CN106874572B - Lightweight design method of aircraft fuel tank bearing structure considering oil mixing characteristic - Google Patents
Lightweight design method of aircraft fuel tank bearing structure considering oil mixing characteristic Download PDFInfo
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Abstract
The invention relates to a lightweight design method of an aircraft fuel tank bearing structure considering oil mixing characteristics, which aims to reduce the weight of a rib plate in the aircraft fuel tank as an optimization target and is assisted by strength constraint and fuel oil mixing constraint to realize the purpose of reducing the weight of the aircraft structure under the condition of ensuring that the design performance is not reduced; compared with mainstream topological optimization methods such as a variable density method and a homogenization method, the method can effectively control the shape of the boundary of the opening, ensure simple and regular boundary and obviously improve the manufacturability of the design scheme; meanwhile, the method completes the simulation of the fuel shaking behavior in the fuel tank by using the related knowledge of smooth particle fluid dynamics, and still keeps the design result to obtain good oil penetration and wave suppression performance on the premise of reducing the mass of the bearing plate as much as possible, thereby shortening the fuel measurement time, promoting the feedback rate, accelerating the recovery time of the gravity center of the airplane and finally endowing the airplane with better flight control performance.
Description
[ technical field ] A method for producing a semiconductor device
The invention belongs to the field of lightweight design of bearing plates inside an aircraft fuel tank, and particularly relates to a lightweight design method of an aircraft fuel tank bearing structure considering oil mixing characteristics.
[ background of the invention ]
In order to fully utilize the limited space in the airplane, the modern airplane is generally provided with a wing structure oil tank in the wing; the design extremely improves the embarrassment of poor utilization of wing space, and obviously increases the endurance of the airplane; however, the wing fuel tank usually covers the main bearing structure of the wing, and the structures with bearing effect, such as longitudinal walls, wing ribs and the like, are generally directly immersed in fuel, so that the fuel is hindered from moving while the wing is supported, the gravity center adjusting time is delayed, and the flight control performance is finally weakened; in order to solve the problems, the traditional method generally selects a larger or even obviously redundant opening design on the plate structures to improve the oil mixing performance, but the means is easy to cause the fluctuation of the fuel liquid level to be aggravated, prolong the oil measuring time of the airplane and finally weaken the flight control performance; meanwhile, on the premise of maintaining the strength of the bearing structure unchanged, the thickness and the mass of structures such as longitudinal walls, wing ribs and the like are increased easily due to the large redundant open hole design, and the design is often considered; in addition to this, there is another problem with the design of the load bearing panels: in order to reduce the quality of the airplane, designers at home and abroad often select topological optimization means such as a homogenization method, a variable density method and the like to complete the opening design of the bearing structure, however, the methods all have the problems of a checkerboard structure, unclear hole boundaries, irregular hole shapes and the like, so that the manufacturability of the design result is poor.
[ summary of the invention ]
In order to overcome the defects of the prior art, the invention provides a lightweight design method of an aircraft fuel tank bearing structure considering the oil mixing characteristic, and the method uses a topology optimization design method based on topology boundary explicit expression, so that the quality of the bearing structure can be reduced on the premise of maintaining the strength of the bearing structure not to be reduced, the hole boundaries of the bearing structure can be ensured to be clear and regular, and the bearing structure is easy to manufacture.
In order to achieve the purpose, the invention adopts the technical scheme that:
the method comprises the following steps:
1) selecting a design working condition;
2) setting design variables of the opening, storing the design variables in the vector
Performing the following steps;
3) defining an area allowing hole opening on the bearing plate as a design area, carrying out grid division on the design area, and describing the hole opening area according to a level set function phi (x, y); constructing a target function;
4) performing mechanical optimization design and fuel flow simulation, determining constraint conditions and constructing a constraint function;
5) and solving partial derivatives of the target function and the constraint function to each design variable by using a finite difference method, substituting the target function value, the constraint function value and the obtained partial derivatives into an MMA optimization algorithm, iteratively updating the variables until the target function converges under the condition of meeting constraint conditions, and finishing the design of the open pore of the bearing plate under the design working condition.
Further, in the step 3), a four-node quadrilateral grid is used for carrying out grid division on the design area to obtain Esum units and Nsum nodes; the constructed objective function is a quality function of the bearing plate, and the construction steps specifically comprise:
301) the level set function φ (x, y) satisfies the following condition: taking a point with coordinates (x, y) in the design area, and if the point is in the opening area, the corresponding level set function value is larger than zero; if on the hole boundary, the level set function value of the point is zero, and if the point is outside the hole, the level set function value is less than zero;
302) n is uniformly arranged on the bearing platerecA rectangular hole and ncirRound holes, each opening of which is expressed by a level set function respectively, and obtaining (n)rec+ncir) A number of different level set functions;
303) integrating the level set functions obtained in the step 302), wherein in the hole opening area, the level set function values of the nodes are all set to be 1, and the values outside the hole are set to be 0;
304) defining the mass of the intact non-perforated original bearing plate as a constant MComplete (complete)The mass function of the load bearing plate is then:
wherein n iswThe number of nodes with level set function value of 1 in the four nodes on the w-th unit is rhoSupport for supportingDensity of material used for the load-bearing plates, VwIs the volume of unit number w.
