CN115859717A - Topological optimization design method of latticed shell structure assembled node - Google Patents
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Abstract
The invention discloses a topological optimization design method of a reticulated shell structure fabricated node, which establishes a refined node geometric model, considers the contact slip effect among all components of the fabricated node, establishes a topological optimization constraint condition considering the contact effect, and adopts an SIMP method to carry out topological optimization design. The method combines the advantages of the additive manufacturing technology and the topological optimization technology, enables the obtained topological structure to be the optimal topological structure, can directly print without other processing, and guarantees the application rationality of the method in practical use.
Description
Technical Field
The invention relates to a topological optimization method for an additive manufacturing technology, in particular to a topological optimization design method for a single-layer free-form surface reticulated shell structure assembled node.
Background
In recent years, with the growing maturity of 3D printing technology, the possibility of manufacturing nodes with complex geometric shapes is provided. The topological optimization is one of the most effective methods for designing the novel node, and the node form can be individually designed according to different load conditions and different relative position relations of the rod pieces. Through the node topology optimization, the node self-weight can be greatly reduced while the requirement on the node rigidity is ensured, and the utilization efficiency of materials is improved to the maximum extent.
However, in the existing research, the topological optimization of the spatial structure node mostly focuses on the research of the rigid node, or simplifies the bolt connection of the assembled semi-rigid node, and does not consider the contact slip effect, but in the topological optimization of the node, the optimal topological structure is obtained based on the transmission path of the load. Therefore, neglecting the contact slip of the bolt surface, it is difficult to ensure that the obtained topological structure is the optimal topological structure in the stressed state.
Disclosure of Invention
The invention aims to overcome the problems and provides a topological optimization design method of a reticulated shell structure fabricated node oriented to the additive manufacturing technology, which considers the contact effect of the fabricated node, establishes a topological optimization constraint condition considering the contact effect and adopts an SIMP (simple Isotropic Microstructures with Pearlization) method to carry out topological optimization design. The method ensures that the obtained topological structure is the optimal topological structure, and ensures the application rationality of the topological node model in actual use.
In order to achieve the above purpose, the solution of the invention is:
a topological optimization design method of a latticed shell structure assembled node comprises the following specific steps:
step 2, establishing an accurate node geometric model by using SolidWorks software, assembling nodes according to a relative position relationship, setting an interaction relationship of each contact surface, a pretightening force effect of a bolt, applying load and boundary conditions, and performing finite element analysis by using ABAQUS software;
and 3, creating a topology optimization task according to the finite element model in the step 2, setting a design domain and a non-design domain of the node, an optimization target and a constraint condition, and performing topology optimization design on the node by adopting an SIMP method.
As a further technical scheme of the invention, the single-layer free-form surface mesh shell model established in the step 1 is a single-layer free-form surface mesh shell model which is established based on a genetic algorithm and has a rectangular plane projection, the geometric shape of the single-layer free-form surface mesh shell model is described by adopting a NURBS (non-uniform rational B-spline) method, the coordinates of NURBS control points are taken as optimization variables, and the maximized structural rigidity is taken as an optimization target.
As a further technical scheme of the invention, the assembled node geometric model in the step 2 comprises a node body, a bolt, a connecting piece and a rod piece, and is determined by the optimal curved surface shape of the latticed shell structure obtained in the step 1. And the assembly is completed according to the relative position relationship, the interaction relationship of each contact surface and the pretightening force of the bolt are set, and the load and the boundary condition are applied.
As a further technical solution of the present invention, step 3 specifically is:
(3-1) establishing a topology optimization task by using ABAQUS software, defining unit density as a design variable, and establishing an interpolation function between the unit density and the elastic modulus of the material;
(3-2) dividing a design domain and a non-design domain based on the construction requirement of the fabricated node;
(3-3) establishing volume constraints of the design domain;
(3-4) establishing topological optimization constraint conditions considering contact action;
(3-5) setting a structural optimization target to minimize strain energy;
as a further technical solution of the present invention, the interpolation function in (3-1) is:
E i ＝E 0 (ρ i ) p
in the formula: e i Is the elastic modulus of the ith cell; e 0 The modulus of elasticity at a cell density of 1; rho i Is the density of the ith cell; p denotes a penalty factor, taking p =3.
