the micro-optimal configuration, specifically: arranging the micro-optimal configuration in a square, observing and verifying the connectivity of its structure, requiring that there be no breaks at the structural connections.

[0012] Building upon the first aspect, the specific method for mapping macroscopic sub-design domain information onto the microscopic level as a constraint for microscopic optimization is as follows:

[0013] The mechanical finite element equation considering dynamic loads is:

[0014] ;

[0015] In the formula, , , These are the mass matrix, damping matrix, and stiffness matrix, respectively. For the applied force field load, The thermal load is caused by thermal expansion. , It has no specific meaning; it is only used to distinguish different loads. For a moment, For overall load, overall load It will change over time. For the first The displacement matrix of the structure at any given time. For the first The velocity matrix of the time-phase structure For the first The acceleration matrix of the time-phase structure;

[0016] The finite element equation for transient heat conduction in a structure is:

[0017]

[0018] In the formula, is a vector matrix of macroscopic design variables, is the number of macroscopic grid elements, is a thermodynamic index, is a heat capacity matrix, is a heat conduction matrix, is a temperature field is a first derivative with respect to time is a thermal load with respect to time .

[0019] According to the finite element equation of the structure transient heat conduction, the transient thermal-mechanical coupling finite element equation is:

[0020] .

[0021] In combination with the first aspect, further, the transient temperature load is equivalent static transformation, the equivalent thermal load is introduced to obtain the specific method of the multi-scale topology optimization model:

[0022] The method of equivalent static transformation of the structure transient temperature load is applied, at each time , the transient thermal-mechanical coupling finite element equation can be written as the equivalent displacement field equation:

[0023]

[0024] In the formula, , is the equivalent mechanical load of the first time, is the equivalent displacement vector caused by the first time, is the equivalent acceleration vector caused by the first time, is the equivalent velocity vector caused by the first time; The macroscopic model is defined as:

[0025]

[0026]

[0027] In the formula, is the serial number of the macroscopic unit, is the total number of macroscopic grid elements, represents the first macroscopic design variable, symbolizes the macroscopic scale, represents the heat dissipation weakness of the macroscopic scale (i.e. the objective function of the macroscopic scale), is the first​​​​ The first moment A macroscopic unit temperature vector For duration, This represents the elemental thermal conductivity matrix when the material's relative density is 1. Represents the macroscopic volume constraint function. The penalty factor at the macro scale. This represents the upper limit of the macroscopic structural volume. The minimum relative density of the material is used to prevent the overall thermal conductivity matrix of the structure from being compromised; it is usually taken as 1×10⁻⁶. -9 , Represents the overall heat conduction matrix. It is the first in the design space The equivalent thermal load at time t, It is the first The equivalent temperature field at time t;

[0028] The microscopic model is defined as follows:

[0029]

[0030] In the formula, This represents the serial number of the micro-unit. This represents the total number of micro-grid cells. Indicates the first The first in microstructure One micro-design variable, This represents the total number of microstructure types. The serial number indicating the type of microstructure Symbolizing the microscopic scale, This represents the heat dissipation weakness at the microscale (i.e., the objective function at the microscale). For the first The first moment The first in microstructure Each unit temperature vector This represents the microstructure volume constraint function. As a penalty factor at the microscale, For the first Upper limit of volume of microstructure-like structures For the first Volume constraint function for microstructure-like structures;

[0031] The parallel topology optimization method, which simultaneously optimizes the macroscopic and microscopic models, aims to minimize the heat dissipation weakness at both the microscopic and macroscopic scales. The multi-scale parallel topology optimization mathematical model for transient heat conduction in composite materials is expressed as follows:

[0032] .

[0033] With reference to the first aspect, further, the specific method of step S2 is: performing finite element analysis on the multi-scale topology optimization model in step S1 according to the transient thermal force coupling finite element equation, calculating the objective function and constraint condition of the multi-scale topology optimization model in step S1, including solving the temperature field in a certain time interval using a difference formula, solving a displacement vector matrix using an HHT-alpha method, and calculating the volume fraction of the macro and micro;

[0034] Step S21: solving the temperature field in a certain time interval using a difference formula, that is:

[0035] ;

[0036] In the formula, is the time step; is the equivalent temperature field at the moment; is the equivalent temperature field at the moment, is the moment, is the equivalent thermal load at the moment in the design space, is the heat capacity matrix, is the heat conduction matrix, is the vector matrix of macroscopic design variables, is the number of macroscopic grid elements, is the thermodynamic subscript;

[0037] Step S22: solving the displacement vector matrix using the HHT-alpha method, according to the Newmark-beta finite difference relationship, the update format of displacement and velocity field is:

[0038] ;

[0039] ;

[0040] In the formula, , , are all kinetic algorithm parameters, wherein , ; and are the displacement matrix, velocity matrix and acceleration matrix of the structure at the moment, respectively; and are the displacement matrix, velocity matrix and acceleration matrix of the structure at the moment, respectively;

[0041] Step S23: calculating the volume fraction of the macro, that is, solving ; and the volume fraction of the microstructure is calculated, i.e. ; wherein, is the serial number of the macro unit, is the total number of the macro grid units, denotes the macro design variable, denotes the macro scale, is the serial number of the micro unit, denotes the total number of the micro grid units, denotes the micro design variable in the microstructure of the type, denotes the micro scale.

