WO2021088215A1 - 一种用于榫卯连接结构设计的归选式拓扑优化方法 - Google Patents

一种用于榫卯连接结构设计的归选式拓扑优化方法 Download PDF

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WO2021088215A1
WO2021088215A1 PCT/CN2019/126355 CN2019126355W WO2021088215A1 WO 2021088215 A1 WO2021088215 A1 WO 2021088215A1 CN 2019126355 W CN2019126355 W CN 2019126355W WO 2021088215 A1 WO2021088215 A1 WO 2021088215A1
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tenon
unit
strain energy
groove
tongue
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PCT/CN2019/126355
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French (fr)
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宋凯
程浦
王国春
胡朝辉
周晓斌
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广西艾盛创制科技有限公司
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Priority to JP2022526410A priority Critical patent/JP7418047B2/ja
Publication of WO2021088215A1 publication Critical patent/WO2021088215A1/zh

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]

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  • the invention relates to a topology optimization method, in particular to an optimization design method for assembled parts, butt-joined parts, tenon-and-mortise structures or other structures that depend on the shape of the structure for mutual support, positioning and force transmission.
  • connection part for example, the tenon-and-mortise structure is not limited to the application of traditional wooden structures, but is used in a wider range of fields such as mechanical structure design and manufacturing. In this context, the optimization of this fast connection structure has important practical significance.
  • the method of shape optimization is generally adopted.
  • This method needs to preset shape variables, and the direction and scope of the shape change are limited, so that the optimization process depends too much on the topology and shape of the initial structure, and it is impossible to give a new structural form that is instructive. Therefore, this method can only be used to improve stress concentration and optimize contact conditions, but cannot change the force transmission path of the structure.
  • topology optimization technology can give new structural forms with enlightening significance
  • conventional topology optimization technology regardless of variable density method, progressive structure optimization method, cellular automata method or level set method, can only be applied to a single flexible
  • the optimization of the body is characterized in that the boundary conditions of the structure in the optimization iteration are unchanged or only slightly and regularly changed, so it cannot be applied to the situation where the boundary conditions of the tenon structure and other optimization problems change drastically.
  • the new optimization method developed needs to solve the following technical problems: (1) Different from the shape optimization, the new optimization method needs to improve the global optimization ability and provide a new structural form with enlightening significance; (2) This An optimization method should be different from the conventional topology optimization method. It must be able to handle the optimization of two mutually coordinated structures, that is, the situation where the contact conditions and boundary conditions change drastically and unpredictably. The conventional topology optimization technology with variable boundary conditions is difficult Deal with this kind of problems; (3) In the optimization iteration, the topology and shape of the respective connecting parts of the two parts should be able to be correlated and coordinated to change to ensure the reasonable cooperation of the two parts.
  • the purpose of the present invention is to develop a set of new topology optimization methods, which use the attribution state of the grid unit, that is, the number of the component to which the unit belongs, as a design variable, and select the state according to a certain control rule to achieve the goal of optimal design.
  • the method can be used for the optimal design of assembled parts, butt joint parts, connection parts of tenon and tenon-and-mortise structures or connecting structures with tenon and tenon-and-mortise features. This method has a certain global optimization capability, and can handle situations where contact conditions and boundary conditions change drastically and unpredictably.
  • An alternative topology optimization method for tenon-and-mortise connection structure design which specifically includes the following steps:
  • Step 1 Establish a finite element model of the structure to be optimized.
  • the model includes: tongue and groove, tenon, left-side bearing structure, right-side bearing structure, support, downforce load and constraints on the support, including the elements of the tongue and tenon To optimize the design domain of the problem;
  • Step 2 Select the area where the tongue and groove and the tenon are located as the design domain, and use the attribution status of the unit in the design domain as the design variable. That is, for each unit, there are two attribution statuses: it belongs to the groove or the tenon;
  • Step 3 Select the basic unit, and determine the basic structural form of the tenon and the groove;
  • the basic unit refers to the unit that is not allowed to move during the optimization iteration process, that is, the attribution status of the basic unit is not allowed to change;
  • Step 4 Run a finite element analysis to obtain the element strain energy ⁇ i , and calculate the total strain energy E of the structure, the total strain energy E 1 of the tongue and groove and the average strain energy e 1 , the total strain energy E 2 and the average strain energy of the tenon e 2 ;
  • Step 5 Filter and average the strain energy of the element calculated in Step 4, that is, use the average or weighted average value of the strain energy of all elements in the neighborhood of the central element whose attribution status is the same as that of the central element instead of the original strain energy value, which is still recorded as ⁇ i ;
  • the neighborhood refers to the collection of all units within a certain distance R around the central unit, denoted as ⁇ i ;
  • Step 6 Based on the filtered and averaged strain energy of the unit obtained in step 5, set the amplification coefficient scale, and increase the basic unit and the amplification unit;
  • Step 7 Calculate the neighborhood state of each element in the design domain according to the increased strain energy of the element obtained in Step 6;
  • Step 8 Set local control parameters, construct local control rules, and update unit attribution status, namely: update design variables;
  • Step 9 Take the total strain energy E of the tongue and groove and the tenon head as the objective function to judge the convergence, and set the convergence tolerance ⁇ ;
  • the definition of the convergence criterion is: the average change of the total strain energy E in 2 consecutive iterations is less than or equal to Converges when ⁇ ; if the objective function does not converge at the current iteration step, go to step 4 and start the next iteration process; if the objective function converges at the current iteration step, exit the optimization process and save the current mesh model as the optimized post the result of;
  • Step 10 Analyze and evaluate the optimization results, check the maximum stress value, maximum strain value and total strain energy value of the tongue and groove and the tenon, and the displacement of the key points of the structure.
  • step 1 the established finite element model ensures that the tenon (2) and the tenon groove (1) are completely fitted at the contact surface, and the mesh nodes of the tenon and the tenon groove at the contact surface coincide with each other.
  • step 4 the calculation is performed by the following formula:
  • e 1 E 1 /N 1 N 1 is the number of units of the tongue and groove 1;
  • e 2 E 2 /N 2 N 2 is the number of units of the tenon 2.
  • the information contained in the neighboring state includes: [N i1 , N i2 , n i1 , n i2 ], where N i1 is the unit with the belonging state of 1 in the neighboring area of unit i, that is The sum of the strain energy of the elements belonging to the tongue and groove (1); Ni2 is the unit with the assignment state of 2 in the neighborhood of the element i, that is, the sum of the strain energy of the elements belonging to the tenon (2); n i1 is the assignment in the neighborhood of the element i
  • the element with state 1 is the average value of strain energy of the element belonging to the tongue and groove (1); n i2 is the element belonging to state 2 in the neighborhood of element i, that is, the average value of the strain energy of the element belonging to the tenon (2); where :
  • n i1 N i1 /n 1 n 1 is the number of units belonging to the tongue and groove 1 in the neighborhood of unit i;
  • n i2 N i2 /n 2 n 2 is the number of units belonging to the tenon 2 in the neighborhood of unit i.