Further, the specific step of integrating the obtained level set function distributions in step 303) is:
3031) to be obtained (n)rec+ncir) The individual level set function performs the following: setting the level set function value corresponding to the node in the open pore coverage area as 1 by using a Heaviside function, and setting the rest as 0;
3032) subjecting (n) obtained in step 3031)rec+ncir) The level set function corresponding to each opening is assembled into a level set, and the assembled level set function value phi (x) corresponding to the p-th nodep,yp) Is defined as:
wherein phi (x)p,yp)qThe value of the level set function at the p node for the q aperture.
Further, the constraint conditions include a position constraint, a shape constraint, an intensity constraint, a cross-oil performance constraint and a fuel level fluctuation constraint.
Further, assuming the load-bearing plate is rectangular with a Length and a Width, the position constraint function is:
0≤x≤Length,0≤y≤Width；
the shape constraint function is:
the radius r of the circular hole satisfies: r is more than or equal to 0; the length L and the width T of the rectangular hole meet the following conditions: l is more than or equal to 0, and T is more than or equal to 0.
Further, the strength constraints include stress strength constraints, fatigue strength constraints, and stability strength constraints.
Further, the oil cross-flow performance constraint function is tBalancing≤tStandard of merit，tBalancingFor the equilibrium duration, tStandard of meritAnd giving the maximum recovery time length of the fuel for the actual project.
Further, the balance duration tBalancingThe concrete solving steps comprise:
4011) simulating a fuel oil flow process of a fuel oil tank with a small liquid filling ratio by using an SPH method;
4012) according to the result of the fuel flow simulation in the step a), the centroid coordinate of the fuel at the time t is calculated and is a function formed by time, the position of the opening and the shape of the opening, and the centroid coordinate is written as
4013) Constructing a virtual fluid which is 5 times thicker than the fuel oil, and determining that the motion state of the virtual fluid is a no-flow state when the sum of the accelerations of all particles of the virtual fluid is less than 1% of the sum of the accelerations at the initial moment;
4014) assuming that the tank contains l compartments, the fuel centroid of compartment e at time t is set to
The center of mass of the chamber e in the no-flow state is
Constructing a balance function
To measure the fluctuation of the fuel centroid at the moment t, the expression is as follows:
wherein the content of the first and second substances,
the average fluctuation amplitude of the fuel centroid of all cabins at the time t relative to the centroid in a no-flow state is shown, and V is the total volume of the fuel;
4015) if it is not
Three successive times lower than the standard value BStandard of meritIf it is lower than B for the first timeStandard of meritIs the equilibrium duration tBalancing；BStandard of meritAnd determining the allowable error of fuel measurement given by actual engineering.
Further, the level fluctuation constraint function is
Wherein FStandard of meritAnd (4) fuel measurement allowable errors given for engineering practice.
Further, assuming that the tank contains l compartments,
the specific solving step comprises:
4021) defining the time T from the initial time to the time when the fuel is balancedBalancing(ii) a Simulating fuel oil flow process by using SPH method, and calculating TBalancingThe position and pressure of all fuel particles at the moment;
4022) selecting TBalancingAll points with zero pressure at all times are used as surface particles of the fuel oil, and the surface particles s are selectedeA plurality of; selecting any three non-collinear points of the No. e bulkhead under the no-flow state, and marking as Ae、Be、CeThen T isBalancingMinute particle of fuel liquid level at moment ieDistance d from equilibrium no-flow levelieComprises the following steps:
then
Comprises the following steps:
the invention has the beneficial effects that:
according to the method, the rigidity and the strength are improved through mechanical optimization design, the fuel fluctuation is inhibited and the fuel oil mixing performance is improved through fuel oil flow simulation, the mass of a rib plate in an aircraft fuel tank is reduced as an optimization target, and strength constraint and fuel oil mixing constraint are assisted, so that the open pore design is optimized, and the mass of a support plate is reduced under the condition that the design performance is not reduced; the invention uses the level set function to describe the open pore of the bearing plate, and uses the topological optimization design method based on the explicit expression of the topological boundary, so that the bearing structure with clear open pore boundary and simple and controllable open pore shape can be obtained, the quality of the bearing structure can be reduced on the premise of maintaining the strength of the bearing structure without reduction, the pore boundary of the bearing structure can be ensured to be clear and regular, the manufacture is easy, and the manufacturability is obviously better than that of the similar topological optimization method; because the method simultaneously considers the quality, the strength, the oil mixing performance and the wave suppression performance of the bearing structure in the oil tank, the obtained design result can endow the airplane with good feedback capacity, ensure good flight control performance, simultaneously can lighten the quality of the airplane, improve the effective load and the endurance capacity of the airplane and has obvious engineering advantages; the invention applies a topological optimization method and a fluid simulation technology, and reduces the quality of the bearing structure to the maximum extent on the premise of improving the oil mixing performance, inhibiting the liquid level fluctuation and ensuring that the strength of the bearing plate meets the engineering requirements.
