CN113449454B - Topology optimization method of steel truss structure - Google Patents
Topology optimization method of steel truss structure Download PDFInfo
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- 238000005457 optimization Methods 0.000 title claims abstract description 118
- 229910000831 Steel Inorganic materials 0.000 title claims abstract description 30
- 238000000034 method Methods 0.000 title claims abstract description 30
- 239000010959 steel Substances 0.000 title claims abstract description 30
- 238000004458 analytical method Methods 0.000 claims abstract description 21
- 230000004044 response Effects 0.000 claims abstract description 13
- 239000007787 solid Substances 0.000 claims abstract description 12
- 230000008569 process Effects 0.000 claims abstract description 4
- 239000000463 material Substances 0.000 claims description 13
- 238000004364 calculation method Methods 0.000 claims description 7
- 230000014759 maintenance of location Effects 0.000 claims description 5
- 230000008439 repair process Effects 0.000 claims description 5
- 229910000746 Structural steel Inorganic materials 0.000 claims description 4
- 230000003068 static effect Effects 0.000 claims description 4
- 238000006073 displacement reaction Methods 0.000 claims description 2
- 239000011159 matrix material Substances 0.000 claims description 2
- 230000009286 beneficial effect Effects 0.000 abstract description 2
- 238000010586 diagram Methods 0.000 description 9
- 238000010276 construction Methods 0.000 description 5
- 230000006872 improvement Effects 0.000 description 2
- 230000000694 effects Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000007717 exclusion Effects 0.000 description 1
- 230000008676 import Effects 0.000 description 1
- 238000002347 injection Methods 0.000 description 1
- 239000007924 injection Substances 0.000 description 1
- 238000012805 post-processing Methods 0.000 description 1
- 239000000243 solution Substances 0.000 description 1
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- 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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- 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
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
- G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation
- G06T17/205—Re-meshing
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/04—Constraint-based CAD
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- G—PHYSICS
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- G06F2111/00—Details relating to CAD techniques
- G06F2111/10—Numerical modelling
Abstract
The invention discloses a topology optimization method of a novel steel truss structure, which comprises the following steps: step one, determining an optimization domain; step two, solid modeling; thirdly, modeling by adopting a solid unit or a shell unit; step four, dividing grids; step five, constraint and appointed load are applied; step six, comparing analysis results; step seven, setting parameters of a solver; step eight, setting boundaries which do not need to be optimized in optimization; step nine, setting response constraint; step ten, applying symmetrical structure constraint; step eleven, setting optimization target parameters; step twelve, obtaining an initial truss optimization model; thirteenth, observing and optimizing the size and the shape of the model; fourteen, carrying out post-treatment on the optimization model; fifteen, repairing the checkerboard entity; sixthly, solving a model; seventeenth, ending the process, failing to optimize, and returning to step nine. The beneficial effects are that: the advantages of the truss structure in mechanical properties can be maintained while steel can be saved greatly.
Description
Technical Field
The invention relates to a topology optimization method, in particular to a topology optimization method of a steel truss structure.
Background
At present, the large-span overhanging steel truss structure has the advantages of light self weight, good strength and toughness, short construction period, high degree of mechanization, good earthquake resistance, wind resistance and the like, is widely used, and also meets the requirements of ultra-large span, ultra-high space and comprehensive functions. Due to the improvement of calculation means and the continuous improvement of construction level, the design and construction technology of the large-span steel truss structure are mature, but the problems of large steel consumption and insufficient fine node design exist, and the two problems greatly limit the application range of the large-span overhanging steel truss structure in related engineering.
Disclosure of Invention
The invention aims to solve the problems of large steel consumption and insufficient fine node design of the existing large-span overhanging steel truss structure.