[0042] In combination with the first aspect, further, in order to ensure the accurate simulation of the displacement vector matrix at the moment in time in the dynamic process in the solving step S22, the step S2 further comprises a step S24, specifically as follows:

[0043] Step S24: constructing the residual of the discrete form control equation at the moment in time, so that the residual is 0, i.e.

[0044] ;

[0045] In the formula, is the residual of the discrete form control equation at the moment in time; is the acceleration matrix at the moment in time; and are the velocity matrix and the acceleration matrix of the structure at the moment in time, respectively; is the dynamic algorithm parameter, taking 0.05; is the external load column matrix at the moment in time; is the external load column matrix at the moment in time; , are the first coefficient and the second coefficient of the mass matrix in the discrete form; is the first coefficient of the damping matrix in the discrete form; wherein, , and are respectively defined as:

[0046] ;

[0047] And the residual equation at the initial moment in time is:

[0048] ;

[0049] where, is the residual of the governing equation at the initial time; , and are the displacement, velocity and acceleration vectors of the structure at the initial time, respectively; is the external load vector at the initial time.

[0050] In combination with the first aspect, further, the specific method of sensitivity analysis of the objective function and the constraint condition in the step S3 is:

[0051] solving the objective function at the macro scale The sensitivity of any macro design variable is expressed as:

[0052] ;

[0053] where, represents the overall heat conduction matrix, is the objective function at the macro scale, i.e. the heat dissipation weakness at the macro scale; is the macro design variable; is the equivalent heat load at the time at the position is the equivalent temperature field at the macro scale at the time at the position is the time; denotes the macro scale; is the duration;

[0054] sensitivity calculation under the macro volume constraint ;

[0055] ;

[0056] where, is the upper limit of the macro structure volume; is the serial number of the macro unit; is the total number of macro grid units; denotes the macro design variable;

[0057] solving the objective function at the micro scale The sensitivity of any micro design variable is expressed as:

[0058] ;

[0059] where, is the The equivalent temperature field at the microscale; denotes the stiffness matrix; is the micro design variable;

[0060] The first The volume constraint function of the microstructure The sensitivity is expressed as:

[0061] ;

[0062] wherein, is the upper limit of the volume of the microstructure; denotes the micro design variable in the microstructure; is the serial number of the micro unit; denotes the microscale; denotes the total number of micro grid units. In combination with the first aspect, further, the moving asymptote (MMA) criterion method is used as a solver for updating the macro design variable in the multi-scale topology optimization model, and iterative calculation is performed to obtain the macro design variable at the last step after iteration, and the specific method is as follows:

[0063]

[0064]

[0065] In the formula, is the macro design variable, denotes the heat dissipation weakness of the macro scale, i.e. the objective function of the macro scale, is the artificial variable, is the serial number of the macro unit, is the total number of macro grid units, and are real numbers, and both are greater than 0; and are also real numbers, and satisfy , is the relaxation factor of the macro scale, is the volume constraint function of the macro scale;

[0066] Then, the moving asymptote (MMA) approximation equation of the objective function or the volume constraint function of the macro scale is expressed as:

[0067]

[0068] In the formula, is the moving asymptote (MMA) approximation equation of the objective function or the constraint function of the macro, is the iteration number, is the macro scale​​​ MMA equation of the next iteration, denotes the macro design variable of the macro unit, denotes the macro design variable of the macro unit after the next iteration, which is obtained by iteration of the moving asymptote method, denotes the upper moving asymptote of the macro scale, denotes the lower moving asymptote of the macro scale, , is the MMA moving parameter, which is respectively denoted as:

[0069] ;

[0070] ;

[0071] Similarly, the micro design variable of the last step after iteration is obtained.

[0072] In a second aspect, the present application provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the steps of the thermal force coupling multi-scale parallel topology optimization method for additive manufacturing.

[0073] In a third aspect, the present application provides a computer device, which comprises:

[0074] a memory for storing a computer program;

[0075] a processor for executing the computer program to implement the steps of the thermal force coupling multi-scale parallel topology optimization method for additive manufacturing.

[0076] In a fourth aspect, the present application provides a computer program product, which comprises a computer program, and the computer program is executed by a processor to implement the steps of the thermal force coupling multi-scale parallel topology optimization method for additive manufacturing.

