CN-116070492-B - Discrete truss structure layout optimization design and manufacturing method based on repetitive units

CN116070492BCN 116070492 BCN116070492 BCN 116070492BCN-116070492-B

Abstract

The invention relates to a discrete truss structure layout optimization design and manufacturing method based on a repetitive unit, which comprises the following steps: and establishing a truss layout optimization mathematical model, namely firstly determining two-step solution of a unit layout based on direct solution of a repetitive unit, and performing 3D printing manufacturing and integrated assembly. The method has the advantages that extra constraint and variable aiming at the characteristics of the repetitive units are introduced, a direct solving method based on the repetitive units is provided, so that truss layout optimization results have the characteristics of the repetitive units, the direct solving method based on the repetitive units can be independently and directly used, a mathematical model can be provided for two-step solving of the unit layout, and when the problem of large scale is solved, two-step solving of the unit mode layout and the internal structure of the unit mode is provided, the stress path of the structure is clearer, and the calculation efficiency is remarkably improved under the condition that the influence on the final optimized structure volume is small.

Inventors

WANG ZHEN
YE JUN
ZHAO YANG
LIU YUFENG
LU HONGJIA
QUAN GUAN
TANG HUIPING

Assignees

浙大城市学院
浙江大学

Dates

Publication Date: 20260505
Application Date: 20230213

Claims (7)

1. The structural layout optimization design and manufacturing method based on the repetitive units is characterized by comprising the following steps of: S1, establishing a truss layout optimization mathematical model, namely, firstly giving a structural design domain, inputting size, load working condition and boundary constraint, and designating a unit mode and complexity of a corresponding unit mode; S2, directly solving based on a repetitive unit, namely setting a limited number of unit modes, carrying out unit division to ensure that all rod pieces belong to a certain unit mode and rod pieces in a cross-unit mode do not exist, wherein the unit layout of the same unit mode and the area of the rod pieces in the corresponding position are completely the same; S3, firstly determining two-step solution of unit layout, namely firstly reducing the complexity of each unit mode, carrying out first solution according to the step S2 to obtain a unit mode variable t c which is activated correspondingly to each unit mode, and then substituting t c into a repetitive unit nonlinear constraint expression of each rod piece in the step S2 according to the normal complexity of each unit mode to convert into linear constraint, and carrying out second solution to obtain an optimized result; S4, 3D printing manufacturing and integrated assembly, namely 3D modeling is carried out, various repetitive units in the optimized result model are respectively sliced, a printing path is generated, 3D printing manufacturing is carried out, and the optimized structure is manufactured through integrated assembly among the repetitive units.
2. The method for optimizing design and manufacture of a structural layout based on a repeating unit according to claim 1, wherein in step S1, the objective function corresponding to the design objective with the minimum total volume of the bars is, The expression of the constraint is that, Wherein l is a length vector of the rod, a is an area vector of the rod, B is a balance matrix, q is an internal force vector of the rod, f is a node load vector, and sigma c and sigma t are respectively compression strength and tensile strength vectors of the rod; The three constraint conditions in the formula (2) respectively represent a force balance equation, a stress constraint of the rod and a non-negative constraint of the rod area, the design variables are a rod area vector a and a rod internal force vector q, B and l respectively represent a constant matrix and a constant vector generated according to a rod topological mode, and f, sigma c and sigma t are constants determined by practical working conditions.
3. The structural layout optimization design and manufacturing method based on the repetitive units according to claim 2, wherein in the step S1, when the balance matrix B of the minimum connection base structure in the initial state is optimized, the member length threshold and the grid density in the minimum connection base structure are increased, the minimum connection base structure in the initial state is optimized after updating is formed, and the solution is performed again.
4. The structural layout optimization design and manufacturing method based on the repetitive units according to claim 1, wherein in the step S2, binary variables of the active unit mode are set for each rod, the repetitive unit constraint is added for each rod of the truss structure, namely, the design domain is filled with the unit modes first, nodes inside each unit mode are connected into the rod in pairs to form the repetitive units, in order to ensure that the areas of the rods in the same type unit mode at the same position are the same, when n unit modes exist in the structure, the following constraint is added for each rod, t c1 +t c2 +…+t cn =1 (3) a i ＝a m1 ·t c1 +a m2 ·t c2 +…+a mn ·t cn (4) Wherein a i is the sectional area of the rod, c is the number of the unit mode to which the rod belongs, m is the position number of the rod in the unit mode, t c1 、t c2 、…、t cn is the binary variable of the unit mode to which the rod belongs, the value is 1 or 0,1 represents the activated unit mode, 0 represents the non-activated unit mode, a m1 、a m2 、…、a mn is the possible sectional area corresponding to the position of the rod in the unit mode, and a m1 、a m2 、…、a mn and t c1 、t c2 、…、t cn are both variables in the formula (4) and are multiplied to form nonlinear constraint.
5. The structural layout optimization design and manufacture method based on the repetitive units according to claim 4, wherein in the step S2, the nonlinear constraint of the formula (4) is converted into the linear constraint by adopting a large M method to obtain the formula (5), Wherein M is a constant, each row in formula (5) represents the constraint of one unit mode on the rod at the position, when the unit mode of a i is activated in the first unit mode, t c1 =1, the rest t cx =0, the 1 st row of the constraint formula (5) becomes a i ＝a m1 , other inequalities are relaxed and do not actually work, when the unit mode of a i is activated in the second unit mode, i.e. t c2 =1, the rest t cx =0, the 2 nd row of the constraint formula (5) becomes a i ＝a m2 , the other inequalities are relaxed and do not work, and the like, when the unit mode of a rod is activated in the unit mode of a unit mode, the constraint of the rod at the corresponding row of the rod is effective, and the inequality constraint of the other rows is relaxed.
6. The method for optimizing design and manufacturing structural layout based on repeated units according to claim 4, wherein step S3 is specifically implemented by firstly reducing complexity of unit modes, namely reducing the number of nodes on the basis of a normal unit mode structure to obtain a simplified unit mode structure, performing first solving by using a method of step S2 to obtain a unit mode variable t c activated by each unit mode, which is equivalent to obtaining the layout of the unit mode taken by each rod piece in a design domain, then setting the complexity of the unit mode as normal and regenerating the structure, substituting t c obtained by the first solving into formula (4), changing an optimization problem into linear programming, and directly performing second solving.
7. The structural layout optimization design and manufacturing method based on the repetitive units, which is disclosed in claim 1, is characterized in that step S4 is specifically implemented by extracting structural information of the repetitive units according to an optimization result, wherein the structural information comprises a repetitive unit mode, a repetitive unit position, repetitive unit connection and a repetitive unit rod section size, establishing a 3D solid model after rod assembly and node generation processing of the repetitive units, slicing various repetitive units in the solid model respectively, generating printing paths, performing 3D printing manufacturing, connecting among the repetitive units, performing integrated assembly, and manufacturing the optimized structure.