The invention provides a topology optimization method of a steel truss structure, which comprises the following steps:
Firstly, preliminarily determining the structure size of a steel truss, obtaining three basic indexes of the length, the width and the height of a single truss, determining an optimization domain, and drawing up an entity;
Step two, opening finite element analysis software, defining the material as structural steel, redefining if the strength of the steel is higher, and performing solid modeling on the optimized domain;
modeling the optimized domain by adopting a solid unit or a shell unit, wherein the solid unit is a non-rectangular optimized domain, and the shell unit is a rectangular optimized domain;
fourthly, adopting Hex Dominant Method regular hexahedron grid division for the rectangular optimization domain, and adopting local control grid division for the non-rectangular optimization domain;
Step five, constraint and appointed load are applied to the optimization domain;
step six, finite element analysis of a statics mode is carried out, and three indexes of equivalent stress, deformation and equivalent strain are obtained, so that the three indexes are compared with finite element analysis results of an optimization model;
step seven, exiting a finite element analysis mode, entering a Topology Optimization topology optimization mode, and setting parameters of a topology optimization solver under the mode, wherein the parameters comprise a maximum iteration number parameter, a discrete unit minimum density and a calculation precision parameter, a rectangular optimization domain selection optimization criterion method and a non-rectangular optimization domain selection sequence convex programming method in the solver;
Step eight, setting a boundary which does not need optimization in optimization, wherein the boundary is used for avoiding the situation that the slenderness ratio of the truss exceeds the limit and materials which do not contribute to topological optimization of the structure on the boundary are deleted;
Step nine, setting response constraint, wherein response parameters are set as Mass in the response constraint, and the retention percentage parameters are set as 45%;
step ten, symmetrical construction constraint is applied to the single truss, so that the situation that an optimization model is asymmetrical is prevented;
Step eleven, setting optimization target parameters, and selecting a minimum by an optimization target;
Step twelve, solving a topological optimization result to obtain a truss initial optimization model;
thirteenth, observing the size and the shape of the optimized model, returning to the ninth step if no holes or single-truss asymmetry occurs in the optimized model, otherwise, entering the next step;
Fourteen, carrying out post-treatment on the optimization model, selecting an optimization threshold value to be between 0.4 and 0.6, and entering the next step after the optimization threshold value is adjusted according to the mechanical property requirement;
Fifteen, importing the optimization model into SPACECLAIM, converting the optimization model into an entity, and repairing the checkerboard entity by using a repair function;
Sixthly, setting materials, constraints and loads which are the same as those in the second step and the fifth step in new finite element analysis by the optimization model, and solving the model;
Seventeenth, comparing the three indexes of the equivalent stress, the deformation and the equivalent strain obtained in the sixteenth with the three indexes of the equivalent stress, the deformation and the equivalent strain obtained in the sixth, if the total ratio is not more than 20%, ending the process, and if the total ratio is more than 20%, failing to optimize, returning to the ninth.
Wherein, the topological optimization adopts a variable density method topological optimization, and the calculation formula is as follows:
Findρ＝{ρ1,ρ2,···,ρn}
MinC＝{U}T[K]{U}
s.t.[K]{U}＝{F}
0≤ρmin≤ρi≤1,i＝1,2,···,n
Wherein ρ i is the relative density of the discrete units, and is a continuous value between [ ρ min, 1 ]; n is the number of design variables; k is the total stiffness matrix; u is a displacement vector of the structure; f is the external force vector applied to the structure; v is the volume of the structure; v 0 is the upper limit of the optimized structure volume; let ρ min =0.001.
The invention has the beneficial effects that:
The topology optimization method of the steel truss structure provided by the invention can be widely applied and popularized under the development of the future assembly type main stream, and can be particularly applied to large-scale steel structure engineering. The large-span truss structure optimized by the topology optimization method can save a large amount of steel, can maintain the superiority of the mechanical property of the truss structure, can effectively prevent the instability problem of the components of the large-span steel truss structure, and the feasibility of the topology optimized large-span overhanging steel truss structure can be better embodied by the refined node design.
Compared with the finite element calculation result of the common large-span overhanging steel truss structure, the method provided by the invention has the advantages that:
drawings
Fig. 1 is a schematic view of a steel truss structure size optimization domain according to the present invention.
Fig. 2 is a schematic diagram of a material definition according to the present invention.
FIG. 3 is a finite element case element modeling schematic according to the present invention.
Fig. 4 is a schematic diagram of finite element meshing according to the present invention.
FIG. 5 is a schematic diagram of constraint application and loading according to the present invention.
Fig. 6 is a schematic diagram of a finite element analysis stress cloud according to the present invention.
Fig. 7 is a schematic diagram of a finite element analysis strain cloud according to the present invention.
Fig. 8 is a schematic view of a finite element analysis deformation cloud according to the present invention.
FIG. 9 is a schematic diagram of a topologically optimized solution environment in accordance with the present invention.
Fig. 10 is a schematic diagram of a topology optimized exclusion boundary according to the present invention.
FIG. 11 is a schematic view of the optimization objective parameter setting according to the present invention.
FIG. 12 is a schematic diagram of an initial model of topology optimization according to the present invention.
FIG. 13 is a schematic diagram of the repair of the optimization model import SPACECLAIM according to the present invention.
FIG. 14 is a schematic representation of the constraint and loading imposed by finite element analysis of an optimization model in accordance with the present invention.