[0077] Compared with the prior art, the present application has the following beneficial effects:

[0078] (1) The present application considers the transient response heat conduction, which can better reflect the real working state of the workpiece than the steady state response heat conduction; considers the simultaneous update of macro structure and micro structure, and considers the design space of the whole structure and material, so as to better play the performance of the structure.

[0079] (2) The present application divides the macro design domain into several macro sub-design domains by fuzzy C clustering method, reduces the number of design variables from multiple categories to specific categories, thereby reducing the calculation time and improving the design efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0080] Figure 1 Flowchart of the heat force coupling multi-scale parallel topology optimization method for additive manufacturing of the present application;

[0081] Figure 2 Structure diagram of the design object of the present application;

[0082] Figure 3 Topological optimization macroscopic result diagram of the design object of the present application;

[0083] Figure 4 Topological optimization microcosmic result diagram of the design object of the present application. DETAILED DESCRIPTION

[0084] The technical solutions of the present application will be described in detail below with the help of the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present application and the specific features in the embodiments are detailed descriptions of the technical solutions of the present application, rather than limitations of the technical solutions of the present application. In the case of no conflict, the technical features in the embodiments of the present application and the embodiments can be combined with each other.

[0085] The term "and / or", only describes the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B, which can represent the three cases of A alone, A and B together, and B alone. In addition, the character " / ", generally represents that the associated objects before and after it are in an "or" relationship.

[0086] Embodiment 1

[0087] As Figure 1 shown, the present embodiment proposes a heat force coupling multi-scale parallel topology optimization method for additive manufacturing, which includes the following steps:

[0088] Step S1, first, define the size, material properties, design domain, boundary conditions and iteration number of the initial structure. Secondly, discretize the grid, divide the macroscopic design domain into a plurality of macroscopic sub-design domains 、 、 、…、 、…、 , wherein, the serial number of the macroscopic sub-design domain is represented by i, the total number of macroscopic sub-design domains is represented by N; map the macroscopic sub-design domain information on the microcosmic as a constraint condition for microcosmic optimization; convert the transient temperature load into an equivalent static state, introduce an equivalent thermal load to obtain a multi-scale topology optimization model.

[0089] It should be noted that: At the macro level, it represents the sequence number of the macro sub-design domain; at the micro level, it represents the sequence number of the microstructure type. At the macro level, it represents the total number of macro-level sub-design domains; at the micro level, it represents the total number of microstructure types. and The values ​​are completely synchronized at both the macro and micro levels, that is, there is a one-to-one mapping relationship.

[0090] Step S11: Define the initial structure's dimensions, material properties, design domain, boundary conditions, and number of iterations.

[0091] Step S12: Macro Design Domain The design domain was divided into multiple macroscopic sub-domains using fuzzy C-clustering. , , … … ,in, Indicates the index of the macroscopic sub-design domain. This indicates the total number of macroscopic sub-design domains; each macroscopic sub-design domain is filled with the same type of microstructure, and the microstructure configurations of different macroscopic sub-design domains are different.

[0092] Step S13: The mechanical finite element equation considering dynamic loads is:

[0093] (1)

[0094] In the formula, , , These are the mass matrix, damping matrix, and stiffness matrix, respectively. For the applied force field load, The thermal load is caused by thermal expansion. , It has no specific meaning; it is only used to distinguish different loads. For a moment, For overall load, overall load It will change over time. For the first The displacement matrix of the structure at any given time. For the first The velocity matrix of the time-phase structure For the first The acceleration matrix of the time-time structure.

[0095] Step S14: The finite element equation for transient heat conduction in the structure can be written as:

[0096] (2)

[0097] In the formula, For macroscopic design variables, a vector matrix, The number of macroscopic grid cells, Thermodynamic subscript The heat capacity matrix, For the heat conduction matrix, It is a temperature field About time The first derivative, It's about time. Thermal load.

[0098] The heat conduction matrix in equation (2) and heat capacity matrix And about time thermal load It can be represented as:

[0099] (3)

[0100] In the formula, Horizontal serial number , Vertical serial number, For unit number, The horizontal serial number is Vertical serial number is unit heat conduction matrix, The horizontal serial number is Vertical serial number is The unit heat capacity matrix, The horizontal serial number is Vertical serial number is The element thermal load matrix, For the horizontal sequence number Vertical serial number is Unit number is The influence of the unit heat conduction matrix, The horizontal serial number is Vertical serial number is Unit number is The correction of the heat transfer matrix by the convective heat transfer boundary of the unit. The horizontal serial number is Vertical serial number is Unit number is The unit heat capacity matrix, For the horizontal sequence number Unit number is , by horizontal serial number heat flow The resulting thermal load on the structural units; is the heat flux of the boundary element with the transverse index , is the heat flux of the boundary element with the transverse index , is the heat flux of the boundary element with the transverse index , is the heat flux of the boundary element with the transverse index , is the heat flux of the boundary element with the transverse index ,

