CN115146377A - Coordinated design method for structural rigidity of aircraft with layout of connecting wings - Google Patents
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Abstract
The invention provides a structural rigidity coordination design method of a connecting wing layout airplane, which adopts a piecewise quadratic function to describe bending/torsion rigidity curves of front and rear wings, utilizes a gradient method to quickly optimize a rigidity curve representation parameter, and further determines the structural configuration and the size based on an evolutionary algorithm. The optimization method has the advantages that the first-stage design variables are few, the second stage is pure numerical calculation, the optimization period is short, and the optimal initial structure scheme of the tie wing layout aircraft with the rigidity coordination characteristic can be quickly obtained.
Description
Technical Field
The invention belongs to the field of aircraft structure design methods, and particularly relates to a coordinated design method for structural rigidity of a connection wing layout aircraft.
Background
The structural design of the high-aspect-ratio wing generally adopts the thin-wall engineering beam theory, namely the internal force (bending moment, shearing force and torque) of the airfoil section can be calculated through the aerodynamic load, the inertial load and the concentrated force, and the size of the section element can be further determined according to a normal stress and shear flow calculation formula. However, for the joined wing layout aircraft, the front wing and the rear wing integrally form a statically indeterminate double-girder structure, the internal force on the front wing and the rear wing can be influenced by the support reaction force at the joint, and the support reaction force at the joint depends on the aerodynamic load distribution, the inertial load distribution and the rigidity distribution of the front wing and the rear wing, so that the internal force of the front wing section and the rear wing section of the joined wing layout aircraft is related to the rigidity distribution of the front wing and the rear wing. At the moment, the internal force cannot be solved, so that the element size cannot be determined, and the traditional theoretical structural design method of the thin-wall engineering beam cannot be applied to the structural design of the connecting wing.
Therefore, the novel optimization design method is crucial to the structural design of the aircraft with the joined wing layout, and the corresponding optimization method can be particularly adopted to design the structural size of the front wing and the rear wing, but the size is taken as the optimization design variable, so that the design variable is more. If the traditional gradient optimization algorithm is adopted for optimization, a local optimal solution is inevitably trapped; if the genetic algorithm is adopted for optimization, the global optimal solution is easy to guarantee, however, numerous design variables bring huge challenges to the evolutionary algorithm and the engineering application thereof, the optimization design period is long, and the method is not suitable for the initial scheme design stage. Therefore, an efficient optimization design model and a solving method suitable for structural rigidity coordination design of the aircraft with the joined wing layout are urgently needed to be developed.
Disclosure of Invention
Aiming at the problems that the traditional design method of the theoretical structure of the thin-wall engineering beam cannot be applied to the structural design of the aircraft with the layout of the connecting wings, and the traditional optimization method has many design variables and long design period, the invention provides a coordinated design method of the structural rigidity of the aircraft with the layout of the connecting wings, which adopts two-stage optimization: in the first-stage optimization, the bending stiffness and the torsional stiffness curves of the front wing and the rear wing are used as design variables, the number of the design variables is small, the optimization period is short, in the second-stage optimization, mechanical analysis or finite element calling is not needed, pure numerical calculation is carried out, and the calculated amount is small; the high-efficiency coordinated design of the structural rigidity of the aircraft with the joined wing layout is realized.
The technical scheme of the invention is as follows:
the coordinated design method for the structural rigidity of the aircraft with the joined wing layout comprises the following steps:
step 1: finite element modeling is carried out on the structure of the aircraft with the layout of the connecting wings; the bending stiffness curve and the torsional stiffness curve of the front wing and the rear wing are fitted by adopting a piecewise quadratic function;
and 2, step: applying the set pneumatic load and the set inertial load to the finite element model nodes established in the step 1;
and 3, step 3: optimally designing by taking the rigidity description parameters of the front wing and the rear wing as design variables and taking the full-aircraft displacement and the minimum torsion angle as design targets to obtain an optimal bending rigidity curve and an optimal torsion rigidity curve of the front wing and the rear wing;
and 4, step 4: and 3, taking the optimal bending stiffness curve and the optimal torsional stiffness curve of the front wing and the rear wing obtained in the step 3 as design targets, taking the structural forms and the structural sizes of the main beams of the front wing and the rear wing as design variables, and taking the set structural sizes and the set weight as constraint conditions to carry out optimal design so as to obtain the optimal structural forms and the optimal structural sizes of the main beams of the front wing and the rear wing.
