CN105447269A - Non-structural mass trimming method for airplane in steady overload state - Google Patents

Abstract

The invention discloses a non-structural mass trimming method for an airplane in a steady overload state. By introducing increment of a non-structural mass unit, the aerodynamic load and the inertial load of the airplane are trimmed, so that a result obtained by analyzing a finite element model without displacement constraint is more reasonable than a result obtained by a displacement constraint method and an inertia relief method. According to the non-structural mass trimming method, a poly-condensed load array is obtained through a poly-condensation technology so as to accurately obtain a non-balance system of force of an airplane structure relative to a reference point; and a trimming load is further obtained by airplane overload, and the trimming load is equivalently converted into an increment attribute of a trimmed non-structural mass unit. According to the method, mass load increments are transferred to structural units by utilizing connection of RBE3 rigid units, namely, an inertial load of the trimmed mass unit is transferred to a force-bearing point of a structural model of an oil tank, a warehouse or an equipment compartment so as to accurately obtain stress characteristics of the airplane structure. The non-structural mass trimming method has important application values and significances for improving the design accuracy of the airplane structure.

Description

The non-structural mass Calculate Ways of a kind of aircraft under permanent overload

Technical field

The present invention relates to field of airplane structure, specifically the non-structural mass Calculate Ways of a kind of aircraft under permanent overload.

Background technology

Aircraft is subject to the effect of various load in flight course, and the load affecting aircraft structure strength mainly contains the inertial load etc. of aloft aerodynamic force, air resistance, motor power and structure.When adopting finite element discretization numerical analysis method to carry out design analysis to aircaft configuration, the situation of aerodynamic force and airplane inertial loading imbalance can be run into.This non-equilibrium state may come from the imbalance of initial gas dynamic loading and inertial load modeling, although also may be aerodynamic loading and structure inertia load be for balancing in an initial condition, the structure inertia loading imbalance after causing aerodynamic loading and optimize in the optimal design stage of aircaft configuration.The optimal design of aircaft configuration is meeting various engineering constraint, under condition as displacement constraint, ess-strain constraint or flexion limit load restraint etc., by the dimensional parameters of change structure parts, as the skin thickness of aircraft, the sectional dimension parameter etc. of beam edge strip, to reach the lightest purpose of design of aircaft configuration quality.The dimensional parameters of airplane structural parts constantly changes in Optimized Iterative process, then correspondingly can cause the imbalance of airplane inertial load and aerodynamic loading.Rationally effective trim loading force system, the optimal design for aircaft configuration has vital impact.

For the flight load imbalance problem in above-mentioned airplane design process, it is displacement constraint method that method conventional in existing aeroplane structure design mainly contains two kinds: one, and another is inertia method for releasing.Displacement constraint method is normally checked district at frame head and tail or wing root place etc. away from load and is applied clamped or freely-supported constraint, former singular equation is converted into nonsingular equation, thus obtains displacement and the internal force distribution of aircaft configuration.But mistrimmed load can be delivered on basis by restraint joint by the method for this set displacement constraint, cause inappropriate load path, and cause the stress of restraint joint correlation unit to be concentrated and be out of shape incorrect, reduce the computational accuracy of design analysis result.Document 1 " MSCNastranLinearStaticAnalysisUser ' sGuide " disclose a kind of inertia release tech.This technology, according to D'Alembert's principle, by the polycondensation method of structural loads array, applies the correction inertial load corresponding to acceleration to aircaft configuration finite element model, thus the unbalanced force system that trim is introduced by the difference of aerodynamic loading and initial inertia load; Again by imposing restriction to rigid motion degree of freedom, obtain the solution of static problem further, thus solve the not enough problem of constraint.But the loaded-up condition of the method and airplane design is runed counter to, because the overload that the design point of aircraft is determined is specified by flight envelope, its numerical value can't change along with the change of out-of-balance force system.

The present invention is directed to displacement constraint method and inertia method for releasing deficiency as above in aeroplane structure design application, propose a kind of non-structural mass Calculate Ways, the method, by the non-structural mass load trim in structured design process, reaches the singularity problem eliminated numerical model and solve.The numerical example shows that this technology is more reliable, does not produce any impact to the load path of structural loads, and the non-structural mass gain that brings when can provide architecture quality change, as the knots modification of fuel oil or equipment.

Summary of the invention

For overcoming in aeroplane structure design, especially in Optimal Structure Designing process, for cause because aircraft aerodynamic loading and inertial load are uneven under state of flight non-displacement constrained finite element model without solution problem, the present invention proposes the non-structural mass Calculate Ways of a kind of aircraft under permanent overload.