  • the local control parameters include: conventional movement coefficient m1, amplifying movement coefficient m2, strain energy proportional control coefficient rt; the local control rules are a set of judgments whether the attribution state of each unit is in this iteration Criteria for changes in steps.
  • step 9 the objective function expression is as follows:
  • O is the objective function.
  • the objective function value is less than or equal to the convergence tolerance ⁇ , the objective function is judged to be convergent and the optimization is completed; it is the current iteration step, in which no convergence judgment is made in the first two iterations ;
  • E it is the sum of the strain energy of the tongue and groove (1) and the tenon (2) after the it iteration;
  • E it-1 and E it-2 are the tongue and groove after it-1 and it-2 iterations ( 1)
  • E 1 is the sum of the strain energy of the tenon (1) and the tenon (2) when not optimized, that is, the strain energy of the initial structure.
  • the method of the present invention can be optimized in a larger range by changing the basic shape of the mating and connected parts of the tenon-and-mortise connection structure, thereby optimizing the force transmission path of the tenon-and-mortise connection structure, and refer to step 8.
  • the strain energy information of all elements in the neighborhood of each element seeks a structure with a more uniform strain energy distribution, thereby improving the contact conditions and stress concentration problems.
  • the optimization results of the embodiments provided by the present invention also prove the feasibility and effectiveness of this method.
  • the method of the present invention can optimize assembled parts, butt-joined parts, tenon-and-mortise structures, or other structures that rely on the shape of the structure to support each other, locate and transmit force, such as bump couplings and part butt joints , Pins and pin holes, slide rails, buckles, etc. This is because this type of structure has the characteristics and properties of the tenon-and-mortise connection structure, such as: relying on the mutual cooperation of the two structural shapes for positioning, support and force transmission, so this method is also suitable for the optimal design of such parts .
  • the method of the present invention does not need to preset shape variables, simplifies the modeling work, and reduces the dependence on the engineering experience of the user at the same time;
  • the method of the present invention does not have the upper and lower limit of the shape variable, and introduces the unit increase and the increase amplitude attenuation rule in step 6, which improves the global optimization ability. Therefore, this method can make the optimization problem not limited to improving contact conditions and stress concentration, etc., and improve the overall force transmission path of the structure, and can obtain a more enlightening structural form;
  • step 2 because the design variable specified in step 2 is the unit attribution state and does not involve the movement of nodes and the deformation of the unit, the method of the present invention will not deform the mesh during the iteration process, and there is no Problems of unqualified element quality and insufficient calculation accuracy caused by excessive mesh deformation;
  • the method of the present invention extends the topology optimization technology to multiple flexible
  • the topology optimization technology is not limited to the topology optimization of a single flexible volume
  • the part number of the unit is used as a design variable, which solves the problem that the shape of the tongue and the tongue and groove need to be changed during the optimization of the tenon joint structure between flexible bodies;
  • the method of the present invention does not use gray cells, that is, does not use the concept of intermediate density, so the structure and structure performance obtained after each iteration step have accurate physical and realistic significance;
  • Figure 1 is a block diagram of the overall architecture of the optimization process of the present invention.
  • Figure 2 is a block diagram of the flow of partial control rules
  • Figure 3 is a schematic diagram of the finite element model of the structure to be optimized
  • Figure 4 is a schematic diagram of the part to be optimized (design area);
  • Figure 5 is a distribution diagram of basic units in the embodiment
  • Figure 6 is a schematic diagram of the optimized tenon joint structure
  • Figure 7 is a diagram of structural changes in previous iterations
  • Figure 8 is the change curve of total strain energy, total strain energy of component 1, and total strain energy of component 2 in previous iterations
  • Figure 9 is the maximum stress change curve of component 1 and component 2 in previous iterations
  • Figure 10 is the maximum strain curve of component 1 and component 2 in previous iterations
  • Figure 11 is the displacement change curve of key points in previous iterations
  • this embodiment provides a selective topology optimization method for tenon-and-mortise connection structure design, which specifically includes the following steps:
  • Step 1 Establish a finite element model of the structure to be optimized, as shown in Figure 3.
  • the model includes: tongue and groove 1, tenon 2, left-side bearing structure 3, right-side bearing structure 4, support 5, downforce load 6, and Constraint 7 for the support, where the unit of the tongue groove 1 and the tongue 2 is the design domain of the optimization problem.
  • the selection of design domain and the definition of design variables will be explained in detail in step 2.
  • the established finite element model needs to ensure that the tongue 2 and the tongue groove 1 are completely fitted at the contact surface, and preferably, the mesh nodes of the tongue 2 and the tongue groove 1 at the contact surface coincide with each other.
  • the purpose of this requirement is to facilitate the update of design variables, that is, to facilitate the change of the belonging state of the grid unit, and to ensure that the grid can maintain reasonable continuity after the belonging state changes.
  • Figure 3 shows the finite element model established in this embodiment.
  • the tongue and groove 1 and the left bearing structure 3 are a whole
  • the tenon 2 and the right bearing structure 4 are a whole
  • the two-part structure is connected with the tenon 2 through the tongue and groove 1 and supported by the support 5, and the structure bears the whole structure.
  • a downward uniformly distributed downforce load6 in this embodiment, in order to simplify the calculation, the cross section of each part in the system is extracted, and the finite element model is simplified to a plane strain problem.
  • Fig. 4 shows a partial situation of the design domain, the tongue groove 1 and the tongue 2 are attached at the contact surface and the nodes overlap with each other.
  • Step 2 Select the area where the tongue groove 1 and the tongue 2 are located as the design domain, and use the attribution status of the unit in the design domain as the design variable, that is, for each unit, there are two attribution statuses: it belongs to the groove 1 or belongs to the tongue 2. .
  • X ⁇ x 1 , x 2 , ..., x i , ..., x n ⁇ x i ⁇ ⁇ 1, 2 ⁇ , where: i is from 1-n, representing the i-th x out of 1-n x, The value range of each x is (1 or 2).
  • Step 3 Select the basic unit and determine the basic structure of the tenon and groove.
  • the basic unit refers to a unit that is not allowed to move during the optimization iteration process, that is, the attribution state of the basic unit is not allowed to change.
  • the basic unit stipulate that the basic form of the structure is a structure with two tongues and grooves on the left side and a structure with two tongues on the right.
  • the function of the basic unit is to prevent the structure from getting out of control in the optimization iteration, which can effectively ensure the stability and controllability of the optimization process, and optimize the structure in the specified direction.
