CN112699477B - Method for determining large-size beam structure configuration under multi-constraint optimization condition - Google Patents
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Abstract
The invention belongs to the technical field of structural strength analysis. The invention provides a structural configuration determining method of a large-size beam under a multi-constraint optimization condition, which adopts a finite element method and an optimization algorithm to optimize the structural configuration and the structural parameters of a girder structure in a combined way, so as to obtain an optimized configuration and optimal structural parameters meeting various constraint conditions.
Description
Technical Field
The invention belongs to the technical field of structural strength analysis, and particularly relates to a structural configuration design of a large-size beam with a large load, a large width-to-thickness ratio and a complex structural failure form.
Background
The large-size beam structure is widely applied to large-scale airplanes, and has the advantages of large height direction and width direction, small girder structure width-thickness ratio, coupling of various stress forms, complex stress working conditions and complex structure failure forms.
The prior art has mastered the design method of the small-size thin web metal beam structure configuration at present, and solves the related problems in the processing, manufacturing and engineering application processes. However, the design and application of the large-size structure from theoretical analysis to manufacturing processing and experimental verification are all challenges which we have not met in the early stage, and the model design difficulty is solved and the technical bottleneck is broken through by carrying out research, comparing and analyzing advantages and disadvantages of different structural forms and determining an analysis method.
Disclosure of Invention
The invention provides a structural configuration determining method of a large-size beam under a multi-constraint optimization condition, which adopts a finite element method and an optimization algorithm to optimize the structural configuration and the structural parameters of a girder structure in a combined way, so as to obtain an optimized configuration and optimal structural parameters meeting various constraint conditions.
The technical scheme of the invention is as follows: the method for determining the structural configuration of the large-size beam under the multi-constraint optimization condition is provided, wherein the large-size beam 1 is connected with a supporting wall plate 3 at the bottom, the large-size beam 1 is connected with large-size supporting frames 2 at two sides, and the upper bottom edge of the large-size beam 1 is a free edge; the structural configuration determining method comprises the following steps:
step 1, carrying out energy minimization and finite element topological optimization under a variable density method under a first multi-constraint condition on a large-size beam bearing an in-plane concentrated load and an out-of-plane concentrated load to obtain a force transmission structure configuration of the large-size beam under a main load;
step 2: according to the obtained force transmission route result of the main configuration of the large-size beam, the continuous redesign of the reinforcement configuration under the main load, the redesign of the sandwich structure under the out-of-plane load and the redesign of the diffusion piece under the main load are carried out;
step 3: after the step 2 is completed, carrying out structural energy minimization and finite element topological optimization under a first multi-constraint condition on a large-size Liang Ci force transmission route under a secondary design load to obtain a force transmission structure configuration of the large-size beam under the secondary load, and combining the force transmission structure configuration with a force transmission structure configuration under a main load to obtain an optimized configuration of the whole large-size beam;
step 4: and (3) taking the weight minimization as an objective function, and optimizing reinforcement parameters and thickness parameters of the whole large-size beam optimization configuration by using a quadratic programming method under a second multi-constraint condition.
In step 1, a preliminary finite element model of a large-size beam structure is built, static finite element preliminary analysis is carried out on the large-size beam, in-plane concentrated load F1 and out-of-plane concentrated load F2 are determined to be main design loads, frame-to-beam distributed shear force Q, and frame and wallboard surrounding structures are given to the beam structure bending moment M and axial pressure load P to be secondary design loads.
Further, the first multi-constraint condition comprises a structural volume ratio constraint of 0.2-0.4 before and after topological optimization and a structural symmetry plane geometric constraint; the second multi-constraint condition comprises volume ratio constraint of 0.1-0.2 before and after size optimization, upper bottom edge deformation constraint of 10-15mm after size optimization and stability constraint of force transmission structure configuration under main load.
Further, in step 1, the force transfer structure configuration under the main load is composed of a ribbed structure connected to large-sized support frames on both sides.
In step 2, according to the obtained force transfer structure configuration under the main load after topological optimization, based on the principle of maximum material utilization rate, designing ribs of the reinforcement structure into a rectangle; based on the principle of structural continuity, the reinforced structure is designed into a continuous frame structure.
Further, in step 2, the sandwich structure is designed as a combined structure composed of an inner panel, an outer panel and a core between the inner and outer panels, and is used for bearing bending moment generated by the out-of-plane concentrated load F2.