Further, in step 1, the finite element modeling of the structure of the aircraft with the bonded wing layout comprises: the main beams of the front wing and the rear wing adopt I-shaped cantilever beam models, and the wing rib section is modeled by adopting concentrated mass points and the beam models to obtain a full-aircraft roof beam fishbone structure model.
Further, in step 1, the bending stiffness curve and the torsional stiffness curve of the front wing and the rear wing are expressed as:
where EI denotes the bending stiffness of the front or rear wing, GJ denotes the torsional stiffness of the front or rear wing, EI root ，GJ root And x root Respectively representing the bending stiffness, torsional stiffness and spanwise attitude, EI, of the front or rear wing root section tip ，GJ tip And x tip Respectively representing the bending stiffness, torsional stiffness and spanwise attitude, EI, of the front or rear wing tip section extreme And x EI,extreme Respectively representing the bending rigidity and the spanwise station, GJ, of the extreme bending rigidity profile of the front wing or the rear wing extreme And x GJ,extreme Respectively representing the torsional rigidity and the spanwise station position of the extreme torsional rigidity profile of the front wing or the rear wing.
Furthermore, in the step 2, the pneumatic load is applied to the finite element model nodes by adopting a three-point picking method, a multi-point picking method, a spline interpolation method or a proxy model method.
Further, in the step 2, in the process of applying the pneumatic load to the finite element model nodes, a CR column algorithm of three-dimensional beam unit analysis based on an updated Lagrange method is adopted, the minimum potential energy principle is used for solving, the structural deformation is calculated, and then the unit internal force is obtained.
Further, in step 3, the stiffness description parameters of the front wing and the rear wing as design variables comprise component stiffness, section stiffness, strain energy density and structural equivalent stiffness of the component.
Further, in step 3, an optimization algorithm for optimizing based on gradient information is adopted for optimization design, and the optimization algorithm for optimizing based on gradient information comprises a feasible direction method or a sequential quadratic programming method.
Further, in step 4, the structural types of the main beams serving as design variables comprise circular tube beams and box-type beams; when the circular tubular beam is adopted as a main beam structure type, the main beam structure size design variables are the outer diameter and the wall thickness; when box beams are used as the main beam structural style, the main beam structural dimensional design variables are width, height, web thickness, and flange thickness.
Further, in step 4, an evolutionary algorithm is adopted for optimization design, wherein the evolutionary algorithm comprises a genetic algorithm, a particle swarm algorithm or a fish swarm algorithm.
Advantageous effects
The invention has the beneficial effects that: according to the structural rigidity coordination design method of the aircraft with the coupled wing layout, the bending/torsion rigidity curves of the front wing and the rear wing are described by adopting a piecewise quadratic function, the characteristic parameters of the rigidity curves are rapidly optimized by utilizing a gradient method, and further structural configuration and size are determined based on an evolutionary algorithm. The optimization method has the advantages that the first-stage design variables are few, the second stage is pure numerical calculation, the optimization period is short, and the optimal initial structure scheme of the tie wing layout aircraft with the rigidity coordination characteristic can be quickly obtained.