Description

Discrete truss structure layout optimization design and manufacturing method based on repetitive units Technical Field The invention belongs to the technical field of structural engineering and additive manufacturing, and particularly relates to a discrete truss structure layout optimization design and manufacturing method based on a repetitive unit. Background Increasingly complex engineering needs have led to an increasing need for complex truss structure optimization designs and 3D printing integration assemblies. The topological optimization object of the structure comprises a discrete body structure and a continuous body structure, and the topological optimization object belongs to the category of topological optimization of the discrete structure in practical engineering. The layout optimization of truss structures is a linear programming problem, and although the solution of the conventional truss layout optimization algorithm can be optimized in numerical value, in actual manufacturing, the situation that the truss structure is difficult to manufacture or even impossible to manufacture is easy to occur due to the complexity of the truss structure. In order to reduce the manufacturing cost, the general method is to add additional constraints such as rod sorting and structure complexity limitation, so as to make the final result as easy to manufacture as possible, but optimizing the solution becomes more complex. The introduction of the repeatability unit is a reasonable and efficient solution for simplifying the layout optimization problem. The optimization method for introducing the concept of the repetitive units is provided in the continuous body optimization process and mainly comprises a homogenization method (Homogenization Method) and a small-scale unified optimization method. The homogenization method is equivalent to macroscopic uniform media, so that the whole structure can macroscopically perform coarse-granularity finite element analysis, but the homogenization method can not control the connectivity among units under the condition of not introducing additional constraint, and the small-scale unified optimization method is used for unifying the whole structure on a smaller scale for optimization, so that the cost is high calculation cost. The units in the building engineering are generally of discrete body structures and have a limited size relative to a design domain, so the repetitive unit algorithm oriented to continuous body optimization cannot be directly used for solving the problem of layout optimization of truss structures. In summary, it is necessary to research a design and a manufacturing method for optimizing the layout of a discrete truss structure based on a repeating unit, and to implement the optimization of the layout of the repeating unit, 3D printing manufacturing and integrated assembly of a complex truss structure. Disclosure of Invention The invention aims to overcome the defects in the prior art and provides a discrete truss structure layout optimization design and manufacturing method based on a repetitive unit. The structural layout optimization design and manufacturing method based on the repetitive units comprises the following steps: S1, establishing a truss layout optimization mathematical model, namely, firstly giving a structural design domain, inputting size, load working condition and boundary constraint, and designating a unit mode and complexity of a corresponding unit mode; S2, directly solving based on a repetitive unit, namely setting a limited number of unit modes, carrying out unit division to ensure that all rod pieces belong to a certain unit mode and rod pieces in a cross-unit mode do not exist, wherein the unit layout of the same unit mode and the area of the rod pieces in the corresponding position are completely the same; S3, firstly determining two-step solution of the cell layout, namely firstly reducing the complexity of each cell mode, and carrying out first solution according to the step S2 to obtain a cell mode variable which is activated correspondingly for each cell mode And then according to the normal complexity of each unit modeSubstituting the linear constraint expression of the repetitive unit of each rod in the step S2 to convert the linear constraint expression into linear constraint, and carrying out second solving to obtain an optimization result; s4, 3D printing manufacturing and integrated assembly, namely 3D modeling is carried out, various repetitive units in the optimized result model are respectively sliced, a printing path is generated, 3D printing manufacturing is carried out, integrated assembly is carried out among the repetitive units, and the optimized structure is manufactured. Preferably, in the step S1, the objective function corresponding to the design objective with the minimum total volume of the rod pieces is as follows, The expression of the constraint is that, In the formula,Is the length vector of the rod