[0101] Step S15: According to the finite element equation of transient heat conduction described above, the transient thermo-mechanical coupled finite element equation is:

[0102] (4)

[0103] Because the temperature field is different at each time , the thermal load caused by thermal expansion can be expressed as:

[0104] (5)

[0105] In the formula, represents the number of macroscopic grid elements, represents the structure strain matrix, is the elastic matrix, is the thermal strain caused by the temperature field, , represents the defined boundary temperature, is the equivalent temperature field at the time, is the thermal expansion coefficient, so the thermal load caused by thermal expansion can be further described as:

[0106] (6)

[0107] Step S16: Apply the method of converting the structure into a transient temperature load equivalent static state, at each time , the transient thermo-mechanical coupled finite element equation can be written as an equivalent displacement field equation:

[0108] (7)

[0109] In the formula, , is the equivalent mechanical load at the time, is the at the the induced equivalent displacement vector, the first the induced equivalent acceleration vector at the time the induced equivalent velocity vector at the time the first the induced equivalent velocity vector at the time the induced equivalent velocity vector at the time

[0110] Step S17: define the macroscopic model as:

[0111] (8)

[0112] wherein, is the serial number of the macroscopic unit, is the total number of macroscopic grid units, represents the first macroscopic design variable, denotes the macroscopic scale, represents the heat dissipation weakness of the macroscopic scale (i.e., the objective function of the macroscopic scale), is the first macroscopic unit temperature vector at the time is the duration, represents the unit heat conduction matrix when the relative density of the material is 1, represents the macroscopic volume constraint function, is the penalty factor of the macroscopic scale, is the upper limit of the macroscopic structure volume, is the minimum relative density of the material, represents the overall heat conduction matrix, is the equivalent thermal load at the time at the position in the design space, is the equivalent temperature field at the time at the position.

[0113] define the microscopic model as:

[0114] (9)

[0115] wherein, is the serial number of the microscopic unit, represents the total number of microscopic grid units, represents the first microscopic design variable in the first microstructure, represents the total number of microstructure types, represents the serial number of the microstructure type, denotes the microscopic scale, represents the heat dissipation weakness of the microscopic scale (i.e., the objective function of the microscopic scale),​ the first the first the first unit temperature vector in the first represents a microstructure volume constraint function, is a microscale penalty factor, the first volume upper limit of the first volume constraint function of the first volume constraint function of the first

[0116] A parallel topology optimization method using macroscopic model (see formula (8)) and microscopic model (see formula (9)) is adopted to minimize the heat dissipation weakness at the micro and macro scales as the optimization objective. The mathematical model of multi-scale parallel topology optimization under the transient heat conduction condition of composite materials can be expressed as:

[0117] (10)

[0118] In the formula, represents the total number of microstructure types, represents the serial number of the microstructure type.

[0119] Step S2: Finite element analysis is performed on the multi-scale topology optimization model (i.e. formula (10)) in step S1 according to the transient thermal force coupling finite element equation described in formula (4), and the objective function and constraint conditions of the multi-scale topology optimization model in step S1 are calculated, including solving the equivalent temperature field at a certain time interval using the difference formula as described in formula (11), solving the displacement vector matrix using the HHT-α method as described in formula (12), and calculating the volume fraction of macro and micro.

[0120] Step S21: The equivalent temperature field at a certain time interval is solved using the difference formula, that is:

[0121] (11)

[0122] In the formula, is the time step; is the equivalent temperature field at the first moment; is the equivalent temperature field at the first moment.

[0123] Step S22: The displacement vector matrix is solved using the HHT-α method, and according to the Newmark-β finite difference relationship, the update format of the displacement and velocity field is:

[0124] (12)

[0125] (13)

[0126] wherein, , , are the dynamic algorithm parameters, wherein, , ; and are the displacement matrix, velocity matrix and acceleration matrix of the structure at the time t ; and are the displacement matrix, velocity matrix and acceleration matrix of the structure at the time t .

[0127] Step S23: calculating the macroscopic volume fraction, i.e. solving ; and calculating the microscopic volume fraction, i.e. solving .

[0128] Step S24: in order to ensure the accurate simulation of the displacement vector matrix at the time t in the dynamic process, the residual of the discrete form control equation at the time t is constructed, so that the residual is 0, i.e.

