Thermal coupling multi-scale parallel topological optimization method for additive manufacturing

Abstract

The invention relates to the technical field of topological optimization, and discloses a thermal coupling multi-scale parallel topological optimization method for additive manufacturing, and the method comprises the steps: dividing a macroscopic design domain into a plurality of macroscopic sub-design domains through a fuzzy C clustering method, and mapping the information of the macroscopic sub-design domains on the microcosmic level as the constraint condition of microcosmic optimization; performing equivalent static conversion on the transient temperature load, and introducing an equivalent thermal load into the multi-scale topological optimization model; macroscopic and microscopic thermal coupling finite element analysis is carried out according to the thermal coupling control equation, and a displacement vector matrix is solved by using an HHT-alpha method; sensitivity analysis is carried out on macro and micro objective functions and constraint conditions, and a moving asymptote MMA method is used as a solver for macro and micro design variable updating; and filling the microstructure into the macroscopic configuration to obtain an overall configuration, judging a convergence condition, and if the condition is met, outputting an optimal material distribution structure and an optimal microscopic configuration. The method can better reflect the real working state of the workpiece.

Description

Technical Field

[0001] The present invention belongs to the technical field of topology optimization, and in particular relates to a thermomechanical coupling multi-scale parallel topology optimization method for additive manufacturing. Background Art

[0002] Many industrial equipment are affected by mechanical loads and high temperatures when working, such as rockets and steam turbines. Therefore, it is necessary to study the structural optimization of temperature fields and force fields in structural optimization. When the temperature rises above this temperature range, the structure of the equipment is mostly unable to effectively dissipate heat, and the equipment may be damaged due to excessive temperature. In addition, the structure should have a certain strength to ensure that the equipment will not be damaged under external loads.

[0003] At present, there are many studies on the optimization design of thermal-mechanical coupling problems, but most of them focus on steady-state heat conduction. When rockets, high-speed aircraft, etc. are moving, the temperature often has a transient effect, so the thermal stress will change with time. Transient heat conduction analysis involves a lot of computational costs, especially when the time step is very small, the computational cost will be more, and when the time step is increased, the temperature field at different times will fluctuate. Moreover, most of the thermal-mechanical coupling for additive manufacturing and considering transient response are concentrated on the macroscopic scale, and there is little research on multi-scale design, which limits the further development of material structural performance. Summary of the invention

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

[0005] In order to solve the above technical problems, the present invention is implemented by adopting the following technical solutions.

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

[0007] Step S1, define the size, material properties, design domain, boundary conditions and number of iterations of the macro initial structure, and divide the macro design domain of the multiphase material structure into Discretize into several macro sub-design domains, and map the information of macro sub-design domains to the micro level as constraints for micro optimization; perform equivalent static transformation on transient temperature loads, introduce equivalent thermal loads to obtain a multi-scale topology optimization model;

[0008] Step S2, performing finite element analysis on the multi-scale topology optimization model to calculate the objective function and constraint conditions, including solving the equivalent temperature field at a certain time interval, solving the displacement vector matrix, and calculating the macro and micro volume fractions;

[0009] Step S3, performing sensitivity analysis on the objective function and constraint conditions, and using the moving asymptote MMA criterion method as a solver for updating macro and micro design variables in the multi-scale topology optimization model, performing iterative calculations to obtain the macro and micro design variables of the last step after iteration;

[0010] Step S4, fill the macro design variables of the last step into the macro design domain, fill the micro design variables of the last step into the macro sub-design domain to obtain the overall configuration, and judge the convergence conditions. If the convergence conditions are met, output the optimal material distribution structure and the micro optimal configuration.

[0011] In combination with the first aspect, further, the thermal-mechanically coupled multi-scale parallel topology optimization method of the present invention also includes the step of observing and verifying the microscopic optimal configuration, specifically: arranging the microscopic optimal configuration in a square, observing and verifying the connectivity of its structure, requiring that there should be no faults at the structural joints.

[0012] In combination with the first aspect, further, a specific method of mapping the macro sub-design domain information at the micro level as a constraint condition for micro optimization is:

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

[0014] ;

[0015] In the formula, , , They are mass matrix, damping matrix and stiffness matrix respectively; is the applied force field load, is the thermal load caused by thermal expansion, , No specific meaning, only used to distinguish different loads. For the moment, is the overall load, the overall load will change over time, For the The displacement matrix of the structure at that moment, For the The velocity matrix of the moment structure, For the The acceleration matrix of the moment structure;

[0016] The finite element equation for transient heat conduction of the structure is:

[0017]

[0018] In the formula, is the vector matrix of macro design variables, is the number of macro grid cells, is the thermodynamic subscript, is the heat capacity matrix, is the heat conduction matrix, is the temperature field About Moment The first derivative of It's about time heat load;

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

[0020] .