Furthermore, the invention uses smooth particle fluid dynamics knowledge (hereinafter referred to as 'SPH') to simulate fuel flow, and ensures that the oil mixing capability and the fluctuation inhibition capability of the oil tank are within the engineering allowable range, so that a more real and accurate fluid simulation result can be obtained, and the calculation amount is relatively small, thereby being obviously superior to similar fluid simulation software, helping the aircraft to recover the center of gravity as soon as possible, and endowing the aircraft with better flight control performance.
[ description of the drawings ]
FIG. 1 is a schematic diagram of the basic concept of the present embodiment;
FIG. 2(a) is a schematic view of a small liquid filling ratio operating condition with a liquid filling ratio of 30% at an inclination angle of 15 degrees, wherein FIG. 2(b) is a schematic view of a medium liquid filling ratio operating condition with a liquid filling ratio of 50% at an inclination angle of 15 degrees, and wherein FIG. 2(c) is a schematic view of a large liquid filling ratio operating condition with a liquid filling ratio of 70% at an inclination angle of 15 degrees;
FIG. 3 is an opening layout of a carrier plate before (initial) optimization according to an embodiment of the present invention;
FIG. 4(a) is a front view of the holes obtained after assembly as a function of the level set for each point of the carrier plate, FIG. 4(b) is a three-dimensional illustration of the distribution of the level set of the carrier plate, and FIG. 4(c) is an enlarged view of a portion A of FIGS. 4(a) and 4 (b);
FIG. 5(a) is a true pore structure, FIG. 5(b) is a pore structure expressed by a level set function, and FIG. 5(c) is a pore structure in a finite element mesh;
FIG. 6 is a schematic diagram of simulated fuel flow and an optimization result in the embodiment of the invention;
FIG. 7 is an optimized layout of openings in carrier plates;
FIG. 8 is a graph of fuel fluctuation intensity ratio over time before and after optimization;
FIG. 9(a) is a diagram illustrating the boundary of an opening according to the present invention, and FIG. 9(b) is a diagram illustrating the boundary of an opening according to a conventional topology optimization method;
[ detailed description ] embodiments
The present invention will be described in further detail with reference to the accompanying drawings.
The invention comprises the following steps:
1) selecting design condition-30% liquid filling ratio
The method takes 30% of liquid filling ratio as a preferential design working condition, defines the working condition as a working condition with small liquid filling ratio, and gradually selects a larger liquid filling ratio for design in the subsequent steps;
2) describing design variables
The method is described by taking the most adopted rectangle and circle in engineering as the shape of the opening, and the openings with other shapes can also be obtained by changing the level set function according to the step 3;
when rectangular apertures are used, each aperture is set to contain 5 design variables, respectively: coordinate x of central point of rectangular hole0、y0The length L and the width T of the rectangular hole and the inclination angle theta of the rectangular hole; when using circular openings, each hole is set to contain 3 design variables, respectively: circular hole center coordinate x0、y0And a radius r;
before the optimization begins, n is uniformly arranged on the bearing plate by the methodrecA rectangular hole and ncirRound holes, in this case (5 n)rec+3ncir) A design variable; defining these design variables to be stored in vectors
Performing the following steps;
3) constructing an objective function
The method takes the reduction of the mass of the bearing plate as a design target, an objective function is a mass function of the bearing plate, and the solving method comprises the following steps:
301) design area meshing
Defining an area allowing the opening on the surface of the bearing plate as a design area; uniformly and compactly dividing the bearing plate by using a four-node quadrilateral grid to obtain Esum units and Nsum nodes;
302) description of the open area
Taking a point in the design area, wherein the coordinate of the point is (x, y), and if the point is in the opening area, the corresponding level set function value phi (x, y) is greater than zero; if on the hole boundary, the level set function value phi (x, y) for that point is zero, and if the point is outside the hole, the level set function value is less than zero; at the moment, the opening area can be described according to the level set function phi (x, y); selecting a proper level set function to describe the open pore area according to the setting;
303) obtaining a level set function
Aiming at rectangular open pores, the method selects a level set function as follows:
aiming at circular holes, the method selects a level set function as follows:
φ(x,y)＝-(x-x0)2-(y-y0)2+r2(2)
the method is co-arranged with (n)rec+ncir) Calculating the level set function value of each hole on all Nsum nodes, and writing the level set function value of the p-th node corresponding to the q-th hole as phi (x)p,yp)q；
In the method, each opening is expressed by a level set function, and finally (n) is obtainedrec+ncir) A number of different level set function distributions;
304) design area level set assembly
All (n) obtained in step 303rec+ncir) Each opening corresponds to (n)rec+ncir) The method integrates different levels, and comprises the following specific steps:
3041) arranging the level set distribution corresponding to each open pore
(n) obtained in step 303rec+ncir) The individual level set function distributions are processed as follows: setting the level set function value corresponding to the node in the open pore coverage area as 1 by using a Heaviside function, and setting the rest as 0;
3042) the horizontal collection distribution of each opening is assembled into a whole