The invention has stronger applicability: (1) In the first-stage optimization, the bending stiffness and torsional stiffness curves of the front wing and the rear wing are used as design variables, the number of the design variables is small, and the optimization period is short; (2) In the second-stage optimization, mechanical analysis or finite element calling is not needed, pure numerical calculation is achieved, and the calculated amount is small. The two-stage optimization concept is not only suitable for the structural design of the aircraft with the layout of the connecting wings, but also suitable for the structural design of the wings of the conventional aircraft.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1: coupling wing layout aerodynamic layout example of the present invention
FIG. 2: the invention relates to a method for describing a bending and torsion stiffness curve by a piecewise quadratic function
FIG. 3: front wing beam fish bone structure model of optimized embodiment of the invention
FIG. 4 is a schematic view of: rear wing spar type fishbone structure model of optimized embodiment of the invention
FIG. 5: 'multipoint picking' pneumatic load applying method of optimized embodiment of the invention
FIG. 6: schematic diagram of circular tube main beam structure scheme of optimized embodiment of the invention
FIG. 7: schematic diagram of box type main beam structure scheme of optimized embodiment of invention
FIG. 8: genetic algorithm implementation procedure for optimized embodiments of the invention
In the figure: 1. a front wing outer section; 2. a rear wing; 3. hanging the tail; 4. an end plate; 5. a radar antenna; 6. a front wing.
Detailed Description
The following detailed description of embodiments of the invention is intended to be illustrative, and not to be construed as limiting the invention.
Fig. 1 shows a typical joined wing aircraft, which includes a front wing and a rear wing connected by an end plate. Unlike conventional large aspect ratio wing engineering beam force transfer, the coupling wing layout front wing and rear wing force transfer paths are unclear. The bending stiffness and the torsional stiffness of the conventional large-exhibition specific wing are a curve which monotonically decreases, but the optimal stiffness curve mathematical characteristic of the layout of the tie wing is unknown, and the monotonically decreasing function description is not suitable for the stiffness curves of the front wing and the rear wing of the layout of the tie wing. Therefore, in order to better adapt to the rigidity matching requirement of the front wing and the rear wing and widen the design space, when the finite element modeling of the structure of the aircraft with the layout of the connecting wings is carried out, the bending rigidity curve and the torsional rigidity curve of the front wing and the rear wing adopt the piecewise quadratic function fitting and are defined by parameterization, and the considered parameters are the position of the segmentation point of the piecewise quadratic function, the front slope and the rear slope of the segmentation point and the positioning parameters of the quadratic functions in different segmentation areas.
The specific piecewise quadratic function is:
where EI denotes the bending stiffness of the front or rear wing, GJ denotes the torsional stiffness of the front or rear wing, EI root ，GJ root And x root Respectively representing the bending stiffness, torsional stiffness and spanwise attitude, EI, of the front or rear wing root section tip ，GJ tip And x tip Respectively representing the bending stiffness, torsional stiffness and spanwise attitude, EI, of the front or rear wing tip section extreme And x EI,extreme Respectively representing the bending rigidity and the spanwise station, GJ, of the extreme bending rigidity profile of the front wing or the rear wing extreme And x GJ,extreme Respectively representing the torsional rigidity and the spanwise station position of the extreme torsional rigidity profile of the front wing or the rear wing.
It can be seen that the characteristic variables of the bending stiffness curves of the front wing and the rear wing are as follows: EI (electronic instrument) root 、EI tip 、x EI,extreme 、EI extreme The torsional rigidity curve characterization variables of the front wing and the rear wing are respectively as follows: GJ root 、GJ tip 、x GJ,extreme 、GJ extreme A total of 16 characterizing variables.
In the specific finite element modeling of the structure of the aircraft with the layout of the connecting wings, the main beams of the front wing and the rear wing adopt I-shaped cantilever beam models, and the wing rib section is modeled by adopting concentrated mass points and beam models to obtain a full-aircraft Liangshi fishbone structure model. The front wing and the rear wing structural models are shown in fig. 3 and 4.
Then applying the set pneumatic load and the set inertial load to the nodes of the established finite element model; the pneumatic load can be applied to the finite element model nodes by adopting a three-point picking method, a multi-point picking method, a spline interpolation method or a proxy model method. In the process of applying the pneumatic load to the finite element model nodes, a CR column algorithm of three-dimensional beam unit analysis based on an updated Lagrange method is adopted, the minimum potential energy principle is applied to solve, structural deformation is calculated, and then unit internal force is obtained.