[0129] (14)

[0130] wherein, is the residual of the discrete form control equation at the time t ; is the acceleration matrix at the time t ; and are the velocity matrix and acceleration matrix of the structure at the time t ; is the dynamic algorithm parameter, and is 0.05; is the external load column matrix at the time t ; is the external load column matrix at the time t ; , are the first coefficient and second coefficient of the mass matrix in the discrete form; is the first coefficient of the damping matrix in the discrete form; wherein, , and are respectively defined as:

[0131] (15)

[0132] and the residual equation at the initial time is:

[0133] (16)

[0134] where, is the residual of the governing equation at the initial time; , and are the displacement, velocity and acceleration vectors of the structure at the initial time, respectively; is the external load vector at the initial time.

[0135] Step S3, sensitivity analysis of the objective function and the constraints in step S2, i.e. calculating the first order derivatives of the objective function and the constraints with respect to the macro and micro design variables, providing the input data for the subsequent use of the moving asymptotes (MMA) criterion method as the solver for the update of the macro and micro design variables in the multi-scale topology optimization model in step S1, obtaining the macro and micro design variables after the last iteration.

[0136] Step S31: calculating the objective function of the macro scale The sensitivity of any macro design variable can be expressed as:

[0137] (17)

[0138] where, represents the global heat conduction matrix, is the objective function of the macro scale, i.e. the heat dissipation weakness of the macro scale; is the equivalent temperature field of the macro scale at the time;

[0139] The sensitivity calculation under the macro volume constraint :

[0140] (18)

[0141] calculating the objective function of the micro scale The sensitivity of any micro design variable can be expressed as:

[0142] (19)

[0143] where, is the equivalent temperature field of the micro scale at the time.

[0144] The sensitivity calculation under the volume constraint function of the first class microstructure :

[0145] (20)

[0146] Step S32: Using the sensitivity of the macro-scale objective function and constraint condition obtained in step S31 as input, the moving asymptote (MMA) criterion method is used as the solver for the topology optimization of the transient heat conduction problem, and iterative calculation is performed to update the macro-design variable. The corresponding optimization sub-problem can be expressed as:

[0147] (21)

[0148] In the formula, is the macro-design variable, represents the macro-scale heat dissipation weakness (i.e., the macro-scale objective function), is the artificial variable, is the serial number of the macro unit, is the total number of macro-grid units, and are real numbers and are greater than 0, and are usually taken as 0.1, 0.8; and are also real numbers and satisfy , and are usually and are taken as 0.6, 0.4, respectively, is the macro-scale relaxation factor, and is usually taken as 0.5, is the macro-scale volume constraint function.

[0149] The moving asymptote (MMA) approximation equation of the macro-scale objective function or volume constraint function is expressed as:

[0150] (22)

[0151] In the formula, is the moving asymptote (MMA) approximation equation of the macro objective function or constraint function, is the iteration number, is the moving asymptote (MMA) equation of the macro-scale in the th iteration, represents the macro-design variable of the th macro unit, represents the macro-design variable of the th macro unit after the th iteration, which is obtained by iterative solution of the moving asymptote method, represents the upper moving asymptote of the macro-scale, is the lower moving asymptote of the macro-scale, , is the MMA moving parameter, which is expressed as:

[0152] (23)

[0153] (24)

[0154] Step S33: At the same time, the sensitivity of the micro-scale objective function and the constraint condition obtained in step S31 is taken as input, the moving asymptote MMA criterion method is taken as the solver of the topology optimization of the transient heat conduction problem, and iterative calculation is performed to update the micro-design variable. The corresponding optimization sub-problem can be expressed as:

[0155] (25)

[0156] In the formula, is the micro-design variable, indicates the micro-scale heat dissipation weakness (that is, the micro-scale objective function), is the artificial variable, is the serial number of the micro unit, is the total number of micro grid units, and are real numbers and are greater than 0, and are usually taken as 0.1, 0.8; and are also real numbers and satisfy , usually and are taken as 0.6, 0.4, is the micro-scale relaxation factor, usually taken as 0.5, is the volume constraint function of the micro-scale first microstructure.

[0157] Then, the moving asymptote MMA approximation equation of the micro-scale objective function or the volume constraint function is expressed as:

[0158] (26)

[0159] In the formula, is the moving asymptote MMA approximation equation of the micro objective function or the constraint function, is the iteration number, is the moving asymptote MMA equation of the micro-scale first iteration, indicates the micro-design variable of the first macro unit, indicates the micro-design variable of the first micro unit after the first iteration, which is obtained by iterative solution of the moving asymptotic method, indicates the upper moving asymptote for the micro scale, a lower moving asymptote of micro-scale, , MMA is a moving parameter, respectively represented as:

[0160] (27)

[0161] (28)

[0162] Step S4, the macro design variable value of the last step of iteration in step S3 is filled into the macro design domain, the micro design variable value is filled into the macro sub-design domain divided by the macro design domain in step S1 to obtain the overall configuration, and the convergence condition is judged. If the condition is met, the optimal material distribution structure and the micro optimal configuration are output; at the same time, the micro optimal configuration is placed in a square, and the operator observes and inspects the connectivity of the structure, and requires that there is no fault in the structure connection.