Detailed process of the present invention is:

Step 1, the division of finite element unstrctured grid: according to the aircraft cad data that user is given, adopts Hypermesh software to carry out the division of finite element unstrctured grid to aircraft CAD geometric model.

Step 2, inputs the parameter of each part material of aircraft in Hypermesh software.The parameter of each part material of described aircraft comprises: Young modulus E, and unit is MPa; Shear modulus G, unit is MPa; Poisson ratio μ and density p, unit is Kg/mm ³; And composite plys one-way tape material property; Described composite plys one-way tape material property comprises 1-direction Young modulus E ₁, 2-direction Young modulus E ₂, 1-2 plane Poisson ratio μ ₁₂,-2 plane shear modulus G ₁₂, 1-3 plane shear modulus G ₁₃, 2-3 plane shear modulus G ₂₃and density p.

Step 3, imports Patran software by establishing later wing finite element model file.

Step 4, sets up lumped mass point: establish two lumped mass points at fuel tank load Nodes, to simulate the effect of oil tank fuel load to aircaft configuration.In described aircraft, fuel tank is positioned at frame sections.In aircraft Finite element design, fuel oil adopts lumped mass unit to replace usually, by the effect of web by its dynamic changes process to fuselage.

Step 5, sets up non-structural trim mass unit: set up a mass unit in the lower end of the fuselage plane of symmetry.This mass unit x-is consistent to coordinate with the x-of fuel tank load node to position, is designated as non-structural trim mass unit.In finite element initial analysis, the quality settings of non-structural trim mass unit is zero, and is connected to by the RBE3 unit in Nastran software on two lumped mass cell nodes of foundation in step 4.

Step 6, obtain initial stiffness matrix K, initial mass battle array M and aerodynamic loading array { F}: the aerodynamic loading inputting the given aircraft of user in Patran software, final generation Nastran software can perform BDF model file, and is committed to initial stiffness matrix K, initial mass battle array M and aerodynamic loading array { F} that Nastran software calculates also derived type structure.

Step 7, solve aircraft finite element structure model panel load array P}: the initial mass battle array M derived according to Nastran software and the given aerodynamic loading of user { F} solves the panel load array { P} of aircraft finite element structure model.Load column P} comprise external action aerodynamic loading F} and architecture quality inertial load G}, mass inertia load G} by designer according to the loading factor n under current flight state _ypropose.Make the node total number in aircraft finite element model be n, then the vector acceleration of each node is expressed as:

$a={\[a_1^T,\mathrm{...},a_i^T,\mathrm{...},a_n^T\]}^T,i=1,\mathrm{...},n$

In formula, a _i=[0a _y0000] ^t, a _y=n _yg, a _yfor the accekeration in airplane ascensional force direction, g is acceleration of gravity.When aircraft is at the uniform velocity flat fly time, n _ywhen=1, the inertial load of aircraft is expressed as:

G＝Ma

By above formula obtain aircraft finite element structure model panel load array P} is:

{P}＝{F}-{G}

Step 8, chooses relative reference point: choose a finite element node as relative reference point at fuselage plane of symmetry lower end, be designated as r-collection.Relative reference point x-is consistent to coordinate with the x-of fuel tank load node to position, and coordinate is (1781.0 ,-449.964,0.0).If translation displacements and the corner displacement of relative reference point are constrained to zero.

Step 9: piecemeal process is carried out to stiffness matrix: the complete set of node of definition aircraft finite element model is a-collection, and reference mode is r-collection, and is concentrated by a-the set of node not comprising r-collection to be designated as l-collection, is called residue set of node.Then the stiffness matrix Partitioning Expression of A of aircaft configuration is

$K=K_{aa}=\left[\begin{array}{cc}{K}_{rr}& K_{rl}\\ K_{lr}& K_{ll}\end{array}\right]$

Described K _aathe stiffness matrix that a-collection is relevant, K _rrthe stiffness matrix that r-collection is relevant, K _llthe stiffness matrix that l-collection is relevant, K _lrthe Coupling stiffness matrix of l-collection and r-collection, K _rlit is the Coupling stiffness matrix of r-collection and l-collection.