All of (n) obtained in step 3041rec+ncir) The level set function corresponding to each opening is assembled into a level set, and the assembled level set function value phi (x) corresponding to the p-th nodep,yp) Is defined as:
in the above formula, phi (x)p,yp)qThe values of the level set distribution function corresponding to the qth opening at the pth node are obtained in step 303;
to this end, all the openings have been integrated, in the area of the openings, the level set function values of the nodes are all set to 1, outside the holes to 0;
305) constructing a mass function
Defining the mass of the intact non-perforated original bearing plate as a constant MComplete (complete)Then, the functional expression of the mass M of the load bearing plate is written as:
in the above formula nwIn four nodes on the w-th cellNumber of nodes having a level set function value of 1, ρSupport for supportingDensity of material used for the load-bearing plates, VwThe volume of the w-th unit can be calculated by coordinates of four nodes on the unit and the thickness of the bearing plate;
the quality function obtained so far is the objective function;
4) constructing a location constraint function
The openings are uniformly distributed in the bearing plate, so that the method restrains the central coordinates of the openings in a design area; assuming that the loading plate is rectangular with Length and Width, the constraint is written as:
0≤x≤Length,0≤y≤Width (6)
the bearing plates with other shapes are adjusted according to the above formula;
5) constructing shape constraint functions
The radius r of the circular hole satisfies:
r≥0 (7)
the length L and the width T of the rectangular hole meet the following conditions:
L≥0 (8)
T≥0 (9)
the method is not limited to circular openings and rectangular openings, the design of openings with other shapes is realized by changing variables, and a user can flexibly change the design in practice;
6) constructing an intensity constraint function
The method restricts the stress borne by the bearing plate not to exceed the allowable stress, and the specific calculation method is as follows;
601) determination of the modulus of elasticity of a plate
Respectively determining the elastic modulus of each unit of the bearing plate, wherein the elastic modulus E of No. w unitwComprises the following steps:
in the above formula E is the actual modulus of elasticity of the material used for the carrier plate, nwThe number of nodes with the level set function value of 1 in the four nodes on the unit w is the number;
602) obtaining stress [ sigma ] of each node according to a finite element method;
6021) determining unit stiffness matrixes of each unit according to the result in the step 601), and assembling the unit stiffness matrixes into an overall stiffness matrix K;
6022) obtaining stress [ sigma ] on the node;
first, the displacement { d } of each node is calculated:
{d}＝K-1·{F} (11)
in the above formula, { F } is the load on the carrier;
next, the stress [ sigma ] at the Gaussian integration point is calculatedgauss}：
{σgauss}＝[D]·[B]·{d} (12)
In the above formula, [ B ] is a geometric matrix in the finite element method, and [ D ] is an elastic matrix in the finite element method;
then, utilizing the shape function of the unit to extrapolate the stress value on the Gaussian point to the node of the unit, and obtaining the stress strain value of the node on the unit;
for a common node shared by a plurality of units, taking the mean value of the stress of different units on the node, and writing the stress on the node as [ sigma ];
603) determining an intensity constraint
The method adopts the safety coefficient of 1.5 and the strength constraint is written as follows:
1.5×[σ]≤[σ]extreme limit(13)
[σ]Extreme limitThe bearing plate is made of a bearing plate material capable of bearing ultimate stress;
the fatigue strength constraint and the stability strength constraint are obtained by using the method in the step 6, and are not described otherwise;
7) constructing a string oil performance constraint function
The method uses an SPH method to simulate the flowing behavior of fuel in a fuel tank, takes the time length from the excitation end to the fuel recovery no-flow state as a constraint function, and is named as a balance time length tBalancingThen the function t is constrainedBalancingMust not exceed the value actually given by the projectMaximum fuel recovery period tStandard of merit：
tBalancing≤tStandard of merit(14)
Length of equilibrium tBalancingThe concrete solving steps are as follows:
701) fuel flow simulation
Simulating the fuel flow process of a fuel tank with a small liquid filling ratio by using an SPH (Sprah method), and calculating the physical properties of the fuel particles at all times, wherein the physical properties comprise: density, position, velocity, acceleration, pressure;
702) solving for the equilibrium duration tBalancing
7021) Calculating the position of the center of mass
Calculating the mass center coordinate of the fuel at each moment according to the result of the fuel flow simulation in the step 701, wherein the mass center coordinate of the fuel is a function consisting of time, the position of the opening and the shape of the opening and is written as
It characterizes the fluid centroid position at time t, where the vector is
Storing design variables, namely the position and shape information of the opening on the bearing plate;
7022) building a no-flow regime
Under the condition that all conditions are not changed, constructing a virtual fluid obviously thicker than fuel oil, taking the viscosity of the virtual fluid to be 5 times of the viscosity of the fuel oil, and when the sum of the accelerations of all particles of the virtual fluid is less than 1% of the sum of the accelerations at the initial moment, determining that the motion state of the virtual fluid at the moment is a no-flow state;
7023) constructing a balance function
Assuming that the tank contains l compartments, the fuel centroid of compartment e at time t is set to
The center of mass of the chamber e in the no-flow state is
Method for constructing balance function
The expression of the fluctuation of the fuel centroid at the moment t is as follows:
in the above formula, the first and second carbon atoms are,
the average fluctuation amplitude of the fuel centroid of all cabins at the time t relative to the centroid in a no-flow state is shown, and V is the total volume of the fuel; at this time, the balance function
Representing the fluctuation intensity of fuel centroid in all cabins at the time t, which is dimensionless quantity;
7024) calculating the equilibrium duration tBalancing
If it is not
Three successive times lower than the standard value BStandard of meritIf it is lower than B for the first timeStandard of meritIs the equilibrium duration tBalancing；BStandard of meritThe fuel measurement allowed error given by the actual engineering is determined, and is generally 5%; to this end, the method has obtained a constraint function, the equilibrium duration tBalancingThe function being of
An implicit function of (d);
8) constructing a level fluctuation restriction function
The method uses a fluctuation function
The fluctuation intensity of the fuel level is represented, and the fluctuation function value is restricted not to exceed the allowable standard value FStandard of merit(ii) a The specific calculation method is as follows:
801) fuel flow simulation
The definition starts from an initial time and passes through tBalancingThe time reached after the time length is TBalancing(ii) a Simulating fuel oil flow process by using SPH method, and calculating TBalancingPhysical properties of all fuel particles at the moment, including: location and pressure;
802) construction of constraint function-wave function
Selecting TBalancingAll points with zero pressure at all times are used as surface particles of the fuel oil, and the surface particles s are selectedeA plurality of; selecting any three non-collinear points of the No. e bulkhead under the no-flow state, and marking as Ae、Be、CeThen T isBalancingMinute particle of fuel liquid level at moment ieDistance d from equilibrium no-flow levelieComprises the following steps:
to this end, a heave constraint function is defined
Comprises the following steps:
803) constraint of fluctuation function
The fuel level fluctuation constraint is as follows:
Fstandard of meritThe allowed error of fuel measurement is given for the actual engineering, and is generally 5%;
9) iterative optimization
Calculating partial derivatives of the target function and the constraint function to each design variable by using a finite difference method, substituting the target function value, the constraint function value and the partial derivatives of the target function and the constraint function to each design variable in the step 2 into an MMA (moving asymptote) optimization algorithm, and iteratively updating the design variables until the target function converges under the condition of meeting the constraint condition to obtain an optimization result; therefore, the method provides the design of the hole of the bearing plate under the working condition of small liquid filling ratio;
10) hole design for bearing plate of medium liquid ratio oil tank
Defining a 50% liquid filling ratio commonly used in engineering design as a medium liquid filling ratio working condition; keeping the hole design obtained under the working condition of the small liquid filling ratio unchanged, and repeatedly using the method in the steps 2-9 to obtain a hole design scheme on the bearing plate under the working condition of the medium liquid filling ratio;
11) hole design of oil tank bearing plate with large liquid filling ratio
Defining the working condition that 70 percent of liquid filling ratio commonly used in engineering design is large liquid filling ratio; keeping the obtained hole design unchanged under the working condition of medium liquid filling ratio, and repeatedly using the method in the steps 2-9 to obtain a hole design scheme on the bearing plate under the working condition of large liquid filling ratio;
12) rounding treatment
The design of the open pore of the bearing plate is rounded according to the production process requirement, so that the obtained bearing structure is qualified in strength, good in oil mixing performance and minimum in material consumption.
Example 1
The invention is further explained below by taking a cuboid oil tank with uniformly arranged holes as an example;
the basic idea of this embodiment is shown in fig. 1, and the specific steps are as follows:
1) selecting design condition-30% liquid filling ratio
In the embodiment, a 30% liquid filling ratio is taken as a priority design working condition, the working condition is defined as a small liquid filling ratio working condition, and 50% and 70% liquid filling ratios are selected for design in the subsequent steps, wherein the liquid filling conditions of the oil tank are shown in fig. 2(a) to 2 (c); in the embodiment, the extreme working condition that the plane returns to the flat flying state from the 15-degree rolling angle is researched, and the initial oil tank liquid level and the oil tank bottom plate plane form an angle of 15 degrees;
2) describing design variables
In this embodiment, the circular hole is used as the openingTo illustrate the shape, for a circular opening, each hole was set to contain 3 design variables, respectively: circular hole center coordinate x0、y0And a radius r;
before the optimization begins, 16 round holes are uniformly distributed on the bearing plate, the bearing plate is made of aviation aluminum material, and the density of the bearing plate is 2800kg/m3The size is 0.3m × 0.3m × 0.1m, and the shape is as shown in fig. 3, and there are 48 design variables; defining these design variables to be stored in vectors
Performing the following steps;
3) constructing an objective function
In this embodiment, the mass of the bearing plate is reduced as a design objective, and the objective function is a mass function of the bearing plate, and the solving method thereof is as follows:
3.1) design area meshing