[0163] The micro optimal configuration is placed in a square to test the reliability and stability of the micro optimal configuration in the connectivity. Preferably, the micro optimal configuration is placed in 3x3, which is more simple and convenient than other square placement modes (such as 4x4, 5x5).

[0164] The obtained microstructure is mapped into the macro sub-design domain with a corresponding volume fraction by using MATLAB software 、 、 、…、 、…、 ( represents the serial number of the macro sub-design domain, represents the total number of macro sub-design domains) into the macro sub-design domain with a corresponding volume fraction by using MATLAB software. The convergence condition is that the relative density value of the current design variable and the last design variable is less than 0.001, then the convergence condition and the connectivity of the structure are met, at this time the optimal material distribution structure and the micro optimal configuration can be output, if not, return to step S1.

[0165] Example 2

[0166] As shown in Figure 2 , in this embodiment, the design object is a cantilever beam model, the initial structure design domain is defined as 2m in length, 1m in width, 0.01mm in thickness, the material properties are shown in Table 1, the boundary condition is that the left end of the cantilever beam model is fixed, the iteration number is 200, the macro design domain is divided into 3 macro sub-design domains, the total number of macro grid units , the total number of micro grid units ; the thermal load at the first time is applied inside (unit: kN), equivalent temperature field K. The equivalent mechanical load is applied at the center of the right boundary, for the first time, the equivalent mechanical load is 1 kN. The duration of the thermal-mechanical coupling process is s, the duration is divided into 15 time steps, and the time step is 0.1 s. The bottom of the cantilever beam is a heat dissipation boundary ℃, and the macroscopic volume constraint and the microscopic volume constraint are and respectively.

[0167] As shown in

[0168] , the macroscopic structure after optimization of the cantilever beam structure using the thermal-mechanical coupling multi-scale parallel topology optimization method of the present application is an overall upper and lower symmetric structure due to the axial symmetry of the applied boundary conditions, forming a clear force transmission path between the applied force load and the fixed end on the left. The optimized heat dissipation weakness is 131.7. If multi-scale topology optimization is not considered as in the present application, the optimized heat dissipation weakness is 151.7. Since the higher the heat dissipation weakness, the worse the heat dissipation performance, the present embodiment 1 has further improved in terms of heat dissipation performance; and the whole is composed of three types of different microstructures, and the volume fractions are 0.272, 0.517, and 0.5816 respectively. Arranging them in a 3x3 array, it is found that their connectivity is also better. Figure 3 Embodiment 3

[0169] Based on the same inventive concept as other embodiments, this embodiment introduces a computer readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing described above.

[0170] Embodiment 4

[0171] Based on the same inventive concept as other embodiments, this embodiment introduces a computer device, comprising: a memory for storing a computer program; a processor for executing the computer program to implement the steps of the thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing described above.

[0172] Embodiment 5

[0173] Based on the same inventive concept as other embodiments, this embodiment introduces a computer device, comprising: a memory for storing a computer program; a processor for executing the computer program to implement the steps of the thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing described above.

[0174] Based on the same inventive concept as other embodiments, the present embodiment introduces a computer program product comprising a computer program which, when executed by a processor, implements the steps of the additive manufacturing-oriented coupled thermal-mechanical multi-scale parallel topology optimization method described above.

[0175] Those skilled in the art will appreciate that embodiments of the present application can be supplied as a method, a system, or a computer program product. Accordingly, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer-readable program code.

[0176] The present application is described in reference to the flowchart and / or block diagrams of the method, apparatus (system) and computer program product according to embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagrams, as well as combinations of flows and / or blocks in the flowchart and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, a special purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions, which are executed via the processor of the computer or other programmable data processing apparatus, generate a means for implementing the functions specified in the flowchart and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 means for functionally implementing the flow and / or blocks in one or more flows and / or blocks.

[0177] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to work in a specific manner, so that the instructions stored in the computer-readable memory produce a manufacture product including an instruction means, which implements the functions specified in the flowchart and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 means for functionally implementing the flow and / or blocks in one or more flows and / or blocks.

[0178] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus, so that a series of operational steps are performed on the computer or other programmable data processing apparatus to generate a computer-implemented process, so that the instructions executed on the computer or other programmable data processing apparatus provide a process for implementing the functions specified in the flowchart and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 means for functionally implementing the flow and / or blocks in one or more flows and / or blocks.

[0179] The embodiments of the present application are described above with reference to the accompanying drawings, but the present application is not limited to the above-described specific embodiments, and the above-described specific embodiments are merely illustrative, but not restrictive, and a person of ordinary skill in the art can make many forms under the inspiration of the present application, and these all belong to the protection of the present application.