  • the increase refers to artificially adding a large enough value to the strain energy of the basic unit so that the basic unit is judged as an efficient unit, so that no change in the attribution state occurs.
  • the specific content of the unit increase will be elaborated in step 6.
  • the cells in the black area shown in FIG. 5 are the basic cells in this embodiment.
  • the attribution status of these basic units does not change in the optimization iteration. Therefore, the tenon groove 1 can still maintain the structure of the two tenon grooves after optimization, and the tenon 2 can still maintain the structure of the two tenon grooves after optimization.
  • a specific basic unit can be selected according to actual needs to optimize the desired structure. The setting of the basic unit ensures the controllability and stability of the optimization algorithm.
  • Step 4 Run a finite element analysis to obtain the element strain energy ⁇ i , and calculate the total strain energy E of the structure, the total strain energy E 1 of the tongue groove 1 and the average strain energy e 1 , the total strain energy E 2 of the tongue 2 and the average Strain energy e 2 .
  • Each parameter is calculated according to the following formula. These parameters will be used in the filtering average of the unit in step 5 and the calculation of the neighborhood state in step 6.
  • Step 5 Filter and average the strain energy of the element calculated in Step 4, that is, use the average or weighted average value of the strain energy of all elements in the neighborhood of the central element whose attribution status is the same as that of the central element instead of the original strain energy value, which is still recorded as ⁇ i .
  • the neighborhood refers to the collection of all units within a certain distance R around the central unit, denoted as ⁇ i .
  • the meaning and operation method of the filtering averaging in this step are exactly the same as the unit filtering averaging technology in the conventional variable density topology optimization method (SIMP). Its function is to make the distribution of strain energy in the design domain more uniform and smooth, thereby making the boundary between the optimized tongue groove 1 and the tongue 2 relatively smooth and smooth, avoiding the appearance of small structural features such as serrations or holes, and making the optimization results have technological rationality And feasibility.
  • SIMP variable density topology optimization method
  • ⁇ i represents the strain energy of unit i after filtering and averaging
  • ⁇ j represents the strain energy of unit j in the neighborhood of unit i before filtering and averaging
  • m represents the number of units in the neighborhood of unit i that have the same attribute as i (including unit i), for example: for the unit i attributable to the tongue and groove 1, the unit included here only includes the unit attributable to 1, and the unit attributable to the tongue 2 is ignored.
  • Step 6 On the basis of the filtered and averaged strain energy of the unit obtained in step 5, an amplification coefficient scale is set, and the basic unit and the amplification unit are increased.
  • the basic unit is the basic unit selected in step 3.
  • the amplifying unit is a unit whose attribution state has changed in the previous iteration step, and the amplifying unit is not set in the first iteration. The increase is to artificially increase the value of the strain energy of the selected element by a value.
  • the purpose of increasing the basic unit is to ensure that the basic unit is judged to be an efficient unit so that the ownership status will not change, ensuring that the final tongue and groove 1 is the basic structure of double tongue and groove, and the tongue 2 is a double tongue.
  • the basic structure form improves the stability and controllability of the algorithm at the same time.
  • the amplitude of increase does not change with the increase of the number of iterations;
  • the purpose of amplifying the amplifying unit is to ensure that this part of the unit is judged as a relatively efficient unit in the next 3 iterations, so that the tiny structural features on the contact surface of the newly generated tongue groove 1 and tongue 2 will not
  • the rapid disappearance due to problems such as stress concentration is conducive to improving the overall optimization capability of the structure, thereby improving the force transmission path of the tenon-and-mortise connection structure.
  • the specific principle of amplifying the amplifying unit is shown in the following formula.
  • the value of the amplification factor scale is 1, and unit i is taken as an example:
  • unit i is not a basic unit, and assuming that the attribution status of unit i has changed in the it-1 iteration, then unit i will be selected as the amplification unit in the it iteration, and in the it iteration In it+3 iterations, the strain energy should be increased and corrected accordingly according to the above formula.
  • Step 7 Calculate the neighborhood state of each element in the design domain according to the increased strain energy of the element obtained in Step 6.
  • the information contained in the neighborhood state is: [N i1 , N i2 , n i1 , n i2 ].
  • N i1 is the sum of the strain energy of the units in the neighborhood of unit i that belong to the state of 1 (that is, the units that belong to the tongue and groove 1); Ni2 is the unit that belongs to the state of 2 in the neighborhood of unit i (that is, the units that belong to the tenon 2 ); n i1 is the average value of the strain energy of the unit in the neighborhood of unit i (that is, the unit belonging to the tongue and groove 1) of the unit i; n i2 is the unit in the neighborhood of unit i (that is The average value of the strain energy of the element belonging to the tenon 2).
  • Each parameter is calculated by the following formula.
  • the calculated neighborhood state [N i1 , N i2 , n i1 , n i2 ] will be used in step 8 for local control and design variable update.
  • n i1 N i1 /n 1 (n 1 is the number of units belonging to component 1 in the neighborhood of unit i)
  • n i2 N i2 /n 2 (n 2 is the number of units belonging to component 2 in the neighborhood of unit i)
  • Step 8 Set local control parameters, construct local control rules, and update unit attribution status, that is, update design variables.
  • the local control parameters include: a conventional movement coefficient m 1 , an amplifying movement coefficient m 2 , and a strain energy proportional control coefficient rt.
  • the local control rules are a set of criteria for judging whether the attribution status of each unit changes in this iterative step.
  • the attribution status x i of the unit i is changed from 1 to 2, and the unit near this unit is updated accordingly.
  • Grid continuity and contact conditions For example, for a certain unit i belonging to the tongue and groove 1, if it is determined according to the local control rules that the attribution status of the unit needs to be changed, the attribution status x i of the unit i is changed from 1 to 2, and the unit near this unit is updated accordingly. Grid continuity and contact conditions.
  • the basic principle of the local control rule of the present invention is to refer to the strain energy of all elements in the neighborhood ⁇ i of a certain element, the ratio of the average strain energy of the tongue 1 and the tongue 2 to seek a way to make the entire design domain
  • the design scheme with relatively uniform strain energy distribution improves the contact conditions and reduces the stress concentration, so that the material at each position can exert a relatively large load-bearing effect, and the connection performance of the tenon-and-mortise structure is improved.