Defining an area allowing the opening on the surface of the bearing plate as a design area; dividing the bearing plate into 112 × 112 finite element grids uniformly and densely by using four-node quadrilateral plate units, and obtaining total of 12544 units and 12769 nodes;
3.2) description of the open pore region
Taking a point in the design area, wherein the coordinate of the point is (x, y), and if the point is in the opening area, the corresponding level set function value phi (x, y) is greater than zero; if on the hole boundary, the level set function value phi (x, y) for that point is zero, and if the point is outside the hole, the level set function value is less than zero; at the moment, the opening area can be described according to the level set function phi (x, y); selecting a proper level set function to describe the open pore area according to the setting;
3.3) obtaining the level set function
In this embodiment, each circular opening is expressed by a level set function, and finally 16 different level set function distributions are obtained;
3.4) design area level set Assembly
And (3) assembling all the level set function distributions obtained in the step (3.3) into a whole, wherein the specific method comprises the following steps:
3.4.1) sorting the level set distribution corresponding to each opening
The 16 level set function distributions obtained in step 3.3 are subjected to the following processing: setting the level set function value corresponding to the node in the open pore coverage area as 1 by using a Heaviside function, and setting the rest as 0;
3.4.2) assembling the horizontal sets of the openings into a whole
All the level set functions obtained in the step 3.4.1 are assembled into a level set, and the assembled level set function value phi (x) corresponding to the p-th nodep,yp) Is defined as:
in the above formula, phi (x)p,yp)qThe value of the level set distribution function corresponding to the qth opening on the pth node is obtained in step 3.3;
to this end, all the openings have been integrated, as shown in fig. 4(a) and 4(b), the region a in fig. 4(a) and 4(b) is the opening region, the level set function value of the node in the region is set to 1, and the value expression outside the opening is set to 0, as shown in fig. 4 (c);
3.5) constructivity quality function
Mass M of a complete, non-perforated, original load-bearing plateComplete (complete)At 2.52 kg, the functional expression for the load bearing plate mass M is written as:
in the above formula nwThe number of nodes with level set function value of 1 in the four nodes on the w-th unit is rhoSupport for supportingThe density of the material used for the carrier plate is here 2800kg/m3，VwThe volume of the w-th unit can be calculated by coordinates of four nodes on the unit and the thickness of the plate; the cell mass determined according to whether the node is in the open area is actually a mass weakening processThe meta-mass weakening process is illustrated in fig. 5(a) to 5 (c);
thus, the embodiment obtains a quality function expression, which is also an objective function;
4) constructing a location constraint function
In this embodiment, if the central coordinate of the constraint aperture is in the design area, the constraint is written as:
0m≤x≤0.3m,0m≤y≤0.3m (3)
5) constructing shape constraint functions
The radius r of the circular hole satisfies:
r≥0m (4)
6) constructing an intensity constraint function
In the embodiment, the stress borne by the bearing plate is restrained not to exceed the allowable stress, and the specific calculation method is as follows;
6.1) determination of the modulus of elasticity of the plate
Respectively determining the elastic modulus of each unit of the bearing plate, wherein the elastic modulus E of No. w unitwComprises the following steps:
in the above formula, E is 7.4X 1010N/m2，nwThe number of nodes having a level set function value of 1 among the four nodes in the w-th cell is set as shown in fig. 5(a) to 5 (c);
6.2) obtaining the stress of each node
Obtaining stress [ sigma ] on the node according to a finite element method;
6.3) determining the intensity constraint
In this embodiment, the safety factor is 1.5, and the strength constraint is written as:
1.5×[σ]≤[σ]extreme limit(6)
[σ]Extreme limitTaking the pressure to be 400 MPa;
the fatigue strength constraint and the stability strength constraint are obtained by using the method in the step 6, and are not described otherwise;
7) constructing a string oil performance constraint function
The method uses smooth particle fluid dynamics knowledge (SPH method) to simulate the flowing behavior of fuel in the fuel tank, takes the time length from the excitation end to the fuel recovery no-flow state as a constraint function, and is named as balance time length tBalancingThen the function t is constrainedBalancingSatisfies the following conditions:
tbalancing≤tStandard of merit(7)
Length of equilibrium tBalancingThe concrete solving steps are as follows:
7.1) Fuel flow simulation
Simulating a fuel flow process by using an SPH (spray plasma enhanced hydrogen) method, and calculating the physical properties of fuel particles at all times, wherein the physical properties comprise: density, position, velocity, acceleration, pressure; FIG. 6 shows the fuel flow behavior obtained by applying the SPH method under the condition that the fuel tank is restored to the horizontal attitude from the inclined attitude;
7.2) solving for the equilibrium duration tBalancing
7.2.1) calculating the centroid position
Calculating the mass center coordinate of the fuel at each moment according to the result obtained in the step 7.1
Then
Representing the position of the center of mass of the fluid at time t as a function of time, position of the opening and shape of the opening, wherein the vector
Storing design variables, namely the position and shape information of the opening on the bearing plate;
7.2.2) construction of No-flow State
Under the condition that other parameters and working conditions are not changed, constructing a virtual fluid with the viscosity 5 times that of the fuel oil, and when the sum of the acceleration of all particles of the virtual fluid is less than 1% of the sum of the acceleration at the initial moment, determining that the motion state of the virtual fluid at the moment is a no-flow state;