Claims

1. A thermomechanically coupled multi-scale parallel topology optimization method for additive manufacturing, characterized in that, Comprise: Step S1, define the size, material properties, design domain, boundary conditions and iteration times of the macro initial structure, divide the macro design domain of the multi-phase material structure by discrete into several macro sub-design domains, map the macro sub-design domain information on the micro as a constraint condition for micro optimization; equivalent static transformation is performed on the transient temperature load, and an equivalent thermal load is introduced to obtain a multi-scale topology optimization model; Step S2, finite element analysis is carried out on the multi-scale topological optimization model, and the objective function and constraint condition are calculated; Step S3, sensitivity analysis is carried out on the objective function and constraint condition, and moving asymptote MMA criterion method is used as the solver for updating the macro-micro design variables in the multi-scale topological optimization model, and iterative calculation is carried out to obtain the macro design variables and micro design variables of the last step after iteration; Step S4, the obtained macro design variables of the last step are filled into the macro design domain, the obtained micro design variables of the last step are filled into the macro sub-design domain to obtain the overall configuration, and the convergence condition is judged, if the convergence condition is met, the optimal material distribution structure and the micro optimal configuration are output; The specific method for mapping the macro sub-design domain information on the micro as the constraint condition of micro optimization is: The mechanical finite element equation considering dynamic load is: ； In the formula, , , are mass matrix, damping matrix and stiffness matrix respectively; is the applied force field load, is the thermal load caused by thermal expansion, , have no specific meaning and are only used to distinguish different loads, is the time, is the overall load, the overall load will change with the change of time, is the displacement matrix of the structure at the time, is the velocity matrix of the structure at the time, is the acceleration matrix of the structure at the time; The finite element equation of structure transient heat conduction is: ； wherein is a vector matrix of macroscopic design variables, is the number of macroscopic grid cells, is a thermodynamic index, is a heat capacity matrix, is a heat conduction matrix, is a temperature field is a first derivative with respect to time at time is a thermal load with respect to time at time According to the finite element equation of structure transient heat conduction, the transient thermal force coupling finite element equation is: ； The specific method for equivalent static transformation of transient temperature load and introduction of equivalent thermal load to obtain the multi-scale topological optimization model is: The method for applying transient temperature load equivalent static conversion of structure, at each time , the transient thermal coupling finite element equation is written as the equivalent displacement field equation: ； wherein , is the equivalent mechanical load at the time instant , is the equivalent displacement vector caused by the load at the time instant , is the equivalent acceleration vector caused by the load at the time instant , is the equivalent velocity vector caused by the load at the time instant , is the equivalent acceleration vector caused by the load at the time instant , is the equivalent velocity vector caused by the load at the time instant The macro model is defined as: ； In the formula, is the serial number of the macroscopic unit, is the total number of macroscopic grid units, represents the macroscopic design variable, symbolizes the macroscopic scale, represents the heat dissipation weakness of the macroscopic scale, that is, the objective function of the macroscopic scale, is the macroscopic unit temperature vector at the moment, is the duration, represents the unit heat conduction matrix when the relative density of the material is 1, represents the macroscopic volume constraint function, is the penalty factor of the macroscopic scale, is the upper limit of the macroscopic structure volume, is the minimum relative density of the material, represents the overall heat conduction matrix, is the equivalent heat load in the design space at the moment, is the equivalent temperature field at the moment; The micro model is defined as: ； In the formula, is the serial number of the micro unit, represents the total number of micro grid units, represents the serial number of the microstructure in the microstructure design variable, represents the total number of microstructure types, represents the serial number of the microstructure type, represents the micro scale, represents the heat dissipation weakness of the micro scale, that is, the objective function of the micro scale, is the temperature vector of the unit in the microstructure at the time, represents the microstructure volume constraint function, is the penalty factor of the micro scale, is the volume upper limit of the microstructure, is the volume constraint function of the microstructure; The parallel topological optimization method using the macro model and the micro model simultaneously optimizes to minimize the heat dissipation weakness on the micro and macro scales, and the multi-scale parallel topological optimization mathematical model under the composite material transient heat conduction condition is expressed as: 。 2. The thermomechanically coupled multi-scale parallel topology optimization method oriented to additive manufacturing according to claim 1, characterized in that, It also includes the step of observing and inspecting the micro optimal configuration, which is specifically: the micro optimal configuration is placed in a square, and the connectivity of the structure is observed and inspected, and the structure connection cannot have a fault.