Step 10: determine the restriction relation in aircaft configuration model between a-collection and r-collection and bunching load column: by Guyan bunching principle, determine the restriction relation in aircaft configuration model between a-collection and r-collection and bunching load column, obtain the restriction relation [G between a-collection and r-collection _ar]:

$\left\{u_a\right\}=\left\{\begin{array}{c}{u}_r\\ u_l\end{array}\right\}=\left[\begin{array}{c}{I}_{rr}\\ G_{lr}\end{array}\right]\left\{u_r\right\}=\[G_{ar}\]\left\{u_r\right\}---\left(1\right)$

Determining the restriction relation [G in described aircaft configuration model between a-collection and r-collection _ar] time, by solving the structure finite element equation of described a-collection:

$\left[\begin{array}{cc}{K}_{rr}& K_{rl}\\ K_{lr}& K_{ll}\end{array}\right]\left\{\begin{array}{c}{u}_r\\ u_l\end{array}\right\}=\left\{\begin{array}{c}0\\ 0\end{array}\right\}$

Obtain:

[K _lr]{u _r}+[K _ll]{u _l}＝0

{u _l}＝-[K _ll] ^-1[K _lr]{u _r}＝[G _lr]{u _r}

In formula, described [G _lr] be the restriction matrix between l-collection and r-collection; u _rthe motion vector of reference mode r-collection, u _lit is the motion vector of reference mode l-collection.

Step 11, sets up and reduces load column { P _r}: retrain [G by the r-collection obtained and a-collection rigid body displacement _ar], obtain reducing load column { P _r}:

{P _r}＝[G _ar] ^T{P _a}＝[G _ar] ^T{P}(2)

Aircraft when gravity direction is the state of flight of loading imbalance on permanent overload and gravity direction, this aircraft x-direction of principal axis and the z-axis direction stressed be zero, obtain the non-equilibrium load { P of rigid body aircraft after bunching _rconcrete form is:

{P _r}＝[0P _n0M ₁0M ₃] ^T(3)

In formula, P _nfor aircraft is along gravity direction load, M ₁for aircraft is along moment of flexure suffered by x-axle, M ₃for aircraft is along moment of flexure suffered by z-axle.

Step 12: determine r-collection trim Mass matrix by r-collection generalized load: make the trim Mass matrix of r-collection be r-collection node acceleration a _r=[0a _y0000] ^t, by reducing load column { P in step 11 _rthe rigid block element that obtains r-collection is

$\[M_{rr}^I\]\left\{a_r\right\}+\left\{P_r\right\}=0$

Therefore

$\[M_{rr}^I\]\left\{a_r\right\}=-\left\{P_r\right\}={\left[\begin{array}{cccccc}0& -P_n& 0& -M_1& 0& -M_3\end{array}\right]}^T---\left(5\right)$

Providing r-collection trim Mass matrix by formula (5) is:

$\[M_{rr}^I\]==\left[\begin{array}{cccccc}-P_n/a_y& 0& 0& 0& 0& 0\\ 0& -P_n/a_y& 0& -M_1/a_y& 0& -M_3/a_y\\ 0& 0& -P_n/a_y& 0& 0& 0\\ 0& -M_1/a_y& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& -M_3/a_y& 0& 0& 0& 0\end{array}\right]---\left(6\right)$

Namely this Mass matrix can ensure the unchangeability of aircraft overload under flight load function, and shows that the increment of trim quality should be-P _n/ a _y.

Step 13: determine the Rigid Constraints relation between r-collection and non-structural trim mass unit node:

Note relative reference point is r point, and non-structural trim mass unit node is s point.The corner of relative reference point and non-structural trim mass unit node is respectively θ _rand θ _s, displacement is d _rand d _s.Then the displacement of non-structural trim mass unit node and the expression matrix of corner and relative reference point displacement and corner close and are:

$u_r=\left[\begin{array}{cccccc}1& 0& 0& 0& d_z& -d_y\\ 0& 1& 0& -d_z& 0& d_x\\ 0& 0& 1& d_y& -d_x& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]u_s=G_{rs}{u}_s---\left(7\right)$

Wherein, u _r=[d _r, θ _r] ^t, u _s=[d _s, θ _s] ^t, d _x, d _y, d _zfor vector r _srat the component in x, y, z direction, G _rsfor the Rigid Constraints relational matrix between relative reference point and non-structural trim mass unit node.The Rigid Constraints relation between r-collection and non-structural trim mass unit node can be determined by formula (7).