  • the judgment standard and process of the local control rule are shown in Figure 2. The specific steps and principles are as follows:
  • Step 8.1 judge whether all the units in the tongue groove 1 and the tongue 2 have been processed. If it has been processed, exit the local control and end the update of the design variables; if it has not been processed, determine the ownership of the currently controlled unit i Status, if it is 1, then go to step 8.2, if it is 2, then the control rules will be set up similar to the following steps 8.2-8.6;
  • Step 8.2 judge whether there is a unit belonging to the tenon 2 in the neighborhood of unit i, if it does not exist, exit the control rule, go to step 8.1 to start the control of the next unit; if it exists, go to step 8.3;
  • Step 8.3 judge whether the unit strain energy ⁇ i , the average strain energy e 1 of the tenon groove 1, the average strain energy e 2 of the tenon 2 and the strain energy proportional control coefficient rt meet the following formula:
  • step 8.4 If it is not met, exit the control rule and go to step 8.1 to start the control of the next unit; if it is met, go to step 8.4;
  • Step 8.4 judge whether the sum of strain energy N i1 of the element belonging to the tongue groove 1 and the sum of strain energy N i2 of the element belonging to the tenon 2 in the neighborhood of the element i satisfy the following formula:
  • step 8.1 If it is not met, exit the control rules and go to step 8.1 to start the control of the next unit; if not, go to step 8.5;
  • Step 8.5 judge whether the average strain energy n i2 of the elements belonging to the tenon 2 in the neighborhood of the element i, the average strain energy e 2 of the tenon 2 and the regular movement coefficient m 1 meet the following conditions:
  • step 3 If it is satisfied, call the unit moving method described in step 3 to move the unit i from the tongue groove 1 to the tongue 2; if it is not satisfied, go to step 8.6;
  • Step 8.6 judge whether the average strain energy n i2 of the element belonging to the tongue groove 1 in the neighborhood of the element i, the average strain energy e 2 of the tongue 2 and the increasing movement coefficient m 2 meet the following conditions:
  • step 8.1 change the attribution status of unit i from 1 to 2, that is: move unit i from tongue 1 to tongue 2, update the mesh continuity and contact conditions after the movement of the unit, and specify that unit i is an amplifying unit , According to the method described in step 6 in the subsequent three iterations to increase and modify; if not satisfied, then exit the control rules, go to step 8.1 to start the control of the next unit;
  • Step 9 take the total strain energy E of the tongue groove 1 and the tongue 2 as the objective function to judge the convergence, and set the convergence tolerance ⁇ .
  • the definition of the convergence criterion is: convergence when the average change of the total strain energy E in 2 consecutive iterations is less than or equal to ⁇ . If the objective function does not converge in the current iteration step, go to step 4 and start the next iteration process; if the objective function converges in the current iteration step, exit the optimization process and save the current mesh model as the optimized result.
  • the objective function expression is as follows:
  • O is the objective function.