[0021] Combined with the first aspect, further, the transient temperature load is converted into an equivalent static state, and the specific method of introducing the equivalent thermal load to obtain the multi-scale topology optimization model is as follows:

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

[0023]

[0024] In the formula, , For the The equivalent mechanical load at time, For the Moment The equivalent displacement vector caused by For the Moment The equivalent acceleration vector caused by For the Moment The equivalent velocity vector caused by

[0025] The macro model is defined as:

[0026]

[0027] In the formula, is the serial number of the macro unit, is the total number of macro grid cells, Indicates macro design variables, Symbolizes the macro scale, represents the macroscopic heat dissipation weakness (i.e., the macroscopic objective function), For the The moment macro-element temperature vector, 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 macro-scale penalty factor, is the upper limit of the macrostructure volume, The minimum relative density of the material is to prevent the overall heat conduction matrix of the structure, usually 1×10 -9 , represents the overall heat transfer matrix, is the first The equivalent heat load at time, It is The equivalent temperature field at time ;

[0028] The microscopic model is defined as:

[0029]

[0030] In the formula, is the serial number of the micro-unit, represents the total number of micro-grid units, Indicates Microstructure micro-design variables, represents the total number of microstructure types, The serial number indicating the type of microstructure, Symbolizes the microscopic scale, represents the heat dissipation weakness at the microscopic scale (i.e., the objective function at the microscopic scale), For the The moment The first element temperature vector, represents the microstructure volume constraint function, is the micro-scale penalty factor, For the The upper limit of the volume of the microstructure, For the Volume constraint function of microstructure-like structure;

[0031] The parallel topology optimization method of simultaneously optimizing the macro model and the micro model is adopted, with the optimization goal of minimizing the heat dissipation weakness at the micro and macro scales. The multi-scale parallel topology optimization mathematical model of transient heat conduction of composite materials is expressed as:

[0032] .

[0033] In combination with 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-mechanical coupling finite element equation, calculating the objective function and constraint conditions of the multi-scale topology optimization model in step S1, including using a differential formula to solve the temperature field at a certain time interval, using the HHT-α method to solve the displacement vector matrix, and calculating the macro-micro volume fraction;

[0034] Step S21, using the differential formula to solve the temperature field at a certain time interval, that is:

[0035] ;

[0036] In the formula, is the time step; For the The equivalent temperature field at time ; For the The equivalent temperature field at time , For the moment, is the first The equivalent heat load at time, is the heat capacity matrix, is the heat conduction matrix, is the vector matrix of macro design variables, is the number of macro grid cells, is the thermodynamic subscript;

[0037] Step S22: Use the HHT-α method to solve the displacement vector matrix. According to the Newmark-β finite difference relationship, the update format of the displacement and velocity field is:

[0038] ;

[0039] ;

[0040] In the formula, , , are all dynamics algorithm parameters, among which, , ; and Respectively The displacement matrix, velocity matrix and acceleration matrix of the moment structure; and They are The displacement matrix, velocity matrix and acceleration matrix of the moment structure;

[0041] Step S23: Calculate the macroscopic volume fraction, i.e. ; and calculate the microscopic volume fraction, that is, ;in, is the serial number of the macro unit, is the total number of macro grid cells, Indicates macro design variables, Symbolizes the macro scale, is the serial number of the micro-unit, represents the total number of micro-grid units, Indicates Microstructure micro-design variables, The serial number indicating the type of microstructure, Symbolizes microscopic scale.

[0042] In combination with the first aspect, further, in order to ensure that the first The accurate simulation of the displacement vector matrix at the moment in the dynamic process, the step S2 also includes step S24, which is as follows:

[0043] Step S24: Construct the The discrete form of the control equation at the moment makes the residual equal to 0, that is:

[0044] ;

[0045] In the formula, For the The residual of the discrete form of the control equation at time; for The acceleration matrix at the moment; and They are Velocity matrix and acceleration matrix of the moment structure; is the dynamics algorithm parameter, which is taken as 0.05; for The external load array at each time; for The external load array at each time; , are the first and second coefficients of the mass matrix in discrete form; is the first coefficient of the damping matrix in discrete form; where, , and They are defined as:

[0046] ;

[0047] The residual equation at the initial moment is:

[0048] ;

[0049] In the formula, is the residual of the control equation at the initial moment; , and are the displacement, velocity and acceleration arrays of the structure at the initial moment respectively; is the external load array at the initial moment.