As a further technical solution of the present invention, the central node body is set as a design domain in (3-2), and all other regions are non-design domains.
As a further technical solution of the present invention, the volume constraint conditions of the design domain in (3-3) are:
0＜ρ min ≤ρ i ≤ρ max
in the formula: v is the optimized volume; rho i Cell density of the ith cell; v. of i Is the volume of the ith cell; v * Is a volume constraint of the structure;
is the volume constraint coefficient; v 0 To design the initial volume of the domain.
As a further technical solution of the present invention, the topological optimization constraint condition considering the contact effect constructed in step 3 is:
σ i,mas ≤f y,mas
σ j,sla ≤f y,sla
in the formula: f. of y Is the yield strength of the material; sigma i,mas Is the ith unit stress on the major surface of the contact surface; sigma i,sla The jth cell stress on the slave face for the contact face; f. of y,mas The yield strength of the material of the main surface of the contact surface; f. of y,sla Is the yield strength of the contact surface slave surface material; delta r The unit relative sliding distance of the intersection nodes of the master surface and the slave surface; d k,mas 、d m,sla Respectively is the sliding distance of the k-th and m-th intersection points of the main surface and the auxiliary surface of the contact surface; l is i The length of the unit of the ith unit of the main surface along the sliding direction; [ Delta ] of]The maximum allowed slip distance for the unit.
As a further technical solution of the present invention, the mathematical model for topology optimization by SIMP in (3-6) is:
in the formula: c (X) is strain energy of the topological structure; f is a load vector; u is an integral displacement matrix; v is the optimized volume of the design domain; rho i Cell density of the ith cell; v. of i Is the volume of the ith cell; v * Designing a volume constraint for the domain for the node;
volume constraint coefficients for the design domain; v 0 To the initial volume of the design domain; k is an integral rigidity matrix; rho min Is cell density ρ i Lower limit of (1), take ρ min ＝0.001；ρ max Is cell density ρ i Upper limit of (1), take ρ max ＝1。
As a further technical scheme of the invention, the convergence judgment of topology optimization by adopting SIMP adopts a target function and unit density dual convergence criterion, which specifically comprises the following steps:
in the formula: c (X) is the strain energy of the structure, namely the objective function value; rho i The cell density q for the ith cell is the number of optimization iteration steps.
Compared with the prior art, the invention has the following remarkable advantages:
1. finite element software ABAQUS is used for carrying out refined modeling on the fabricated nodes, so that the actual stress condition of the nodes is better met, and the optimal topological structure can be obtained;
2. the advantages of an additive manufacturing technology and a topology optimization technology are better combined in the fine modeling of the nodes, so that the obtained topological structure can be directly printed without other processing, and the node assembly requirement can be met;
3. a topological optimization constraint condition considering the contact effect is established, so that the obtained optimal topological structure has enough contact rigidity, and the application rationality of a topological node model in actual use is ensured.
Drawings
Fig. 1 is a basic flow chart of a topology optimization design method of an additive manufacturing technology-oriented fabricated node in the present description;
FIG. 2 is a diagram of the locations of control points in a genetic algorithm;
FIG. 3 is a 100 th generation optimal single-layer free-form surface latticed shell structure created based on a genetic algorithm;
FIG. 4 is an assembled node refined geometric model;
FIG. 5 is a schematic diagram of a topology optimization constraint considering contact effects.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The present invention will be described in further detail with reference to specific examples.
A topological optimization design method of a reticulated shell structure assembled node for an additive manufacturing technology is disclosed, as shown in FIG. 1, and the implementation steps are as follows:
Step 2, establishing an accurate assembly type node geometric model by using SolidWorks software, wherein the model comprises a node body, a bolt, a connecting piece and a rod piece, and completing model assembly according to a position relation; defining material properties of each part of the model, wherein the material properties comprise density, elastic modulus, poisson's ratio and yield strength; when the grids are divided, the grid density of the contact surface from the surface is larger than that of the main surface, so that the cell invasion phenomenon is prevented; defining interaction according to the stress state of the actual Contact surface of the node, setting Contact property of hard Contact on the Contact surface which allows limited sliding, and setting Tie binding connection when sliding is not allowed; the bolts are 10.9-grade high-strength bolts, and the pretightening force of the bolts is set to be 20kN; both the load and the boundary conditions are set at the ends of each rod.