  • the objective function value is less than or equal to the convergence tolerance ⁇ , the objective function is judged to be convergent and the optimization is completed; it is the current iteration step, in which no convergence judgment is made in the first two iterations ; E it is the sum of the strain energy of the tenon groove 1 and the tenon 2 after the it iteration.
  • the it iteration is the current iteration step; E it-1 and E it-2 are respectively the it- The sum of the strain energy of the tenon groove 1 and the tenon 2 after the iterations 1 and it-2.
  • the iterations it-1 and it-2 are the two iteration steps before the current iteration step respectively; E 1 is the sum of the strain energy of the tongue groove 1 and the tongue 2 when not optimized, that is, the strain energy of the initial structure.
  • Step 10 Analysis and evaluation of optimization results. Assess the maximum stress value, maximum strain value and total strain energy value of the tongue and groove 1 and the tongue 2, and the displacement of key points of the structure (ie: stiffness performance).
  • Figure 8 shows the variation curve of the total strain energy E of the tongue groove 1 and the tongue 2;
  • Figure 9 shows the change curve of the maximum stress value of the tongue groove 1 and the tongue 2;
  • Figure 10 shows the change curve of the maximum strain value of the tongue groove 1 and the tongue 2;
  • FIG. 11 shows the change curve of the maximum displacement value of the key point (in this embodiment, the stress point).
  • the optimization results show that after optimization, the total strain energy, maximum stress, maximum strain, and key point displacement (in this example, the displacement of the stress point) of the structure are reduced to varying degrees, the connection stiffness is higher, and the structure performance is better. , Achieved the purpose of structural optimization, and proved the feasibility and effectiveness of this method.

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Abstract

一种用于榫卯连接结构设计的归选式拓扑优化方法，其具体包括以下步骤：步骤1、建立待优化结构的有限元模；步骤2、选取榫槽（1）、榫头（2）所在区域作为设计域；步骤3、选定基础单元，确定榫头（2）和榫槽（1）的基本结构形式；步骤4、运行一次有限元分析；步骤5，对步骤4计算得到的单元应变能进行过滤平均；步骤6、基础单元和增幅单元进行增幅；步骤7、计算设计域内每个单元的邻域状态；步骤8、设定局部控制参数，构造局部控制规则；步骤9、进行收敛判断；步骤10，优化结果分析和评价。本方法通过改变榫卯连接结构中相互配合连接的部位的基本形状形式，能够在较大的范围内进行寻优，进而优化榫卯连接结构的传力路径。

Description

一种用于榫卯连接结构设计的归选式拓扑优化方法
相关申请
本申请主张于2019年11月5日提交的、名称为“一种用于榫卯连接结构设计的归选式拓扑优化方法”的中国发明专利申请：2019110698455的优先权。
技术领域
本发明涉及一种拓扑优化方法，特别涉及一种用于组合装配式零件、对接式零件、榫卯结构或其他依赖于结构自身形状进行相互支撑、定位和传力的结构的优化设计方法。
背景技术
随着工程技术的发展，得益于加工精度的提高和装配技术的升级，组合式、对接式零件等由于其装配效率高、连接性能稳定等优点，已被越来越多地用于机械零件的连接部位设计中，例如榫卯结构已不局限于传统木质结构方面的应用，而是在机械结构设计制造等更广泛的领域被采用。在这一背景下，对这种快速连接结构的优化就具有了重要的实际意义。
目前对于连接部位的优化，一般采用形状优化的方法。这一方法需要预设形状变量，且形状变化的方向和范围有限，使优化进程过多地取决于初始结构的拓扑和形状，无法给出具有启发性的新的结构形式。因而这一方法只能用于改善应力集中、优化接触条件等用途，而无法改变结构的传力路径。
拓扑优化技术虽然能够给出具备启发意义的新的结构形式，然而常规的拓扑优化技术，不论变密度法、渐进结构优化法、元胞自动机法或水平集方法，都只能应用于单一柔性体的优化，其特征在于优化迭代中结构的边界条件不变或仅有微小而规律的变化，因而无法应用于榫接结构等优化问题中边界条件发生剧烈变化的情况。
针对以上情况，开发的新的优化方法需要解决以下技术难题：(1)不同于形状优化，新的优化方法需要提高全局寻优能力，给出具有启发意义的新的结构形式；(2)这一优化方法应区别于常规的拓扑优化方法，要能够处理两个相互配合的结构的优化，即接触条件、边界条件具有剧烈且不可预知地变化的情况，常规的边界条件可变 拓扑优化技术难以处理这类问题；(3)在优化迭代中，两个零件各自的连接部位的拓扑和形状要能够进行关联、协同地变化，以保证两个零件的合理配合。
发明内容
本发明提供的目的是开发一套新型拓扑优化方法，采用网格单元的归属状态，即单元所属部件的编号作为设计变量，并按照某种控制规则进行状态选取而达到优化设计的目的。本方法可用于组合装配式零件、对接式零件、榫卯结构的连接部位或具有榫卯特征的连接结构的优化设计。这一方法具备一定全局寻优能力，能够处理接触条件、边界条件具有剧烈且不可预知地变化的情况。
本发明的技术方案是：
一种用于榫卯连接结构设计的归选式拓扑优化方法，其具体包括以下步骤：