Detailed Description
Please refer to fig. 1 to 14:
Example 1:
the invention provides a topology optimization method of a steel truss structure, which comprises the following steps:
Firstly, preliminarily determining the structure size of a steel truss, obtaining three basic indexes of the length, the width and the height of a single truss, determining an optimization domain, and drawing up an entity; ( And (3) injection: if the dimensions of the single truss are non-rectangular, more relevant parameters, such as angles, etc., need to be obtained to obtain optimal domain modeling )
And step two, opening finite element analysis software, defining the material as structural steel (if the strength of steel is higher, redefined), and performing solid modeling on the optimized domain.
Thirdly, modeling an optimization domain by adopting a solid unit (non-rectangular optimization domain) or a shell unit (rectangular optimization domain); (Note that rectangular optimization fields can also be modeled using solid units, where shell unit modeling is used because shell unit finite element analysis can reduce the computational effort and save analysis time.)
Fourthly, adopting Hex Dominant Method regular hexahedron grid division for the rectangular optimization domain, and adopting local control grid division for the non-rectangular optimization domain;
Step five, constraint and appointed load are applied to the optimization domain;
Step six, carrying out statics (modal) finite element analysis to obtain three indexes of equivalent stress, deformation and equivalent strain, wherein the three indexes are used for comparing with finite element analysis results of an optimization model;
step seven, exiting a finite element analysis mode, entering a Topology Optimization topology optimization mode, and setting topology optimization solver parameters under the mode, wherein the parameters comprise a maximum iteration number parameter (generally taken to be 500), a minimum discrete unit density (generally taken to be 0.001), a calculation precision parameter, a solver rectangular optimization domain selection optimization criterion method and a non-rectangular optimization domain selection sequence convex programming method;
Step eight, setting a boundary which does not need optimization in optimization, wherein the boundary is used for avoiding the situation that the slenderness ratio of the truss exceeds the limit and materials which do not contribute to topological optimization of the structure on the boundary are deleted;
step nine, setting response constraint, wherein response parameter is set as quality (Mass) in the response constraint, and the retention percentage parameter is set as 45% (or more);
step ten, symmetrical construction constraint is applied to the single truss, so that the situation that an optimization model is asymmetrical is prevented;
Step eleven, setting optimization target parameters, and selecting a minimum by an optimization target;
Step twelve, solving a topological optimization result to obtain a truss initial optimization model;
Thirteenth, observing the size and the shape of the optimized model, if no hole or single asymmetric mode exists in the optimized model, returning to the ninth step to lift the retention percentage parameter, otherwise, entering the next step;
Fourteen, post-processing the optimization model, wherein the optimization threshold value is selected to be between 0.4 and 0.6, and adjustment is carried out according to the mechanical properties;
Fifteen, importing the optimization model into SPACECLAIM, converting the optimization model into an entity, and repairing the checkerboard entity by using a repair function;
Sixthly, setting materials, constraints and loads which are the same as those in the second step and the fifth step in new finite element analysis by the optimization model, and solving the model;
seventeenth, comparing the three indexes of the equivalent stress, the deformation and the equivalent strain obtained in the sixteenth with the three indexes of the equivalent stress, the deformation and the equivalent strain obtained in the sixth, if the total ratio is not more than 20%, ending the process, and if the total ratio is more than 20%, returning to the ninth, wherein the optimization effect does not reach the standard.
Example 2:
The method of the invention is further described in terms of topological optimization of the large-span overhanging steel truss.
The single-truss large-span cantilever steel truss of the embodiment has a span of 24.8m and a height of 4m, the optimization model uses a shell unit, the thickness is defined to be 300mm, fixed constraint is applied to one end, and vertical force of 2500kN is applied to the free end. The truss is further optimized by the method of the invention.