In this embodiment, a "multi-point picking" method is used to apply a pneumatic load to a structural node of a finite element model, and the specific process is as follows:
assuming that a virtual beam element exists between all the structural points and the pneumatic points, as shown in fig. 7, the virtual beam element is a cantilever beam with one end of the pneumatic point being a fixed support, and the structural point at the free end of the cantilever beam is distributed to the load P i The deformation energy is
Where EJ is the bending stiffness of the virtual beam element. l i Is the length of the ith cantilever beam, u i Is the deformation energy of the ith cantilever beam。
The deformation of the entire system can then be
Wherein U is the total deformation energy of the system, and n is the total number of the cantilever beams.
The load distributed to the structural points is such that the deformation energy of the system is minimal and the static equivalence conditions are met, i.e.
In the formula, X i ,Z i The x and z coordinates of node i, respectively.
Lagrange multiplier method for establishing Lagrange function
In the formula, λ x ,λ z Is a Lagrange multiplier;
making 3EJ =1, namely
Substituting the formula (6) into the formula (3) to obtain
From formula (7) to give λ, λ x ,λ z And (4) then, replacing the structure points with the formula (6) to obtain the loads distributed by the structure points, wherein the loads of each pneumatic force point on the whole pneumatic network point group are distributed to the structure point group according to the method to obtain the node pneumatic force load array.
And then, taking rigidity description parameters of the front wing and the rear wing as design variables, including component rigidity, section rigidity, strain energy density and structural equivalent rigidity of each part, and taking the minimum of full-aircraft displacement and torsion angle as a design target, and performing optimization design by adopting an optimization algorithm for optimizing based on gradient information, such as a feasible direction method or a sequential quadratic programming method, to obtain a bending rigidity curve and a torsion rigidity curve of the front wing and the rear wing, which are matched with the optimal front wing and the optimal rear wing.
And then, performing optimal design by taking the obtained optimal bending stiffness curve and torsional stiffness curve of the front wing and the rear wing as design targets, taking the structural types and the structural sizes of the main beams of the front wing and the rear wing as design variables and taking the set structural sizes and weights as constraint conditions to obtain the optimal structural types and structural sizes of the main beams of the front wing and the rear wing.
The structural types of the main beam as design variables comprise a round tubular beam and a box beam; when the circular tubular beam is adopted as a main beam structure, the design variables of the main beam structure size are the outer diameter D and the wall thickness t; when a box beam is used as the main beam structure, the design variables of the main beam structure are width b, height h, web thickness t1 and flange plate thickness t2. And the evolutionary algorithm can adopt a genetic algorithm, a particle swarm algorithm or a fish swarm algorithm. The evolutionary algorithm adopted in the embodiment is a real number coding genetic algorithm, the crossover operator adopts analog binary crossover, the mutation operator adopts polynomial mutation and keeps consistent with the reference setting in the NSGA-II algorithm, and the implementation steps of the genetic algorithm are shown in FIG. 8.
In the embodiment, the final optimization result is reduced by 60% compared with the initial scheme, the torsion angle is reduced by 80%, the first-stage optimization is performed, the design variables are reduced from hundreds of dimensions to more than ten, the optimization design period is reduced by 80%, and the efficient coordinated design of the structural rigidity of the aircraft with the joined wing layout is realized
Although embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are exemplary and not to be construed as limiting the present invention, and that those skilled in the art may make variations, modifications, substitutions and alterations within the scope of the present invention without departing from the spirit and scope of the present invention.