步骤1、建立待优化结构的有限元模型，模型包含：榫槽、榫头、左侧承载结构、右侧承载结构、支座、下压力载荷及对支座的约束，其中榫槽和榫头的单元为优化问题的设计域；
步骤2、选取榫槽、榫头所在区域作为设计域，并将设计域内单元的归属状态作为设计变量，即对于每个单元，存在两种归属状态：属于榫槽，或是属于榫头；
步骤3、选定基础单元，确定榫头和榫槽的基本结构形式；所述基础单元是指在优化迭代过程中不允许发生移动的单元，即：基础单元的归属状态不允许发生变化；
步骤4、运行一次有限元分析，获得单元应变能ξ i，并计算结构总应变能E，榫槽的总应变能E 1及平均应变能e 1，榫头的总应变能E 2及平均应变能e 2；
步骤5，对步骤4计算得到的单元应变能进行过滤平均，即：采用中心单元邻域内归属状态与中心单元相同的所有单元的应变能平均值或加权平均值代替原应变能数值，仍记为ξ i；其中，邻域是指中心单元周围一定距离R以内的所有单元的集合，记为Ω i；
步骤6、在步骤5得到的过滤平均后的单元应变能的基础上，设定增幅系数scale，并对基础单元和增幅单元进行增幅；
步骤7、根据步骤6得到的增幅后的单元应变能，计算设计域内每个单元的邻域状态；
步骤8、设定局部控制参数，构造局部控制规则，进行单元归属状态的更新，即： 进行设计变量更新；
步骤9，以榫槽和榫头的总应变能E为目标函数进行收敛判断，设定收敛容差ε；收敛准则的定义为：连续2次迭代中总应变能E的平均值变化量小于或等于ε时收敛；若在当前迭代步下目标函数未收敛，则转至步骤4，开始下一次迭代进程；若当前迭代步下目标函数收敛，则退出优化进程，保存当前网格模型，作为优化后的结果；
步骤10，优化结果分析和评价，考核榫槽和榫头的最大应力值、最大应变值和总应变能数值、结构关键点位移。
进一步地，在步骤1中，建立的有限元模型保证榫头(2)和榫槽(1)在接触面处完全贴合，且榫头和榫槽在接触面处的网格节点相互重合。
进一步地，步骤4中，通过以下公式进行计算：
Figure PCTCN2019126355-appb-000001
e 1＝E 1/N 1 N 1为榫槽1的单元数；
Figure PCTCN2019126355-appb-000002
e 2＝E 2/N 2 N 2为榫头2的单元数。
E＝E 1+E 2
进一步地，步骤7中，对于单元i，邻域状态包含的信息有：[N i1，N i2，n i1，n i2]，其中，N i1为单元i邻域内归属状态为1的单元，即属于榫槽(1)的单元的应变能之和；N i2为单元i邻域内归属状态为2的单元，即属于榫头(2)的单元的应变能之和；n i1为单元i邻域内归属状态为1的单元，即属于榫槽(1)的单元的应变能平均值；n i2为单元i邻域内归属状态为2的单元，即属于榫头(2)的单元的应变能平均值；其中：
Figure PCTCN2019126355-appb-000003
n i1＝N i1/n 1 n 1为单元i邻域内属于榫槽1的单元数；
Figure PCTCN2019126355-appb-000004
n i2＝N i2/n 2 n 2为单元i邻域内属于榫头2的单元数。
进一步地，步骤8中，局部控制参数包含：常规移动系数m1，增幅移动系数m2，应变能比例控制系数rt；所述局部控制规则即为一套判断每个单元的归属状态是否在这一迭代步中发生变化的准则。
进一步地，步骤9中，目标函数表达式如下所示：
Figure PCTCN2019126355-appb-000005
式中，O为目标函数，当目标函数值小于或等于收敛容差ε时，目标函数被判定为收敛，优化完成；it为当前迭代步，其中，在前两次迭代中不进行收敛性判断；E it为第it次迭代后榫槽(1)和榫头(2)的应变能之和；E it-1和E it-2分别为第it-1与it-2次迭代后榫槽(1)和榫头(2)的应变能之和；E 1为未优化时榫槽(1)与榫头(2)的应变能之和，即：初始结构的应变能。
本发明的有益效果在于：
1、本发明方法通过改变榫卯连接结构中相互配合连接的部位的基本形状形式，能够在较大的范围内进行寻优，进而优化榫卯连接结构的传力路径，并在步骤8中参考每个单元邻域内所有单元的应变能信息，寻求一种应变能分布比较均匀的结构形式，从而改善了接触条件和应力集中问题。本发明所提供的实施例的优化结果同样证明了这一方法的可行性和有效性。
2、本发明方法能够对组合装配式零件、对接式零件、榫卯结构或其他依赖于结构自身形状进行相互支撑、定位和传力的结构进行优化，如凸块式联轴器、零件对接头、销与销孔、滑轨、卡扣等。这是由于此类结构都具有榫卯连接结构的特征和性质，如：都是依靠两个结构形状的相互配合来进行定位、支撑和传力，因此本方法同样适用于此类零件的优化设计。
3、相比于形状优化技术，本发明方法不需要预设形状变量，简化了建模工作，同时降低了对使用人员的工程经验的依赖；
4、相比于形状优化技术，本发明方法不存在形状变量的上下限限制，并在步骤6中引入单元增幅及增幅幅度衰减规则，提高了全局寻优能力。因此本方法能够使优化问题不局限于改善接触条件和应力集中等方面，并且改善了结构整体的传力路径，能够得到更加具备启发意义的结构形式；
5、相比于形状优化技术，由于步骤2所指定的设计变量是单元归属状态，不涉及节点的移动和单元的变形，因此本发明方法不会在迭代过程中发生网格的变形，不存在网格变形过大导致的单元质量不合格和计算精度不足的问题；
6、由于本发明方法在步骤2中所指定的设计域不再是单一的联通体，而是两个或多个相互关联的子域，因此，本发明方法将拓扑优化技术扩展到多个柔性体关联优 化的层面，使拓扑优化技术不仅仅局限于单一柔性体的拓扑优化；
7、采用单元的所述部件编号作为设计变量，解决了柔性体间榫接结构优化时，榫头和榫槽的形状需要关联变化的问题；
8、相比于目前应用范围最广的变密度法，本发明方法不采用灰色单元，即不采用中间密度这一概念，因而每一迭代步后得到的结构和结构性能具有准确的物理和现实意义；
9、所述以单元归属状态构成的设计变量、基础单元、增幅及增幅幅度衰减规则、局部控制规则等概念或具体方法由本发明首次提出、阐述并实现。
附图说明
图1是本发明的优化流程整体架构框图；
图2是局部控制规则流程框图；
图3是待优化结构的有限元模型示意图；
图4是待优化部位(设计区域)示意图；
图5是实施例中基本单元分布图；
图6是优化后榫接结构示意图；
图7是历次迭代中结构变化情况图；
图8是历次迭代中总应变能、部件1总应变能、部件2总应变能变化曲线；
图9是历次迭代中部件1和部件2最大应力变化曲线；
图10是历次迭代中部件1和部件2最大应变变化曲线；
图11是历次迭代中关键点位移变化曲线；
其中：1-榫槽，2-榫头，3-左侧承载结构，4-右侧承载结构，5-支座，6-下压力载荷，7-为约束符号，表示支座5是受约束的。
具体实施方式
以下结合附图1-11对本发明涉及的技术方案进行详细说明。
如图1所示，该实施例提供了一种用于榫卯连接结构设计的归选式拓扑优化方法，其具体包括以下步骤：
步骤1、建立待优化结构的有限元模型，如图3所示，该模型包含：榫槽1、榫头2、左侧承载结构3、右侧承载结构4、支座5、下压力载荷6及对支座的约束7，其中榫槽1和榫头2的单元为优化问题的设计域。设计域的选取和设计变量的定义将在步骤2中详细说明。
建立的有限元模型需要保证榫头2和榫槽1在接触面处完全贴合，且优选地，榫头2和榫槽1在接触面处的网格节点相互重合。这一要求的目的是便于设计变量的更新，即：便于网格单元归属状态的变动，并保证归属状态变化后网格仍能保持合理的连贯性。
图3所示为本实施例中所建立的有限元模型。其中，榫槽1与左侧承载结构3为一个整体，榫头2与右侧承载结构4为一个整体，两部分结构通过榫槽1与榫头2连接，并由支座5进行支撑，结构整体承受一个向下的均布的下压力载荷6。在本实施例中为简化计算，提取系统内各零件的横截面，将有限元模型简化为平面应变问题。
图4所示为设计域的局部情况，榫槽1与榫头2在接触面处贴合且节点相互重合。
步骤2、选取榫槽1、榫头2所在区域作为设计域，并将设计域内单元的归属状态作为设计变量，即对于每个单元，存在两种归属状态：属于榫槽1，或是属于榫头2。