In the present example, the refinement geometry model of fabricated nodes is shown in FIG. 4. In order to meet the requirement of bolt assembly, the node body is cut by a depth of 3/D (D is the diameter of the bolt) along the periphery of the bolt to be used as a reserved area to be connected with the bolt, namely a non-design area in topology optimization, and other areas of the node body are used as design areas, as shown in FIG. 4; in order to enable the model after the topology optimization to be directly formed by 3D printing, the embodiment carries out fine modeling on the threaded parts of the high-strength bolt and the sphere, and the length of the threaded parts and the number of threads of the threaded parts are consistent with the actual situation of the bolt.
In the embodiment of the invention, the interaction of each component adopts a contact simulation method to truly simulate the stress state of each component, a surface-surface contact mode in ABAQUS software is selected, and contact attributes are set, wherein the contact attributes comprise tangential behaviors and normal behaviors, the tangential behaviors adopt a penalty function method to input the friction coefficient of the contact surface, the normal behaviors adopt 'hard contact', and the relationship between the main surface and the slave surface of each contact surface is shown in table 1 and is shown by black bold lines in figure 4.
TABLE 1
| Serial number | Major face | From the surface | Serial number | Major face | From the |
||
| 1 | Node body | Sleeve barrel | 4 | Conical head | Bolt | ||
| 2 | Conical | Sleeve barrel | 5 | Conical | Nut cap | ||
| 3 | Bolt | Sleeve barrel |
The established topological optimization constraint condition considering the contact effect is as follows:
σ i,mas ≤f y,mas
σ j,sla ≤f y,sla
in the formula: f. of y Is the yield strength of the material; sigma i,mas Is the ith unit stress on the major surface of the contact surface; sigma i,sla The jth cell stress on the slave face for the contact face; f. of y,mas The yield strength of the material of the main surface of the contact surface; f. of y,sla Is the yield strength of the contact surface slave surface material; delta r The unit relative sliding distance of the intersection nodes of the master surface and the slave surface; d k,mas 、d m,sla Respectively is the sliding distance of the k-th and m-th intersection points of the main surface and the auxiliary surface of the contact surface; l is a radical of an alcohol i Is the ith unit edge of the main surfaceUnit length in the slip direction; [ delta ] is]Allowing a maximum relative sliding distance for the unit in actual use of the structure;
the mathematical model for carrying out topology optimization on the nodes by adopting the SIMP method specifically comprises the following steps:
in the formula: c (X) is strain energy of the structure; f is a load vector; u is an integral displacement matrix; v is the optimized volume; rho i Cell density of the ith cell; v. of i Is the volume of the ith cell; v * Is a volume constraint of the structure;
is the volume constraint coefficient; v 0 To the initial volume of the design domain; k is an integral rigidity matrix; rho min Is cell density ρ e Lower limit of (1), take ρ min ＝0.001；ρ max Is cell density ρ i Upper limit of (1), take ρ max ＝1。
The convergence judgment of topology optimization by adopting SIMP adopts a dual convergence criterion of an objective function and unit density, and specifically comprises the following steps:
in the formula: c (X) is the strain energy of the structure, namely the objective function value; i is the number of cells; rho i Cell density for the ith cell, i.e., the optimization variable; and q is the number of the optimized iteration steps.
The technical means disclosed by the scheme of the invention are not limited to the technical means disclosed by the technical means, and the technical scheme also comprises the technical scheme formed by any combination of the technical characteristics.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention are included in the scope of the present invention, and therefore, the scope of the present invention should be subject to the protection scope of the claims.
Claims (10)
1. A topological optimization design method of a latticed shell structure assembled node is characterized by comprising the following specific steps:
step 1, establishing a single-layer free-form surface net shell model, and performing finite element analysis under uniformly distributed load by using ANSYS software to obtain the internal force of a rod piece of each node;
step 2, establishing an assembly type node geometric model, assembling nodes according to the relative position relation, and performing finite element analysis by using ABAQUS software;
and 3, creating a topology optimization task, setting a design domain and a non-design domain of the node, an optimization target and a constraint condition, and performing topology optimization design on the node by adopting an SIMP method.