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

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

[0052] ;

[0053] In the formula, represents the overall heat transfer matrix, is the objective function at the macro scale, i.e., the heat dissipation weakness at the macro scale; Design variables for the macro; is the first Equivalent heat load at time ; It is The macroscopic equivalent temperature field at time t; for the moment; symbolizes the macroscopic scale; for duration;

[0054] Macro volume constraints The sensitivity calculation is:

[0055] ;

[0056] In the formula, is the upper limit of the volume of the macrostructure; is the serial number of the macro unit; is the total number of macro grid cells; Indicates macro design variables;

[0057] Finding the objective function at the microscopic scale For any micro-design variable The sensitivity is expressed as:

[0058] ;

[0059] In the formula, For the The equivalent temperature field at the microscopic scale at each moment; represents the stiffness matrix; Design variables for micro level;

[0060] No. Volume constraint function of microstructure The sensitivity under is expressed as:

[0061] ;

[0062] in, For the The upper limit of the volume of the microstructure; Indicates Microstructure micro-design variables; is the serial number of the micro-unit; symbolizes the microscopic scale; Represents the total number of micro-grid cells.

[0063] In combination with the first aspect, further, the moving asymptote MMA criterion method is used as a solver for updating the macro design variables in the multi-scale topology optimization model, and iterative calculation is performed to obtain the macro design variables of the last step after iteration. The specific method is:

[0064]

[0065] In the formula, is the macro design variable, represents the macroscopic heat dissipation weakness, which is the macroscopic objective function. is an artificial variable, is the serial number of the macro unit, is the total number of macro grid cells, and are real numbers, and are all greater than 0; and are also real numbers and satisfy , is the macroscopic relaxation factor, is the volume constraint function at the macroscopic scale;

[0066] Then, the moving asymptote MMA approximate equation of the macroscopic objective function or volume constraint function is expressed as:

[0067]

[0068] In the formula, is the moving asymptote MMA approximation equation of the macroscopic objective function or constraint function, is the number of iterations, For macroscopic scale The moving asymptote MMA equation for iterations, Indicates The macro design variables of each macro unit, Indicates Macro unit The macro design variables after the iteration are solved by the moving asymptotic method. Represented as an upward moving asymptote on a macroscopic scale, is the downward moving asymptote on the macro scale, , are MMA movement parameters, respectively expressed as:

[0069] ;

[0070] ;

[0071] Similarly, the micro-design variables of the last step after iteration are obtained.

[0072] In a second aspect, the present invention proposes a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-mentioned thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing.

[0073] In a third aspect, the present invention provides a computer device, comprising:

[0074] Memory for storing computer programs;

[0075] A processor is used to execute the computer program to implement the steps of the above-mentioned thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing.

[0076] In a fourth aspect, the present invention proposes a computer program product, comprising a computer program, which, when executed by a processor, implements the steps of the above-mentioned thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing.

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

[0078] (1) The present invention takes into account the heat conduction of transient response, which can better reflect the actual working state of the workpiece compared with the heat conduction of steady-state response; it takes into account the simultaneous update of the macrostructure and the microstructure, and the design space of the entire structure and material, so as to better exert the performance of the structure.

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

[0080] Figure 1 It is a schematic diagram of the process of the thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing of the present invention;

[0081] Figure 2 It is a structural schematic diagram of the design object of the present invention;

[0082] Figure 3 A schematic diagram of the macroscopic results of topology optimization of the design object of the present invention;

[0083] Figure 4 This is a schematic diagram of the microscopic results of topology optimization of the design object of the present invention. DETAILED DESCRIPTION

[0084] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations on the technical solution of the present invention. The embodiments of the present invention and the technical features in the embodiments may be combined with each other unless there is a conflict.

[0085] The term "and / or" is only a description of the association relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " generally indicates that the related objects are in an "or" relationship.