Further, in step 2, the diffuser redesign under the main load includes a pi-shaped diffuser embedded in the connection point of the reinforcement structure for converting the concentrated load into a distributed diffuser load.
Further, in step 3, the force transfer structure under the secondary load is configured as a combined structure with a rod as a main component and a plate as an auxiliary component.
The invention has the technical effects that: the structural configuration optimization and the structural parameter optimization under the multi-constraint condition are innovatively carried out on the large-size beam with large load, large width-thickness ratio and complex structural failure form by adopting a mode of combining a finite element method and an optimization algorithm.
Drawings
FIG. 1 is a schematic top view of a large-scale beam structure;
FIG. 2 is a schematic diagram of a large beam structure;
FIG. 3 is a multi-constraint topology optimization finite element model under the action of an in-plane concentrated load F1 and an out-of-plane concentrated load F2;
FIG. 4 is a graph of topology optimization transmission under the action of an in-plane concentrated load F1 and an out-of-plane concentrated load F2;
FIG. 5 is a structural continuity in design;
FIG. 6 is a honeycomb sandwich structure under an out-of-plane concentrated load F2;
FIG. 7 shows a diffuser structure under concentrated loads F1, F2;
FIG. 8 is a diagram of a honeycomb sandwich-stiffener combination configuration;
fig. 9 is a parameter optimization result.
Detailed Description
A large aircraft frame beam type structure is known, and comprises a large-size beam 1, a large-size supporting frame 2 and a supporting wall plate 3, wherein the large-size beam is used as a key stress piece, the periphery of the large-size beam is supported by the frame and the wall plate, and the upper bottom edge of the large-size beam is a free edge, as shown in fig. 1.
The embodiment provides a method for determining the structural configuration of a large-size beam under the multi-constraint optimization condition, which specifically comprises the following steps:
a) Preliminary stress analysis was performed on the structure of fig. 1:
the girder structure of fig. 1 mainly bears in-plane concentrated load F1, out-of-plane concentrated load F2, frame-to-girder distributed shear force Q, and bending moment M and axial pressure load P imparted to the girder structure by structures around the frames and the wall plates, see fig. 2.
And establishing a large-size beam structure preliminary finite element model, respectively and independently applying concentrated loads F1 and F2, distributing shearing force Q, endowing the beam structure with bending moment M and distributing axial pressure load P by the frame and wall plate surrounding structures. The static force results show that the concentrated loads F1 and F2 are main loads influencing the structural configuration, so the configuration design takes the in-plane concentrated load F1 and the out-of-plane concentrated load F2 as main design loads.
b) Based on the concentrated loads F1 and F2, adopting a variable density method to topologically optimize the beam to obtain a main force transmission route of the large-size beam:
the structural energy is minimized as an objective function, the structural volume ratio is set to be 0.2-0.4 as a constraint condition, the structural symmetry plane is used as a geometric constraint limit, the structural energy is subjected to topological optimization by a variable density method, 2 modified tetrahedron units are adopted for model dispersion, the unit grid size is 15mm, the result of the optimized force transmission route is shown in fig. 3.
c) Based on the topology optimization results of the in-plane concentrated load F1 and the out-of-plane concentrated load F2 in the step b), engineering stress analysis is carried out, structural continuity redesign is carried out on a topology optimization area, and the purpose of concentrated load diffusion is achieved by arranging the vertical ribs 4 and the inclined ribs 5 under the action of the in-plane concentrated load F1, as shown in fig. 5.
d) Under the action of the out-of-plane concentrated load F2, the large-size beam bears the bending moment M1 in the XZ plane, the problem of structural stability is outstanding, the honeycomb sandwich structure has good finishing bending resistance, the in-plane bending moment is converted into the pulling and pressing of the outer panel and the inner panel, and the honeycomb sandwich structure of FIG. 6Has good out-of-plane bending stiffness ei=1/12 bE f (H 3 -h 3 )；
Wherein EI is the bending rigidity of the structure, b is the width of the sandwich structure, E f Is of thickness t f The tensile modulus H, h of the upper and lower panels is the overall height of the sandwich structure and the core height, respectively.
e) The concentrated load F1 and the concentrated load F2 in the plane are required to be provided with concentrated load diffusion pieces 6 and 7 under the action of the concentrated load F2 in the out of plane, and the configuration form of the diffusion pieces is n-shaped, as shown in figure 7.
f) The force transmission areas except the in-plane concentrated load F1 and the out-of-plane concentrated load F2 are designed into a reinforced structure form, and the honeycomb sandwich-reinforced combined structure is shown in figure 8.
g) And carrying out parameter optimization on the honeycomb sandwich-reinforcement combination configuration and the subareas.