设计变量的形式如下，当x i＝1时，表示单元i属于榫槽1；当x i＝2时表示单元i属于榫头2，i表示单元编号，1≤i≤n：
X＝{x 1，x 2，…，x i，…，x n}x i∈{1，2}，其中：i是从1-n，表示1-n个x中的第i个x，每个x的取值范围都是(1或2)。
步骤3、选定基础单元，确定榫头和榫槽的基本结构形式。
所述基础单元是指在优化迭代过程中不允许发生移动的单元，即：基础单元的归属状态不允许发生变化。
这些基础单元规定了结构的基本形式是左侧为两个榫槽的结构形式，右侧为两个榫头的结构形式。基础单元的作用是使结构在优化迭代中不会发生失控的情况，可以有效保证优化进程的稳定性和可控性，使结构在规定的方向进行优化。
为了使基础单元的归属状态在优化迭代中不发生变化，需要给基础单元进行增幅。所述增幅是指人为地给基础单元的应变能增加一个足够大的值，使基础单元被判定为高效的单元，从而不发生归属状态的变化。单元增幅的具体内容将在步骤6进行 详细阐述。
图5所示黑色区域内的单元为本实施例中的基础单元。这些基础单元的归属状态在优化迭代中不发生变化，因此，榫槽1在优化后仍能保持两个榫槽的结构形式，榫头2在优化后仍能保持两个榫头的结构形式。此外，可以根据实际需要选定特定的基础单元来优化得到期望的结构形式，基础单元的设定保证了优化算法的可控和稳定。
步骤4、运行一次有限元分析，获得单元应变能ξ i，并计算结构总应变能E，榫槽1的总应变能E 1及平均应变能e 1，榫头2的总应变能E 2及平均应变能e 2。
各项参数按照以下公式进行计算。这些参数将用于步骤5中的单元的过滤平均以及步骤6中的邻域状态的计算。
Figure PCTCN2019126355-appb-000006
e 1＝E 1/N 1 (N 1为部件1的单元数)
Figure PCTCN2019126355-appb-000007
e 2＝E 2/N 2 (N 2为部件2的单元数)
E＝E 1+E 2
步骤5，对步骤4计算得到的单元应变能进行过滤平均，即：采用中心单元邻域内归属状态与中心单元相同的所有单元的应变能平均值或加权平均值代替原应变能数值，仍记为ξ i。其中，邻域是指中心单元周围一定距离R以内的所有单元的集合，记为Ω i。
本步骤所述过滤平均的含义和操作方法与常规的变密度拓扑优化方法(SIMP)中的单元过滤平均技术完全相同。其作用是使设计域内应变能的分布更加均匀平滑，进而使优化后的榫槽1和榫头2的边界相对平顺光滑，避免出现锯齿或孔洞等微小结构特征，使优化结果具有工艺上的合理性和可行性。
在本实施例中，选取邻域半径R＝0.35mm，单元距离用单元形心之间的距离表示。则邻域可以表示为：与某一单元形心距离小于或等于0.35mm的所有单元的集合。对于单元i，过滤平均的计算过程如下式所示。
Figure PCTCN2019126355-appb-000008
式中，ξ i表示过滤平均后单元i的应变能；ξ j表示过滤平均前单元i邻域内的单元j的应变能；m表示单元i邻域内归属状态与i相同的单元个数(包含单元i)，例如：对于归属于榫槽1的单元i，此处计入的单元只包扩归属于1的单元，忽略掉 归属于榫头2的单元。
步骤6、在步骤5得到的过滤平均后的单元应变能的基础上，设定增幅系数scale，并对基础单元和增幅单元进行增幅。所述基础单元即为步骤3中选取的基础单元。所述增幅单元为上一迭代步中归属状态发生变化的单元，在初次迭代中不设置增幅单元。所述增幅就是给选定单元的应变能的数值人为地增加一个值。
本步骤中进行单元增幅的目的体现在两个方面：
(1)对基础单元增幅的目的在于保证基础单元被判定为高效的单元从而不会发生归属状态的改变，确保了最终榫槽1是双榫槽的基本结构形式，而榫头2是双榫头的基本结构形式，同时改善了算法的稳定性和可控性。增幅幅度不随迭代次数的增加而变化；
(2)对增幅单元进行增幅的目的在于确保这一部分单元在接下来的3次迭代中被判定为相对高效的单元，使新生成的榫槽1和榫头2接触面上的微小结构特征不会因为应力集中等问题而快速消失，有利于提升结构的全局寻优能力，进而改善榫卯连接结构的传力路径。对增幅单元进行增幅的具体原理如下式所示。
Figure PCTCN2019126355-appb-000009
Figure PCTCN2019126355-appb-000010
Figure PCTCN2019126355-appb-000011
Figure PCTCN2019126355-appb-000012
在本实施例中，增幅系数scale取值为1，并以单元i为例：
(1)若单元i为基础单元，则应在过滤平均后的单元i的应变能基础上，额外加上1倍的单元i邻域内平均应变能的数值，并在此后所有迭代中这一增幅操作永久生效；
(2)若单元i不是基础单元，并假设在第it-1次迭代中单元i的归属状态发生了变化，则第it次迭代中单元i就被选定为增幅单元，且在第it次迭代至it+3次迭代中，其应变能应按照上式进行相应的增幅和修正。
步骤7、根据步骤6得到的增幅后的单元应变能，计算设计域内每个单元的邻域状态。对于单元i，邻域状态包含的信息有：[N i1，N i2，n i1，n i2]。其中，N i1为单元i邻域内归属状态为1的单元(即属于榫槽1的单元)的应变能之和；N i2为单元i邻域内归属状态为2的单元(即属于榫头2的单元)的应变能之和；n i1为单元i邻域 内归属状态为1的单元(即属于榫槽1的单元)的应变能平均值；n i2为单元i邻域内归属状态为2的单元(即属于榫头2的单元)的应变能平均值。各参数通过下式进行计算。计算得到的邻域状态[N i1，N i2，n i1，n i2]将用于步骤8中的局部控制和设计变量更新。
Figure PCTCN2019126355-appb-000013
n i1＝N i1/n 1 (n 1为单元i邻域内属于部件1的单元数)
Figure PCTCN2019126355-appb-000014
n i2＝N i2/n 2 (n 2为单元i邻域内属于部件2的单元数)
步骤8、设定局部控制参数，构造局部控制规则，进行单元归属状态的更新，即：进行设计变量更新。所述局部控制参数包含：常规移动系数m 1，增幅移动系数m 2，应变能比例控制系数rt。所述局部控制规则即一套判断每个单元的归属状态是否在这一迭代步中发生变化的准则。
例如对于属于榫槽1的某单元i，若根据局部控制规则判定该单元的归属状态需要发生变化，则将单元i的归属状态x i从1变更为2，并相应地更新这一单元附近的网格连贯性和接触条件。
本发明所述局部控制规则的基本原理是参考某个单元邻域Ω i内所有单元的应变能大小、榫槽1和榫头2的平均应变能大小之比等信息，寻求一种使整个设计域内应变能分布相对均匀的设计方案，从而改善了接触条件、减少了应力集中，使每个位置的材料都能发挥相对较大的承载作用，提高榫卯结构的连接性能。所述局部控制规则的判定标准及流程如图2所示，具体步骤及原理如下：
步骤8.1，判断是否已处理完榫槽1和榫头2内的所有单元，若已处理完，则退出局部控制，结束设计变量的更新；若未处理完，则判断当前进行控制的单元i的所属状态，若为1则进入步骤8.2，若为2，则控制规则按照类似于下述步骤8.2-8.6进行搭建；
步骤8.2，判断单元i邻域内是否存在属于榫头2的单元，若不存在，则退出控制规则，转入步骤8.1开始下一个单元的控制；若存在，则进入步骤8.3；
步骤8.3，判断单元应变能ξ i、榫槽1的平均应变能e 1，榫头2的平均应变能e 2及应变能比例控制系数rt是否满足下式：
ξi<e1<rt*e2
若不满足，则退出控制规则，转入步骤8.1开始下一个单元的控制；若满足，则进入步骤8.4；
步骤8.4，判断单元i的邻域内，属于榫槽1的单元的应变能之和N i1与属于榫头2的单元的应变能之和N i2是否满足下式：
N i1<N i2
若不满足，则退出控制规则，转入步骤8.1开始下一个单元的控制；若不满足，则进入步骤8.5；
步骤8.5，判断单元i的邻域内，属于榫头2的单元的应变能平均值n i2、榫头2的平均应变能e 2和常规移动系数m 1是否满足下述条件：