[0086] Example 1

[0087] like Figure 1 As shown, this embodiment proposes a thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing, including the following steps:

[0088] Step S1: First, define the size, material properties, design domain, boundary conditions and number of iterations of the initial structure. Then, discretize the grid and divide the macroscopic design domain into Design domains for multiple macro subdomains , , , …, , …, ,in, Indicates the sequence number of the macro sub-design domain, Represents the total number of macro sub-design domains; maps the macro sub-design domain information to the micro level as a constraint for micro optimization; performs an equivalent static transformation on the transient temperature load, introduces an equivalent thermal load, and obtains a multi-scale topology optimization model.

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

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

[0091] Step S12: Macro-design domain Divide into multiple macro sub-design domains through fuzzy C clustering method , , , …, , …, ,in, Indicates the sequence number of the macro sub-design domain, Represents the total number of macro sub-design domains; each macro sub-design domain is filled with the same type of microstructures, and the microstructure configurations of different macro sub-design domains are different.

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

[0093] (1)

[0094] In the formula, , , They are mass matrix, damping matrix and stiffness matrix respectively; is the applied force field load, is the thermal load caused by thermal expansion, , No specific meaning, only used to distinguish different loads. For the moment, is the overall load, the overall load will change over time, For the The displacement matrix of the structure at that moment, For the The velocity matrix of the moment structure, For the The acceleration matrix of the structure at that moment.

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

[0096] (2)

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

[0098] The heat conduction matrix in formula (2) and heat capacity matrix And about the moment Heat load It can be expressed as:

[0099] (3)

[0100] In the formula, is the horizontal serial number, , is the vertical serial number, is the unit number, The horizontal serial number is , the vertical sequence number is The unit heat conduction matrix, The horizontal serial number is , the vertical sequence number is The unit heat capacity matrix, The horizontal sequence number is , the vertical sequence number is The unit heat load matrix, For the horizontal sequence number , the vertical sequence number is , unit number is The influence of the unit heat conduction matrix, The horizontal sequence number is , the vertical sequence number is , unit number is The convection heat transfer boundary of the unit modifies the heat transfer matrix. The horizontal sequence number is , the vertical sequence number is , unit number is The unit heat capacity matrix, For the horizontal sequence number , the unit number is , from the horizontal sequence number Heat flow The resulting element thermal loads applied to the structure; For the horizontal sequence number , the unit number is , from the horizontal sequence number The heat flux The thermal load of the constant heat flux boundary element caused by the For the horizontal sequence number , the unit number is , from the horizontal sequence number Convective heat transfer coefficient Convective heat caused by boundary element heat loads.

[0101] Step S15: According to the finite element equation of transient heat conduction of the above structure, the transient thermal-mechanical coupling finite element equation is:

[0102] (4)

[0103] Because every moment The temperature field is different, so the thermal load caused by thermal expansion It can be expressed as:

[0104] (5)

[0105] In the formula, Expressed as the number of macro grid cells, Expressed as the structural strain matrix, is the elasticity matrix, is the thermal strain caused by the temperature field, , represents the defined boundary temperature, For the The equivalent temperature field at time , is the thermal expansion coefficient, so the thermal load caused by thermal expansion It can be further described as:

[0106] (6)

[0107] Step S16: Apply the method of converting the structure into static equivalent transient temperature load at each moment. , the transient thermal-mechanical coupling finite element equation can be written as the equivalent displacement field equation:

[0108] (7)

[0109] In the formula, , For the The equivalent mechanical load at time, For the Moment The equivalent displacement vector caused by For the Moment The equivalent acceleration vector caused by For the Moment The equivalent velocity vector caused by

[0110] Step S17: Define the macro model as:

[0111] (8)

[0112] In the formula, is the serial number of the macro unit, is the total number of macro grid cells, Indicates macro design variables, Symbolizes the macro scale, represents the macroscopic heat dissipation weakness (i.e., the macroscopic objective function), For the The moment macro-element temperature vector, 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 macro-scale penalty factor, is the upper limit of the macrostructure volume, is the minimum relative density of the material, represents the overall heat transfer matrix, is the first The equivalent heat load at time, It is The equivalent temperature field at time .

[0113] The microscopic model is defined as:

[0114] (9)

[0115] In the formula, is the serial number of the micro-unit, represents the total number of micro-grid units, Indicates Microstructure micro-design variables, represents the total number of microstructure types, The serial number indicating the type of microstructure, Symbolizes the microscopic scale, represents the heat dissipation weakness at the microscopic scale (i.e., the objective function at the microscopic scale), For the The moment The first element temperature vector, represents the microstructure volume constraint function, is the micro-scale penalty factor, For the The upper limit of the volume of the microstructure, For the Volume constraint function for microstructure-like structures.