7.2.3) construction of the balance function
The fuel tank of the embodiment comprises 2 cabins, and the fuel mass center of the cabin e at the moment t is set to
The center of mass of the chamber e in the no-flow state is
The embodiment constructs a balance function
The expression of the fluctuation of the fuel centroid at the moment t is as follows:
in the above formula, the total volume V of the fuel oil is 0.0108m3；
7.2.4) calculating the balance time length tBalancing
If it is not
When the time is less than 5% for three times, the time when the time is less than 5% for the first time is taken as the balance time length tBalancing(ii) a To this end, the embodiment has obtained a constraint function, the balance duration tBalancingThe function being of
An implicit function of (d);
8) constructing a level fluctuation restriction function
The present embodiment uses a heave function
Representing the fluctuation strength of the fuel level and constraining the fluctuation function value not to exceed 5 percent; the specific calculation method is as follows:
8.1) Fuel flow simulation
Definition from beginningBeginning at a starting time and passing tBalancingThe time reached after the time length is TBalancingTime of day; simulating a fuel flow process by using an SPH (spray plasma enhanced hydrogen) method, and calculating physical properties of all fuel particles, wherein the physical properties comprise: density, position, velocity, acceleration, pressure;
8.2) construction of constraint function-wave function
Selecting TBalancingAll points with zero pressure at all times are used as surface particles of the fuel oil, and the surface particles s are selectedeA plurality of; selecting any three non-collinear points of the No. e bulkhead under the no-flow state, and marking as Ae、Be、CeThen T isBalancingMinute particle of fuel liquid level at moment ieDistance d from equilibrium no-flow levelieComprises the following steps:
to this end, a heave function is defined
Comprises the following steps:
8.3) undulation function constraints
The fuel level fluctuation constraint is as follows:
9) iterative optimization
Obtaining a target function, a constraint function and partial derivatives of the target function and the constraint function to each variable by using a finite difference method, and substituting the partial derivatives into an MMA optimization algorithm to obtain an optimization result; therefore, the embodiment provides the design of the hole of the bearing plate under the working condition of small liquid filling ratio;
10) hole design for bearing plate of medium liquid ratio oil tank
Defining a 50% liquid filling ratio commonly used in engineering design as a medium liquid filling ratio working condition; keeping the hole design obtained under the working condition of the small liquid filling ratio unchanged, and repeatedly using the method in the steps 2-9 to obtain a hole design scheme on the bearing plate under the working condition of the medium liquid filling ratio;
11) hole design of oil tank bearing plate with large liquid filling ratio
Defining the working condition that 70 percent of liquid filling ratio commonly used in engineering design is large liquid filling ratio; keeping the obtained hole design unchanged under the working condition of medium liquid filling ratio, and repeatedly using the method in the steps 2-9 to obtain a hole design scheme on the bearing plate under the working condition of large liquid filling ratio;
12) rounding treatment
The design of the openings of the bearing plate is rounded according to the production process requirements, so that the obtained bearing structure is qualified in strength, good in oil leakage and minimum in material consumption, and the design result is shown in fig. 7.
It can be seen from fig. 8 that the fuel fluctuation intensity after optimization is always smaller than that before optimization, that is, the fuel can be accelerated to be leveled more quickly by the optimized design, and the center of gravity of the aircraft can be ensured to be quickly stabilized.
The invention uses the SPH method to simulate the liquid flow, ensures that the oil mixing capacity and the fluctuation inhibition capacity of the oil tank are within the engineering allowable range, and helps the airplane to recover the center of gravity as soon as possible, thereby endowing the airplane with better flight control performance; meanwhile, the method also uses a topology optimization design method based on topology boundary explicit expression, so that the quality of the bearing structure can be reduced on the premise of maintaining the strength of the bearing structure not to be reduced, the hole boundaries of the bearing structure can be ensured to be clear and regular, and the bearing structure is easy to manufacture.
The invention takes the mass of the rib plate in the aircraft oil tank as an optimization target, and is assisted by strength constraint and fuel oil stringing constraint, thereby realizing the purpose of weight reduction of the aircraft structure under the condition of ensuring that the design performance is not reduced; compared with the traditional mainstream topological optimization method, such as a variable density method, a homogenization method and the like, the method can effectively control the shape of the boundary of the opening, ensure the simple and regular boundary and obviously improve the manufacturability of the design scheme; meanwhile, the method completes the simulation of the fuel shaking behavior in the fuel tank by using the related knowledge of smooth particle fluid dynamics, and still keeps the design result to obtain good oil penetration and wave suppression performance on the premise of reducing the mass of the bearing plate as much as possible, thereby shortening the fuel measurement time, promoting the feedback rate, accelerating the recovery time of the gravity center of the airplane and finally endowing the airplane with better flight control performance.