3. The thermomechanically coupled multi-scale parallel topology optimization method oriented to additive manufacturing according to claim 1, characterized in that, The specific method of step S2 is: according to the transient thermal force coupling finite element equation, the multi-scale topological optimization model in step S1 is analyzed by finite element method, and the objective function and constraint condition of the multi-scale topological optimization model in step S1 are calculated, including using difference formula to solve the equivalent temperature field in a certain time interval, using HHT-α method to solve the displacement vector matrix, and calculating the volume fraction of macro and micro; Step S21, the difference formula is used to solve the equivalent temperature field in a certain time interval, that is: ； wherein is the time step; is the equivalent temperature field at the is the equivalent temperature field at the is the equivalent temperature field at the is the equivalent temperature field at the is the time instant, is the equivalent thermal load at the is the equivalent thermal load at the is the thermal capacitance matrix, is the thermal conduction matrix, is the vector matrix of macro design variables, is the number of macro mesh elements, is the thermodynamic index; Step S22: the HHT-α method is used to solve the displacement vector matrix, according to the Newmark-β finite difference relationship, the update format of displacement and velocity field is: ； ； In the formula, , , All are dynamic algorithm parameters, among which, , ; and The first Displacement matrix, velocity matrix, and acceleration matrix of the structure at any given moment; and They are respectively Displacement matrix, velocity matrix, and acceleration matrix of the structure at any given moment; Step S23: Calculate the macroscopic volume fraction, i.e., find And calculate the microscopic volume fraction, that is, find ;in, The serial number of the macroscopic unit. This represents the total number of macroscopic grid cells. Indicates the first One macro-design variable, Symbolizing a macroscopic scale, This represents the serial number of the micro-unit. This represents the total number of micro-grid cells. Indicates the first The first in microstructure One micro-design variable, The serial number indicating the type of microstructure Symbolizing the microscopic scale.

4. The thermomechanically coupled multi-scale parallel topology optimization method oriented to additive manufacturing according to claim 1, characterized in that, The specific method of step S3 for sensitivity analysis of the objective function and constraint condition is: Objective function at macro scale The sensitivity of any macro design variable is expressed as: ； wherein, represents the overall heat conduction matrix, is the macro-scale objective function, i.e., the macro-scale heat dissipation weakness; is the macro-design variable; is the equivalent heat load at the time instant at the point in the design space; is the macro-scale equivalent temperature field at the time instant; is the time instant; denotes the macro-scale; is the time duration; Macroscopic volume constraint Sensitivity calculation under ； wherein is the upper limit of the macro-structure volume; is the serial number of the macro-unit; is the total number of macro-grid units; denotes the macro-design variable; Objective function at microscale The sensitivity of any micro design variable is expressed as: ； In the formula, is the first instantaneous microscale equivalent temperature field; denotes the stiffness matrix; is the microscale design variable; The first Volume constraint function for microstructure classes The sensitivity under the constraint is expressed as: ； wherein, is the volume limit for microstructures of class denotes the micro-design variable in microstructure of class is the index of the micro-unit; denotes the micro-scale; denotes the total number of micro-grid cells.​ 5. The thermomechanically coupled multi-scale parallel topology optimization method oriented to additive manufacturing according to claim 4, characterized in that, The moving asymptote MMA criterion method is used as the solver for updating the macro design variables in the multi-scale topological optimization model, and iterative calculation is carried out to obtain the macro design variables of the last step after iteration, and the specific method is: ； wherein, is a macro design variable, denotes the macro scale heat dissipation weakness, i.e., the macro scale objective function, is an artificial variable, is the serial number of the macro unit, is the total number of macro grid units, and are real numbers and are both greater than 0; and are also real numbers and satisfy , is a macro scale relaxation factor, is a macro scale volume constraint function; Then, the moving asymptote MMA approximate equation of the objective function or volume constraint function of macro scale is represented as: ； wherein, is the moving asymptote MMA approximation equation of the macroscopic objective function or constraint function, is the iteration number, is the moving asymptote MMA equation of the macroscopic scale, is the moving asymptote MMA equation of the macroscopic scale, denotes the macroscopic design variable of the th macroscopic unit, denotes the macroscopic design variable of the th macroscopic unit after the th iteration, which is obtained by iterative solution by the moving asymptotic method, denotes the upper moving asymptote of the macroscopic scale, denotes the lower moving asymptote of the macroscopic scale, , is the MMA moving parameter, respectively denoted as: ； ； Similarly, the micro design variables of the last step after iteration are obtained.

6. A computer readable storage medium having stored thereon a computer program, characterized in that: The computer program is executed by the processor to realize the steps of the thermal force coupling multi-scale parallel topological optimization method for additive manufacturing in any one of claims 1-5.

7. A computer device, characterized by Comprise: Memory for storing computer programs; A processor for executing the computer program to implement the steps of the method of topology optimization for thermal-mechanical coupled multi-scale parallelism oriented to additive manufacturing according to any one of claims 1-5.

8. A computer program product comprising a computer program, characterized in that: The computer program is executed by a processor to implement the steps of the method of topology optimization for thermal-mechanical coupled multi-scale parallelism oriented to additive manufacturing according to any one of claims 1-5.

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