[0116] The parallel topology optimization method is used to optimize the macro model (see formula (8)) and the micro model (see formula (9)) at the same time, with the optimization goal of minimizing the heat dissipation weakness at the micro and macro scales. The mathematical model of multi-scale parallel topology optimization under transient heat conduction of composite materials can be expressed as:

[0117] (10)

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

[0119] Step S2, performing finite element analysis on the multi-scale topology optimization model in step S1 (i.e., formula (10)) according to the transient thermal-mechanical coupling finite element equation described in formula (4), calculating the objective function and constraint conditions of the multi-scale topology optimization model in step S1, including using the differential formula described in formula (11) to solve the equivalent temperature field at a certain time interval, using the HHT-α method described in formula (12) to solve the displacement vector matrix, and calculating the macro-micro volume fractions.

[0120] Step S21: Use the differential formula to solve the equivalent temperature field at a certain time interval, that is:

[0121] (11)

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

[0123] Step S22: Use the HHT-α method to solve the displacement vector matrix. According to the Newmark-β finite difference relationship, the update format of the displacement and velocity field is:

[0124] (12)

[0125] (13)

[0126] In the formula, , , are all dynamics algorithm parameters, among which, , ; and Respectively The displacement matrix, velocity matrix and acceleration matrix of the moment structure; and They are The displacement matrix, velocity matrix and acceleration matrix of the structure at each moment.

[0127] Step S23: Calculate the macroscopic volume fraction, i.e. ; and calculate the microscopic volume fraction, that is, .

[0128] Step S24: To ensure that the solution of step S22 The displacement vector matrix at the moment is accurately simulated in the dynamic process, and the The discrete form of the control equation at the moment makes the residual equal to 0, that is:

[0129] (14)

[0130] In the formula, For the The residual of the discrete form of the control equation at time; for The acceleration matrix at the moment; and They are Velocity matrix and acceleration matrix of the moment structure; is the dynamics algorithm parameter, which is taken as 0.05; for The external load array at each time; for The external load array at each time; , are the first and second coefficients of the mass matrix in discrete form; is the first coefficient of the damping matrix in discrete form; where, , and They are defined as:

[0131] (15)

[0132] The residual equation at the initial moment is:

[0133] (16)

[0134] In the formula, is the residual of the control equation at the initial moment; , and are the displacement, velocity and acceleration arrays of the structure at the initial moment respectively; is the external load array at the initial moment.

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

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

[0137] (17)

[0138] In the formula, represents the overall heat transfer matrix, is the objective function at the macro scale, i.e., the heat dissipation weakness at the macro scale; It is The macroscopic equivalent temperature field at time t;

[0139] Macro volume constraints The sensitivity calculation is:

[0140] (18)

[0141] Finding the objective function at the microscopic scale For any micro-design variable The sensitivity can be expressed as:

[0142] (19)

[0143] In the formula, For the The equivalent temperature field at the microscopic scale at each moment.

[0144] No. Volume constraint function of microstructure The sensitivity under can be expressed as:

[0145] (20)

[0146] Step S32: The macroscopic objective function and the sensitivity of the constraint conditions obtained in step S31 are used as input, and the moving asymptote MMA criterion method is used as the solver for the topology optimization of the transient heat conduction problem. Iterative calculation is performed to update the macroscopic design variables. The corresponding optimization subproblem can be expressed as:

[0147] (twenty one)

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

[0149] Then, the moving asymptote MMA approximate equation of the macroscopic objective function or volume constraint function is expressed as:

[0150] (twenty two)

[0151] In the formula, is the moving asymptote MMA approximation equation of the macroscopic objective function or constraint function, is the number of iterations, For macroscopic scale The moving asymptote MMA equation for iterations, Indicates The macro design variables of each macro unit, Indicates Macro unit The macro design variables after the iteration are solved by the moving asymptotic method. Represented as an upward moving asymptote on a macroscopic scale, is the downward moving asymptote on the macro scale, , are MMA movement parameters, respectively expressed as:

[0152] (twenty three)

[0153] (twenty four)