Claims (3)
1. A lightweight design method of an aircraft fuel tank bearing structure considering the oil mixing characteristic is characterized by comprising the following steps: the method comprises the following steps:
1) selecting a design working condition;
2) setting design variables of the opening, storing the design variables in the vector
Performing the following steps;
3) defining an area allowing hole opening on the bearing plate as a design area, carrying out grid division on the design area, and describing the hole opening area according to a level set function phi (x, y); constructing a target function; carrying out grid division on a design area by using a four-node quadrilateral grid to obtain Esum units and Nsum nodes; the constructed objective function is a quality function of the bearing plate, and the construction steps specifically comprise:
301) the level set function φ (x, y) satisfies the following condition: taking a point with coordinates (x, y) in the design area, and if the point is in the opening area, the corresponding level set function value is larger than zero; if on the hole boundary, the level set function value of the point is zero, and if the point is outside the hole, the level set function value is less than zero;
302) n is uniformly arranged on the bearing platerecA rectangular hole and ncirRound holes, each opening of which is expressed by a level set function respectively, and obtaining (n)rec+ncir) A number of different level set functions;
303) integrating the level set functions obtained in the step 302), setting the level set function values of the nodes to be 1 in the hole opening area, and setting the values outside the hole to be 0: the concrete steps of integrating the obtained level set function distribution into a whole are as follows:
3031) to be obtained (n)rec+ncir) The individual level set function performs the following: setting the level set function value corresponding to the node in the open pore coverage area as 1 by using a Heaviside function, and setting the rest as 0;
3032) subjecting (n) obtained in step 3031)rec+ncir) The level set function corresponding to each opening is assembled into a level set, and the assembled level set function value phi (x) corresponding to the p-th nodep,yp) Is defined as:
wherein phi (x)p,yp)qThe value of the level set function at the p node for the q opening;
304) defining the mass of the intact non-perforated original bearing plate as a constant MComplete (complete)The mass function of the load bearing plate is then:
wherein n iswThe number of nodes with level set function value of 1 in the four nodes on the w-th unit is rhoSupport for supportingDensity of material used for the load-bearing plates, VwIs the volume of unit No. w;
4) performing mechanical optimization design and fuel flow simulation, determining constraint conditions and constructing a constraint function: the constraint conditions comprise position constraint, shape constraint, strength constraint, oil mixing performance constraint and fuel level fluctuation constraint;
assuming that the load-bearing plate is rectangular with a Length and a Width, the position constraint function is:
0≤x≤Length,0≤y≤Width；
the shape constraint function is:
the radius r of the circular hole satisfies: r is more than or equal to 0; the length L and the width T of the rectangular hole meet the following conditions: l is more than or equal to 0, and T is more than or equal to 0;
the strength constraint comprises stress strength constraint, fatigue strength constraint and stability strength constraint;
oil cross-flow performance constraint function is tBalancing≤tStandard of merit，tBalancingFor the equilibrium duration, tStandard of meritSetting the maximum recovery time length of fuel for the actual project; the liquid level fluctuation constraint function is
Wherein FStandard of meritFuel measurement allowable error given for engineering practice;
5) and solving partial derivatives of the target function and the constraint function to each design variable by using a finite difference method, substituting the target function value, the constraint function value and the obtained partial derivatives into an MMA optimization algorithm, iteratively updating the variables until the target function converges under the condition of meeting constraint conditions, and finishing the design of the open pore of the bearing plate under the design working condition.
2. The method for designing the lightweight aircraft fuel tank bearing structure considering the oil mixing characteristic as claimed in claim 1, wherein: length of equilibrium tBalancingThe concrete solving steps comprise:
4011) simulating a fuel oil flow process of a fuel oil tank with a small liquid filling ratio by using an SPH method;
4012) according to the result of the fuel flow simulation in the step a), the centroid coordinate of the fuel at the time t is calculated and is a function formed by time, the position of the opening and the shape of the opening, and the centroid coordinate is written as
4013) Constructing a virtual fluid which is 5 times thicker than the fuel oil, and determining that the motion state of the virtual fluid is a no-flow state when the sum of the accelerations of all particles of the virtual fluid is less than 1% of the sum of the accelerations at the initial moment;
4014) assuming that the tank contains l compartments, the fuel centroid of compartment e at time t is set to
Chamber in no-flow statee center of mass of
Constructing a balance function
To measure the fluctuation of the fuel centroid at the moment t, the expression is as follows:
wherein the content of the first and second substances,
the average fluctuation amplitude of the fuel centroid of all cabins at the time t relative to the centroid in a no-flow state is shown, and V is the total volume of the fuel;
4015) if it is not
Three successive times lower than the standard value BStandard of meritIf it is lower than B for the first timeStandard of meritIs the equilibrium duration tBalancing；BStandard of meritAnd determining the allowable error of fuel measurement given by actual engineering.
3. The method for designing the lightweight aircraft fuel tank bearing structure considering the oil mixing characteristic as claimed in claim 1, wherein: it is assumed that the tank contains l compartments,
the specific solving step comprises:
4021) defining the time T from the initial time to the time when the fuel is balancedBalancing(ii) a Simulating fuel oil flow process by using SPH method, and calculating TBalancingThe position and pressure of all fuel particles at the moment;
4022) selecting TBalancingAll pressure at one time being zeroFor surface particles of fuel, co-selected surface particles seA plurality of; selecting any three non-collinear points of the No. e bulkhead under the no-flow state, and marking as Ae、Be、CeThen T isBalancingMinute particle of fuel liquid level at moment ieDistance d from equilibrium no-flow levelieComprises the following steps:
then
Comprises the following steps:
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