The structural weight is minimized as an objective function, the volume ratio of 0.1, the deformation of the upper bottom edge (the maximum deformation of 15 mm) and the structural stability are taken as constraint conditions, the reinforcement parameters and the thickness parameters of the whole large-size beam optimization configuration are optimized by using a quadratic programming method, and the optimized structural parameters are divided into b1, b2, b3 and b4 areas, as shown in figure 9.
Claims (7)
1. A method for determining the structural configuration of a large-size beam under the multi-constraint optimization condition comprises the steps that the large-size beam (1) is connected with a supporting wall plate (3) at the bottom, the large-size beam (1) is connected with large-size supporting frames (2) at two sides, and the upper bottom edge of the large-size beam (1) is a free edge;
the method for determining the structural configuration is characterized by comprising the following steps:
step 1, carrying out energy minimization and finite element topological optimization under a variable density method under a first multi-constraint condition on a large-size beam bearing an in-plane concentrated load and an out-of-plane concentrated load to obtain a force transmission structure configuration of the large-size beam under a main load; in the step 1, a preliminary finite element model of a large-size beam structure is established, static finite element preliminary analysis is carried out on the large-size beam, in-plane concentrated load F1 and out-of-plane concentrated load F2 are determined as main design loads, frame-to-beam distributed shear force Q, and frame and wallboard surrounding structures are endowed with beam structure bending moment M and axial pressure load P as secondary design loads;
step 2: according to the obtained force transmission route result of the main configuration of the large-size beam, the continuous redesign of the reinforcement configuration under the main load, the redesign of the sandwich structure under the out-of-plane load and the redesign of the diffusion piece under the main load are carried out;
step 3: after the step 2 is completed, carrying out structural energy minimization and finite element topological optimization under a first multi-constraint condition on a large-size Liang Ci force transmission route under a secondary design load to obtain a force transmission structure configuration of the large-size beam under the secondary load, and combining the force transmission structure configuration with a force transmission structure configuration under a main load to obtain an optimized configuration of the whole large-size beam;
step 4: and (3) taking the weight minimization as an objective function, and optimizing reinforcement parameters and thickness parameters of the whole large-size beam optimization configuration by using a quadratic programming method under a second multi-constraint condition.
2. The method for determining the structural configuration of the large-size beam according to claim 1, wherein the first multi-constraint condition comprises a structural volume ratio constraint of 0.2-0.4 before and after topological optimization and a structural symmetry plane geometric constraint; the second multi-constraint condition comprises volume ratio constraint of 0.1-0.2 before and after size optimization, upper bottom edge deformation constraint of 10-15mm after size optimization and stability constraint of force transmission structure configuration under main load.
3. The method of determining the configuration of a large-scale beam structure according to claim 1, wherein in step 1, the force-transmitting structure configuration under the main load is composed of a reinforcement structure connected to large-scale support frames on both sides.
4. The method for determining the structural configuration of the large-size beam according to claim 3, wherein in the step 2, according to the obtained structural configuration of the force transmission under the main load after topological optimization, ribs of the reinforcement structure are designed to be rectangular based on the principle of maximum material utilization; based on the principle of structural continuity, the reinforced structure is designed into a continuous frame structure.
5. The method of determining the configuration of a large-scale beam structure according to claim 4, wherein in the step 2, the sandwich structure is designed as a combined structure composed of an inner panel, an outer panel and a core between the inner and outer panels for receiving bending moment generated by the out-of-plane concentrated load F2.
6. The method of claim 5, wherein in step 2, the diffuser redesign under the primary load comprises a pi diffuser embedded in the connection points of the reinforcement structure for converting the concentrated load into a distributed diffuser load.
7. A method of determining the configuration of a large beam structure according to claim 1, wherein in step 3, the force transfer structure under the secondary load is configured as a bar-based, plate-based composite structure.
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