[0154] Step S33: At the same time, the objective function and the sensitivity of the constraint conditions at the microscopic scale obtained in step S31 are used as input, and the moving asymptote MMA criterion method is used as the solver for the topological optimization of the transient heat conduction problem to perform iterative calculations to update the microscopic design variables. The corresponding optimization subproblem can be expressed as:

[0155] (25)

[0156] In the formula, is the micro-design variable, represents the heat dissipation weakness at the microscopic scale (i.e., the objective function at the microscopic scale), is an artificial variable, is the serial number of the micro-unit, is the total number of micro-grid units, and is a real number, and is greater than 0, usually 0.1, 0.8; and are also real numbers and satisfy ,generally and Take 0.6 and 0.4 respectively, is the microscopic relaxation factor, usually taken as 0.5, For microscopic scale Volume constraint function of the quasi-microstructure.

[0157] Then, the moving asymptote MMA approximate equation of the microscopic objective function or volume constraint function is expressed as:

[0158] (26)

[0159] In the formula, is the moving asymptote MMA approximation equation of the microscopic objective function or constraint function, is the number of iterations, For microscopic scale The moving asymptote MMA equation for iterations, Indicates The micro-design variables of a macro-unit, Indicates Microscopic unit The micro-design variables after iterations are solved by the moving asymptotic method. Represented as an upward moving asymptote at the microscopic scale, is the downward moving asymptote at the microscopic scale, , are MMA movement parameters, respectively expressed as:

[0160] (27)

[0161] (28)

[0162] Step S4, fill the macro design variable values ​​of the last step of step S3 into the macro design domain, fill the micro design variable values ​​into the macro sub-design domain divided by the macro design domain in step S1 to obtain the overall configuration, and judge the convergence conditions. If the conditions are met, output the optimal material distribution structure and the micro optimal configuration; at the same time, arrange the micro optimal configuration in a square, and observe and check the connectivity of the structure by the operator, requiring that there should be no faults at the structural joints.

[0163] The purpose of placing the micro-optimal configuration in a square is to test the reliability and stability of the micro-optimal configuration in terms of connectivity. Preferably, the micro-optimal configuration is placed in a 3×3 arrangement, which is simpler and more convenient than other square arrangements (such as 4×4, 5×5).

[0164] The obtained microstructure is mapped into the macro sub-design domain of the corresponding volume fraction using MATLAB software , , , …, , …, ( Indicates the sequence number of the macro sub-design domain, represents the total number of macro sub-design domains), the convergence condition is that when the relative density value between the current design variable and the previous design variable is less than 0.001, the convergence condition and the connectivity of the structure are met. At this time, the optimal material distribution structure and the microscopic optimal configuration can be output. If not, return to step S1.

[0165] Example 2

[0166] like Figure 2 As shown, in this embodiment, the design object is a cantilever arm model, and the initial structural design domain is defined as 2m in length, 1m in width, and 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, and the number of iterations is is 200, the macro design domain is divided into 3 macro sub-design domains, and the total number of macro grid units is , the total number of micro-grid units ; Internally applied Heat load at time (Unit: kN), equivalent temperature field K. The center of the right boundary is the equivalent mechanical load application point. For the The equivalent mechanical load at the moment is 1kN. The duration of the thermal coupling process is s, the duration The time step is 15 equal steps. s, the bottom of the cantilever beam is the heat dissipation boundary ℃, the macroscopic volume constraint and microscopic volume constraint are and ( ).

[0167]

[0168] like Figure 3 As shown, it is a macroscopic structure after the cantilever beam structure is optimized using the thermomechanical coupling multi-scale parallel topology optimization method of the present invention. Due to the axial symmetry of the applied boundary conditions, the optimized whole is a vertically symmetrical structure, and a clear force transmission path is formed between the applied force load and the left fixed end. The optimized heat dissipation weakness is 131.7. If multi-scale topology optimization is not considered like the present invention, the optimized heat dissipation weakness is 151.7. Since the higher the heat dissipation weakness, the worse the heat dissipation performance, Example 1 of the present invention has further improved the heat dissipation performance; and the whole is composed of three types of microstructures with different structures, and their volume fractions are 0.272, 0.517, and 0.5816, respectively. They are arranged in a 3×3 array, and it is found that their connectivity is also better.

[0169] Example 3

[0170] Based on the same inventive concept as other embodiments, this embodiment introduces a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the above-mentioned thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing are implemented.