Step one, defining the size of a steel truss structure as 24.8m long, 4m high and 300mm wide (as shown in figure 1), determining an optimized domain, and planning an entity;
Step two, opening finite element analysis software, defining materials as structural steel, and performing solid modeling on an optimized domain, wherein the material properties are shown in the following table 1;
Modeling the optimized domain by adopting a shell unit (rectangular optimized domain), and defining the thickness of 300mm (as shown in figure 2);
Fourthly, adopting Hex Dominant Method regular hexahedron grid division (as shown in figure 3) for the rectangular optimization domain;
step five, applying fixed constraint to one end of the optimization domain, and designating the concentrated force load to be 2500kN (as shown in figure 4) at the other end;
Step six, carrying out statics finite element analysis to obtain three indexes of equivalent stress, deformation and equivalent strain (as shown in figures 5,6 and 7);
Step seven, exiting the finite element analysis mode, entering a Topology Optimization topology optimization mode, and setting the parameters of a topology optimization solver in the mode as shown in the following table 2;
step eight, setting boundaries which do not need to be optimized in optimization as four edges (as shown in fig. 8);
Step nine, setting response constraint, wherein response parameters are set to be Mass (Mass) in the response constraint, and the retention percentage parameters are set to be 45%;
Tenth, symmetrical structure constraint is applied to the single truss;
step eleven, setting optimization target parameters as shown in the following table 3;
step twelve, solving a topological optimization result to obtain a truss initial optimization model (as shown in fig. 9);
Thirteenth, observing and optimizing the size and the shape of the model, wherein the size and the shape of the model are symmetrical and holes appear, and entering fourteen steps;
fourteen, carrying out post-treatment on the optimization model, wherein the optimization threshold value is selected to be between 0.4 and 0.6 according to the mechanical property requirement, and is selected to be 0.58;
Fifteen, importing the optimization model into SPACECLAIM, converting the optimization model into an entity, and repairing the checkerboard entity by using a repair function (as shown in figure 10);
Sixthly, importing the optimized model into finite element analysis, setting materials, constraints and loads the same as those in the second step and the fifth step, and solving the model (as shown in FIG. 11);
Seventeenth, comparing the three indexes of the equivalent stress, the deformation and the equivalent strain obtained in the sixteenth with the three indexes of the equivalent stress, the deformation and the equivalent strain obtained in the sixth (fig. 12, 13 and 14), wherein the total ratio is not more than 20%, and ending the topology optimization flow.
Claims (1)
1. A topology optimization method of a steel truss structure is characterized by comprising the following steps of: the method comprises the following steps:
Firstly, preliminarily determining the structure size of a steel truss, obtaining three basic indexes of the length, the width and the height of a single truss, determining an optimization domain, and drawing up an entity;
Step two, opening finite element analysis software, defining the material as structural steel, redefining if the strength of the steel is higher, and performing solid modeling on the optimized domain;
modeling the optimized domain by adopting a solid unit or a shell unit, wherein the solid unit is a non-rectangular optimized domain, and the shell unit is a rectangular optimized domain;
fourthly, adopting Hex Dominant Method regular hexahedron grid division for the rectangular optimization domain, and adopting local control grid division for the non-rectangular optimization domain;
Step five, applying fixed constraint to one end of the optimization domain, and applying concentrated load to the other end of the optimization domain;
step six, finite element analysis of a statics mode is carried out, and three indexes of equivalent stress, deformation and equivalent strain are obtained;
step seven, exiting a finite element analysis mode, entering a Topology Optimization topology optimization mode, and setting parameters of a topology optimization solver under the mode, wherein the parameters comprise a maximum iteration number parameter, a discrete unit minimum density and a calculation precision parameter, a rectangular optimization domain selection optimization criterion method and a non-rectangular optimization domain selection sequence convex programming method in the solver;
step eight, setting a boundary which does not need optimization in optimization, and avoiding the conditions that the slenderness ratio of the truss exceeds the limit and materials which do not contribute to topological optimization of the structure on the boundary are deleted;
Step nine, setting response constraint, wherein response parameters are set as Mass in the response constraint, and the retention percentage parameters are set as 45%;
Tenth, symmetrical structure constraint is applied to the single truss;
Step eleven, setting optimization target parameters, and selecting a minimum by an optimization target;
Step twelve, solving a topological optimization result to obtain a truss initial optimization model;
thirteenth, observing the size and the shape of the optimized model, returning to the ninth step if no holes or single-truss asymmetry occurs in the optimized model, otherwise, entering the next step;
Fourteen, carrying out post-treatment on the optimization model, selecting an optimization threshold value to be between 0.4 and 0.6, and entering the next step after the optimization threshold value is adjusted according to the mechanical property requirement;
Fifteen, importing the optimization model into SPACECLAIM, converting the optimization model into an entity, and repairing the checkerboard entity by using a repair function;
Sixthly, setting materials, constraints and loads which are the same as those in the second step and the fifth step in new finite element analysis by the optimization model, and solving the model;
Seventeenth, comparing the three indexes of the equivalent stress, the deformation and the equivalent strain obtained in the sixteenth with the three indexes of the equivalent stress, the deformation and the equivalent strain obtained in the sixth, if the total ratio is not more than 20%, ending the process, and if the total ratio is more than 20%, failing to optimize, returning to the ninth;
Wherein, the topological optimization adopts a variable density method topological optimization, and the calculation formula is as follows:
Findρ＝{ρ1,ρ2,···,ρn}
MinC＝{U}T[K]{U}
s.t.[K]{U}＝{F}
0≤ρmin≤ρi≤1,i＝1,2,···,n；
wherein ρ i is a continuous value between [ ρ min, 1 ]; n is the number of design variables; k is the total stiffness matrix; u is a displacement vector of the structure; f is the external force vector applied to the structure; v is the volume of the structure; let ρ min =0.001.
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