Claims (9)
1. A coordinated design method for structural rigidity of a connecting wing layout aircraft is characterized by comprising the following steps: the method comprises the following steps:
step 1: finite element modeling of the structure of the aircraft with the joined wing layout is carried out; the bending stiffness curve and the torsional stiffness curve of the front wing and the rear wing are fitted by adopting a piecewise quadratic function;
and 2, step: applying the set pneumatic load and the set inertial load to the finite element model nodes established in the step 1;
and step 3: optimally designing by taking the rigidity description parameters of the front wing and the rear wing as design variables and taking the full-aircraft displacement and the minimum torsion angle as design targets to obtain an optimal bending rigidity curve and an optimal torsion rigidity curve of the front wing and the rear wing;
and 4, step 4: and (4) taking the optimal bending stiffness curve and torsional stiffness curve of the front wing and the rear wing obtained in the step (3) as design targets, taking the structural types and the structural sizes of the main beams of the front wing and the rear wing as design variables, and taking the set structural sizes and weights as constraint conditions to carry out optimal design, so as to obtain the optimal structural types and the structural sizes of the main beams of the front wing and the rear wing.
2. A method for coordinately designing structural rigidity of a tie wing aircraft according to claim 1, wherein: in step 1, the finite element modeling of the structure of the aircraft with the layout of the connecting wing comprises the following steps: the main beams of the front wing and the rear wing adopt I-shaped cantilever beam models, and the wing rib section is modeled by adopting concentrated mass points and the beam models to obtain a full-aircraft roof beam fishbone structure model.
3. A coordinated design method for structural rigidity of a join wing layout aircraft according to claim 1 or 2, characterized in that: in step 1, the bending stiffness curve and the torsional stiffness curve of the front wing and the rear wing are expressed as:
where EI denotes the bending stiffness of the front or rear wing, GJ denotes the torsional stiffness of the front or rear wing, EI root ，GJ root And x root Respectively, the bending rigidity, torsional rigidity and the spanwise position, EI, of the root section of the front wing or the rear wing tip ，GJ tip And x tip Respectively, the bending rigidity, torsional rigidity and the spanwise position, EI, of the front wing or rear wing tip section extreme And x EI,extreme Respectively representing the bending rigidity and the spanwise station, GJ, of the extreme bending rigidity profile of the front wing or the rear wing extreme And x GJ,extreme Respectively representing the torsional rigidity and the spanwise station position of the extreme torsional rigidity profile of the front wing or the rear wing.
4. A method for coordinately designing structural rigidity of a tie wing aircraft according to claim 1, wherein: and step 2, applying the pneumatic load to the finite element model nodes by adopting a three-point picking method, a multi-point picking method, a spline interpolation method or a proxy model method.
5. A coordinated design method for structural rigidity of a join wing layout aircraft according to claim 4 is characterized in that: in the step 2, in the process of applying the pneumatic load to the finite element model nodes, a CR column algorithm of three-dimensional beam unit analysis based on an updated Lagrange method is adopted, the minimum potential energy principle is applied to solve, structural deformation is calculated, and then unit internal force is obtained.
6. A method for coordinately designing structural rigidity of a tie wing aircraft according to claim 1, wherein: in step 3, the rigidity description parameters of the front wing and the rear wing as design variables comprise component rigidity, section rigidity, strain energy density and structural equivalent rigidity of the part.
7. A method for coordinately designing structural rigidity of a tie wing aircraft according to claim 1, wherein: in step 3, an optimization algorithm for optimizing based on gradient information is adopted for optimization design, wherein the optimization algorithm for optimizing based on gradient information comprises a feasible direction method or a sequence quadratic programming method.
8. A method for coordinately designing structural rigidity of a tie wing aircraft according to claim 1, wherein: in step 4, the structural forms of the main beams serving as design variables comprise circular tube beams and box-type beams; when the circular tubular beam is adopted as a main beam structure type, the main beam structure size design variables are the outer diameter and the wall thickness; when box beams are used as the main beam structural style, the main beam structural dimensional design variables are width, height, web thickness, and flange thickness.
9. A coordinated design method for structural rigidity of a tie wing aircraft according to claim 1, characterized in that: and 4, performing optimization design by adopting an evolutionary algorithm, wherein the evolutionary algorithm comprises a genetic algorithm, a particle swarm algorithm or a fish swarm algorithm.
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