[0171] Example 4

[0172] Based on the same inventive concept as other embodiments, this embodiment introduces a computer device, including: a memory for storing a computer program; a processor for executing the computer program to implement the steps of the above-mentioned thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing.

[0173] Example 5

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

[0175] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0176] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, 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 device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0177] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0178] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0179] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Ordinary technicians in this field can also make many forms under the guidance of the present invention, which all fall within the protection of the present invention.

Claims

1. A thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing, characterized in that: include: Step S1, define the size, material properties, design domain, boundary conditions and number of iterations of the macro initial structure, and divide the macro design domain of the multiphase material structure into Discretize into several macro sub-design domains, and map the information of macro sub-design domains to the micro level as constraints for micro optimization; perform equivalent static transformation on transient temperature loads, introduce equivalent thermal loads to obtain a multi-scale topology optimization model; Step S2, performing finite element analysis on the multi-scale topology optimization model to calculate the objective function and constraint conditions; Step S3, performing sensitivity analysis on the objective function and constraint conditions, and using the moving asymptote MMA criterion method as a solver for updating macro and micro design variables in the multi-scale topology optimization model, performing iterative calculations to obtain the macro and micro design variables of the last step after iteration; Step S4, fill the macro design variables of the last step into the macro design domain, fill the micro design variables of the last step into the macro sub-design domain to obtain the overall configuration, and judge the convergence conditions. If the convergence conditions are met, output the optimal material distribution structure and the micro optimal configuration.

2. The thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing according to claim 1, characterized in that: The method also includes the steps of observing and testing the micro-optimal configuration, specifically: arranging the micro-optimal configuration in a square, observing and testing the connectivity of its structure, and requiring that there should be no faults at the structural joints.

3. The thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing according to claim 1, characterized in that: The specific method of mapping the macro sub-design domain information to the micro level as the constraint condition of micro optimization is: The mechanical finite element equation considering dynamic loads is: ； In the formula, , , They are mass matrix, damping matrix and stiffness matrix respectively; is the applied force field load, is the thermal load caused by thermal expansion, , No specific meaning, only used to distinguish different loads. For the moment, is the overall load, the overall load will change over time, For the The displacement matrix of the structure at that moment, For the The velocity matrix of the moment structure, For the The acceleration matrix of the moment structure; The finite element equation for transient heat conduction of the structure is: ； In the formula, is the vector matrix of macro design variables, is the number of macro grid cells, is the thermodynamic subscript, is the heat capacity matrix, is the heat conduction matrix, is the temperature field About Moment The first derivative of It's about the moment heat load; According to the finite element equation of transient heat conduction of the structure, the transient thermal-mechanical coupling finite element equation is: 。 4. The thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing according to claim 3, characterized in that: The specific method of converting transient temperature load into equivalent static state and introducing equivalent thermal load to obtain multi-scale topology optimization model is as follows: The method of converting the transient temperature load of the structure into static equivalent is applied. , the transient thermal-mechanical coupling finite element equation can be written as the equivalent displacement field equation: ； In the formula, , For the The equivalent mechanical load at time, For the Moment The equivalent displacement vector caused by For the Moment The equivalent acceleration vector caused by For the Moment The equivalent velocity vector caused by The macro model is defined as: ； In the formula, is the serial number of the macro unit, is the total number of macro grid cells, Indicates macro design variables, Symbolizes the macro scale, represents the macroscopic heat dissipation weakness, which is the macroscopic objective function. For the The moment macro-element temperature vector, 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 macro-scale penalty factor, is the upper limit of the macrostructure volume, is the minimum relative density of the material, represents the overall heat transfer matrix, is the first The equivalent heat load at time, It is The equivalent temperature field at time ; The microscopic model is defined as: ； In the formula, is the serial number of the micro-unit, represents the total number of micro-grid units, Indicates Microstructure micro-design variables, represents the total number of microstructure types, The serial number indicating the type of microstructure, Symbolizes the microscopic scale, represents the heat dissipation weakness at the microscopic scale, which is the objective function at the microscopic scale. For the The moment The first element temperature vector, represents the microstructure volume constraint function, is the micro-scale penalty factor, For the The upper limit of the volume of the microstructure, For the Volume constraint function of microstructure-like structure; The parallel topology optimization method of simultaneously optimizing the macro model and the micro model is adopted, with the optimization goal of minimizing the heat dissipation weakness at the micro and macro scales. The multi-scale parallel topology optimization mathematical model of transient heat conduction of composite materials is expressed as: 。 5. The thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing according to claim 1, characterized in that: 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-mechanical coupling finite element equation, calculating the objective function and constraint conditions of the multi-scale topology optimization model in step S1, including using a differential formula to solve the equivalent temperature field at a certain time interval, using the HHT-α method to solve the displacement vector matrix, and calculating the macro-micro volume fraction; Step S21, using the differential formula to solve the equivalent temperature field at a certain time interval, that is: ； In the formula, is the time step; For the The equivalent temperature field at time ; For the The equivalent temperature field at time , For the moment, is the first The equivalent heat load at time, is the heat capacity matrix, is the heat conduction matrix, is the vector matrix of macro design variables, is the number of macro grid cells, is the thermodynamic subscript; Step S22: Use the HHT-α method to solve the displacement vector matrix. According to the Newmark-β finite difference relationship, the update format of the displacement and velocity field is: ； ； In the formula, , , are all dynamics algorithm parameters, among which, , ; and Respectively The displacement matrix, velocity matrix and acceleration matrix of the moment structure; and They are The displacement matrix, velocity matrix and acceleration matrix of the moment structure; Step S23: Calculate the macroscopic volume fraction, i.e. ; and calculate the microscopic volume fraction, that is, ;in, is the serial number of the macro unit, is the total number of macro grid cells, Indicates macro design variables, Symbolizes the macro scale, is the serial number of the micro-unit, represents the total number of micro-grid units, Indicates Microstructure micro-design variables, The serial number indicating the type of microstructure, Symbolizes microscopic scale.