2. The topological optimization design method of the fabricated nodes of the latticed shell structure according to claim 1, wherein the single-layer free-form surface latticed shell model in step 1 is a single-layer free-form surface latticed shell model with a plane projection being a rectangle, which is established based on a genetic algorithm, the geometric shape of the model is described by adopting a non-uniform rational B-spline NURBS method, NURBS control point coordinates are used as optimization variables, and maximized structural rigidity is used as an optimization target.
3. The topological optimization design method of the fabricated node of the reticulated shell structure according to claim 1, wherein the fabricated node geometric model in the step 2 comprises a node body, a bolt, a connecting piece and a rod piece, the assembly is completed according to the relative position relationship, the interaction relationship of each contact surface, the pretightening force of the bolt, the applied load and the boundary condition are set.
4. The topological optimization design method of the fabricated nodes of the reticulated shell structure according to claim 1, wherein the step 3 specifically comprises:
(3-1) establishing a topology optimization task by using ABAQUS software, defining unit density as a design variable, and establishing an interpolation function between the unit density and the elastic modulus of the material;
(3-2) dividing a design domain and a non-design domain based on the construction requirements of the fabricated nodes;
(3-3) establishing volume constraints of the design domain;
(3-4) establishing a topological optimization constraint condition considering the contact effect;
(3-5) setting a structural optimization target to minimize structural strain energy;
and (3-6) carrying out topology optimization design on the nodes in the step 2 by adopting an SIMP method.
5. The topology optimization design method of the fabricated node of the latticed shell structure according to claim 4, wherein the interpolation function in (3-1) is:
E i ＝E 0 (ρ i ) p
in the formula: e i Is the elastic modulus of the ith cell; e 0 The modulus of elasticity at a cell density of 1; rho i Is the density of the ith cell; p represents a penalty factor.
6. The topology optimization design method of the fabricated nodes of the reticulated shell structure according to claim 4, wherein the central node body in (3-2) is set as a design domain, and other regions are all non-design domains.
7. The topology optimization design method of the fabricated nodes of the reticulated shell structure according to claim 4, wherein the volume constraint conditions of the design domain in (3-3) are as follows:
0＜ρ min ≤ρ i ≤ρ max
in the formula: v is the optimized volume; rho i Cell density of the ith cell; v. of i Is the volume of the ith cell; v * Is a volume constraint of the structure;
is the volume constraint coefficient; v 0 To design the initial volume of the domain.
8. The topology optimization design method of the fabricated nodes of the reticulated shell structure according to claim 4, wherein the topology optimization constraints considering the contact effect in (3-4) are as follows:
σ i,mas ≤f y,mas
σ j,sla ≤f y,sla
in the formula: f. of y Is the yield strength of the material; sigma i,mas Is the ith unit stress on the major surface of the contact surface; sigma i,sla The jth cell stress on the slave face for the contact face; f. of y,mas The yield strength of the material of the main surface of the contact surface; f. of y,sla Is the yield strength of the contact surface slave surface material; delta r The unit relative sliding distance of the intersection nodes of the master surface and the slave surface; d k,mas 、d m,sla Respectively is the sliding distance of the k-th and m-th intersection points of the main surface and the auxiliary surface of the contact surface; l is i The unit length of the ith unit of the main surface of the contact surface along the sliding direction; [ delta ] is]The maximum allowed slip distance for the unit.
9. The topological optimization design method of the fabricated nodes of the reticulated shell structure according to claim 4, wherein the mathematical model for topological optimization by the SIMP method in (3-6) is as follows:
in the formula: c (X) is strain energy of a topological structure; f is a load vector; u is an integral displacement matrix; v is the optimized volume of the design domain; rho i Cell density of the ith cell; v. of i Is the volume of the ith cell; v * Designing a volume constraint for the domain for the node;
volume constraint coefficients for the design domain; v 0 To the initial volume of the design domain; k is an integral rigidity matrix; rho min Is rho i The lower limit of (d); rho max Is cell density ρ i The upper limit of (3).
10. The topological optimization design method of the fabricated nodes of the reticulated shell structure according to claim 9, wherein the convergence determination of topological optimization by SIMP adopts a dual convergence criterion of an objective function and a cell density, and specifically comprises:
in the formula: c (X) is the strain energy of the structure, namely the objective function value; rho i The cell density q for the ith cell is the number of optimization iteration steps.
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