n i2>m 1*e 2
若满足，则调用步骤3所述的单元移动方法，将单元i从榫槽1移动到榫头2；若不满足，则进入步骤8.6；
步骤8.6，判断单元i的邻域内，属于榫槽1的单元的应变能平均值n i2、榫头2的平均应变能e 2和增幅移动系数m 2是否满足下述条件：
n i2<m 2*e 2
若满足，则将单元i的归属状态从1改变为2，即：将单元i从榫槽1移动到榫头2，更新单元移动后的网格连贯性和接触条件，并规定单元i为增幅单元，按照步骤6所述方法在后续的三次迭代中进行增幅和修正；若不满足，则退出控制规则，转入步骤8.1开始下一个单元的控制；
在本实施例中，局部控制参数取值分别为：常规移动系数m 1＝1.05，增幅移动系数m 2＝0.95，应变能比例控制系数rt＝1.1。按照上述流程对榫槽1和榫头2的每个单元的归属状态进行更新，并更新单元移动后的网格连贯性和接触条件，完成本次优化迭代。
步骤9，以榫槽1和榫头2的总应变能E为目标函数进行收敛判断，设定收敛容差ε。
收敛准则的定义为：连续2次迭代中总应变能E的平均值变化量小于或等于ε时收敛。若在当前迭代步下目标函数未收敛，则转至步骤4，开始下一次迭代进程；若当前迭代步下目标函数收敛，则退出优化进程，保存当前网格模型，作为优化后的结果。目标函数表达式如下所示：
Figure PCTCN2019126355-appb-000015
式中，O为目标函数，当目标函数值小于或等于收敛容差ε时，目标函数被判定为收敛，优化完成；it为当前迭代步，其中，在前两次迭代中不进行收敛性判断；E it为第it次迭代后榫槽1和榫头2的应变能之和，在本实施例中，第it次迭代就是当前迭代步；E it-1和E it-2分别为第it-1与it-2次迭代后榫槽1和榫头2的应变能之和，在本实施例中，第it-1与it-2次迭代就分别是当前迭代步之前的两个迭代步；E 1为未优化时榫槽1与榫头2的应变能之和，即：初始结构的应变能。
在本实施例中，当迭代步it＝8时，Ob＝0.0083，满足收敛条件，优化进程结束。优化后的结构形状如图6所示。历次迭代后结构的形状如图7所示。总应变能E的变化曲线如图8所示，为了更详细地描述本优化方法的效果，这里给出了前10次迭代的应变能变化曲线。可以观察到，总应变能最终将收敛于7.0×10 -4N·mm附近，在第8迭代步已充分接近并稳定于这一收敛值附近。
步骤10，优化结果分析和评价。考核榫槽1和榫头2的最大应力值、最大应变值和总应变能数值、结构关键点位移(即：刚度性能)等。
在本实施例中，迭代过程中主要性能变化情况：
图8所示为榫槽1和榫头2的总应变能E的变化曲线；
图9所示为榫槽1和榫头2的最大应力值的变化曲线；
图10所示为榫槽1和榫头2的最大应变值的变化曲线；
图11所示为关键点(在本实施例中为受力点)的最大位移值的变化曲线。
优化结果显示：优化后，结构总应变能，最大应力，最大应变，关键点位移(在本实施例中即受力点的位移)均有不同程度的减少，连接刚度更高，结构性能更优，达到了结构优化的目的，证明了本方法的可行性和有效性。

Claims (6)

  1. 一种用于榫卯连接结构设计的归选式拓扑优化方法，其具体包括以下步骤：
    步骤1、建立待优化结构的有限元模型，模型包含：榫槽(1)、榫头(2)、左侧承载结构(3)、右侧承载结构(4)、支座(5)、下压力载荷(6)及对支座的约束(7)，其中榫槽(1)和榫头(2)的单元为优化问题的设计域；
    步骤2、选取榫槽(1)、榫头(2)所在区域作为设计域，并将设计域内单元的归属状态作为设计变量，即对于每个单元，存在两种归属状态：属于榫槽(1)，或是属于榫头(2)；
    步骤3、选定基础单元，确定榫头(2)和榫槽(1)的基本结构形式；所述基础单元是指在优化迭代过程中不允许发生移动的单元，即：基础单元的归属状态不允许发生变化；
    步骤4、运行一次有限元分析，获得单元应变能ξ i，并计算结构总应变能E，榫槽(1)的总应变能E 1及平均应变能e 1，榫头(2)的总应变能E 2及平均应变能e 2；
    步骤5，对步骤4计算得到的单元应变能进行过滤平均，即：采用中心单元邻域内归属状态与中心单元相同的所有单元的应变能平均值或加权平均值代替原应变能数值，仍记为ξ i；其中，邻域是指中心单元周围一定距离R以内的所有单元的集合，记为Ω i；
    步骤6、在步骤5得到的过滤平均后的单元应变能的基础上，设定增幅系数scale，并对基础单元和增幅单元进行增幅；
    步骤7、根据步骤6得到的增幅后的单元应变能，计算设计域内每个单元的邻域状态；
    步骤8、设定局部控制参数，构造局部控制规则，进行单元归属状态的更新，即：进行设计变量更新；
    步骤9，以榫槽(1)和榫头(2)的总应变能E为目标函数进行收敛判断，设定收敛容差ε；收敛准则的定义为：连续2次迭代中总应变能E的平均值变化量小于或等于ε时收敛；若在当前迭代步下目标函数未收敛，则转至步骤4，开始下一次迭代进程；若当前迭代步下目标函数收敛，则退出优化进程，保存当前网格模型，作为优 化后的结果；
    步骤10，优化结果分析和评价，考核榫槽(1)和榫头(2)的最大应力值、最大应变值和总应变能数值、结构关键点位移。
  2. 根据权利要求1所述的用于榫卯连接结构设计的归选式拓扑优化方法，其特征在于：在步骤1中，建立的有限元模型保证榫头(2)和榫槽(1)在接触面处完全贴合，且榫头(2)和榫槽(1)在接触面处的网格节点相互重合。
  3. 根据权利要求1所述的用于榫卯连接结构设计的归选式拓扑优化方法，其特征在于：步骤4中，通过以下公式进行计算：
    Figure PCTCN2019126355-appb-100001
    e 1＝E 1/N 1    N 1为榫槽1的单元数；
    Figure PCTCN2019126355-appb-100002
    e 2＝E 2/N 2    N 2为榫头2的单元数。
    E＝E 1+E 2
  4. 根据权利要求1所述的用于榫卯连接结构设计的归选式拓扑优化方法，其特征在于：步骤7中，对于单元i，邻域状态包含的信息有：[N i1，N i2，n i1，n i2]，其中，N i1为单元i邻域内归属状态为1的单元，即属于榫槽(1)的单元的应变能之和；N i2为单元i邻域内归属状态为2的单元，即属于榫头(2)的单元的应变能之和；n i1为单元i邻域内归属状态为1的单元，即属于榫槽(1)的单元的应变能平均值；n i2为单元i邻域内归属状态为2的单元，即属于榫头(2)的单元的应变能平均值；其中：
    Figure PCTCN2019126355-appb-100003
    n i1＝N i1/n 1    n 1为单元i邻域内属于榫槽1的单元数；
    Figure PCTCN2019126355-appb-100004
    n i2＝N i2/n 2    n 2为单元i邻域内属于榫头2的单元数。
  5. 根据权利要求1所述的用于榫卯连接结构设计的归选式拓扑优化方法，其特征在于：步骤8中，局部控制参数包含：常规移动系数m1，增幅移动系数m2，应变能比例控制系数rt；所述局部控制规则即为一套判断每个单元的归属状态是否在这一迭代步中发生变化的准则。
  6. 根据权利要求1所述的一种用于榫卯连接结构设计的归选式拓扑优化方法，其特征在于：步骤9中，目标函数表达式如下所示：
    Figure PCTCN2019126355-appb-100005
    式中，O为目标函数，当目标函数值小于或等于收敛容差ε时，目标函数被判定为收敛，优化完成；it为当前迭代步，其中，在前两次迭代中不进行收敛性判断；E it为第it次迭代后榫槽(1)和榫头(2)的应变能之和；E it-1和E it-2分别为第it-1与it-2次迭代后榫槽(1)和榫头(2)的应变能之和；E 1为未优化时榫槽(1)与榫头(2)的应变能之和，即：初始结构的应变能。
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