6. The thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing according to claim 1, characterized in that: The specific method of performing sensitivity analysis on the objective function and constraint conditions in step S3 is: Find the objective function at the macro scale For any macro design variable The sensitivity is expressed as: ； In the formula, represents the overall heat transfer matrix, is the objective function at the macro scale, i.e., the heat dissipation weakness at the macro scale; Design variables for the macro; is the first Equivalent heat load at time ; It is The macroscopic equivalent temperature field at time t; for the moment; symbolizes the macroscopic scale; for duration; Macro volume constraints The sensitivity calculation is: ； In the formula, is the upper limit of the volume of the macrostructure; is the serial number of the macro unit; is the total number of macro grid cells; Indicates macro design variables; Finding the objective function at the microscopic scale For any micro-design variable The sensitivity is expressed as: ； In the formula, For the The equivalent temperature field at the microscopic scale at each moment; represents the stiffness matrix; Design variables for micro level; No. Volume constraint function of microstructure The sensitivity under is expressed as: ； in, For the The upper limit of the volume of the microstructure; Indicates Microstructure micro-design variables; is the serial number of the micro-unit; symbolizes the microscopic scale; Represents the total number of micro-grid cells.

7. The thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing according to claim 6, characterized in that: The moving asymptote MMA criterion method is used as a solver for updating the macro-design variables in the multi-scale topology optimization model, and iterative calculation is performed to obtain the macro-design variables of the last step after iteration. The specific method is: ； In the formula, is the macro design variable, represents the macroscopic heat dissipation weakness, which is the macroscopic objective function. is an artificial variable, is the serial number of the macro unit, is the total number of macro grid cells, and are real numbers, and are all greater than 0; and are also real numbers and satisfy , is the macroscopic relaxation factor, is the volume constraint function at the macroscopic scale; Then, the moving asymptote MMA approximate equation of the macroscopic objective function or volume constraint function is expressed as: ； In the formula, is the moving asymptote MMA approximation equation of the macroscopic objective function or constraint function, is the number of iterations, For macroscopic scale The moving asymptote MMA equation for iterations, Indicates The macro design variables of each macro unit, Indicates Macro unit The macro design variables after the iteration are solved by the moving asymptotic method. Represented as an upward moving asymptote on a macroscopic scale, is the downward moving asymptote on the macro scale, , are MMA movement parameters, respectively expressed as: ； ； Similarly, the micro-design variables of the last step after iteration are obtained.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing described in any one of claims 1 to 7 are implemented.

9. A computer device, characterized in that: include: Memory for storing computer programs; A processor is used to execute the computer program to implement the steps of the thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing according to any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that: When the computer program is executed by a processor, the steps of the thermal-mechanical coupling multi-scale parallel topology optimization method for additive manufacturing described in any one of claims 1 to 7 are implemented.

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