Rapid 14, determine the trim Mass matrix of non-structural trim mass unit: by the trim Mass matrix of non-structural trim mass unit in the r-collection broad sense trim Mass matrix equivalent transformation to step 5 in step 12.The displacement of non-structural trim mass unit and acceleration is made to be respectively u _sand a _s, trim Mass matrix is M _s,

$M_s=G_{rs}^T{M}_{rr}^I{G}_{rs}---\left(8\right)$

Step 15: give non-structural trim mass unit qualitative attribute, and complete finite element analysis: by M _sgive non-structural trim mass unit, namely can complete corresponding nodal displacement and stress distribution analysis further by Nastran solver.So far, the trim of aircraft non-structural mass under permanent overload is completed.

The present invention is basic foundation with the constant overload in Aircraft Load flight envelope curve, for the architecture quality in structured design process uncertain and propose a kind of non-structural mass Calculate Ways, state of flight can be realized to get off the plane the reasonable analysis of structural finite element model, thus provide strong technical support for aeroplane structure design.

Essential characteristic of the present invention is: make aircraft aerodynamic loading and inertial load trim by the increment introducing non-structural mass unit, thus make the result comparatively displacement constraint method that obtained by non-displacement restraining structure finite element model analysis and inertia method for releasing more reasonable.Its object is to meet aircaft configuration optimal design alleviate aircaft configuration quality, increase the basic object of effective mass load.In the present invention, non-structural mass refers to fuel oil quality, equipment quality or commercial transport quality etc. in aircraft.Mainly through the polycondensation technology of load column in method, obtain the load column after polycondensation, thus accurately obtain the unbalanced force system of aircaft configuration relative to reference point; Transshipped by aircraft further again and obtain trim load, and the delta attribute of non-structural mass unit after it being converted into equivalently trim.Thus, utilize the connection of RBE3 rigid element, these quality load increments are delivered on structural unit, are also delivered on the structural model hard point of fuel tank, freight house or equipment compartment by the mass unit inertial load after trim, thus accurately obtain the mechanical characteristic of aircaft configuration.The technology of the present invention has important using value and meaning for the design accuracy improving aircaft configuration.

The present invention is directed to the flight load imbalance problem in airplane design process, first will be translated into counterweight balance problem, and then just carry out numerical simulation analysis by Finite Element Method.It is displacement constraint method that the method that load disposal route is now commonly used mainly contains two kinds: one, and another is inertia method for releasing.Displacement constraint method is normally checked district at frame head and tail or wing root place etc. away from load and is applied clamped or freely-supported constraint, former singular equation is converted into nonsingular equation, thus obtains displacement and the internal force distribution of aircaft configuration.But mistrimmed load can be delivered on basis by restraint joint by the method for this set displacement constraint, cause inappropriate load path, and cause the stress of restraint joint correlation unit to be concentrated and be out of shape incorrect, reduce the computational accuracy of design analysis result.Document 1 " MSCNastranLinearStaticAnalysisUser ' sGuide " disclose a kind of inertia release tech.This technology, according to D'Alembert's principle, by the polycondensation method of structural loads array, applies the correction inertial load corresponding to acceleration to aircaft configuration finite element model, thus the unbalanced force system that trim is introduced by the difference of aerodynamic loading and initial inertia load; Again by imposing restriction to rigid motion degree of freedom, obtain the solution of static problem further, thus solve the not enough problem of constraint.But the loaded-up condition of the method and airplane design is runed counter to, because the overload that the design point of aircraft is determined is specified by flight envelope, its numerical value can't change along with the change of out-of-balance force system.

The present invention is directed to the drawback of aforementioned two kinds of methods, its object is to 2 points: one is can not cause inappropriate load path to structure; Two is the overloads that can not change aircraft.The present invention is by introducing non-structural trim quality trim unit, and by the inertial load of non-structural trim mass unit under given overload, trim is carried out to the non-equilibrium inertial load in aeroplane structure design process, make the inertial load of non-structural trim mass unit and the inertial load of aircraft be zero about the effect sum of relative reference point.This technology ensure that the unchangeability of aircraft overload under the effect of specific external load, and this requirement constant with overload in airplane design process is consistent.

The numerical example shows that this technology can ensure that the overload of aircraft does not change under the effect of non-equilibrium structure load, and does not produce any impact to the load path of structural loads.In addition, can provide the non-structural mass gain that brings when architecture quality changes by the quality of non-structural trim mass unit, as the knots modification etc. of fuel oil or equipment, this has great significance to aeroplane structure design.

Under the present invention is applicable to flight load state, inertial load trim computational problem in aeroplane structure design process during mass change, more specifically, relate to aircraft when gravity direction is permanent overload, in architecture quality design iteration process, the inertial mass load trim of finite element model calculates, achieve state of flight to get off the plane the reasonable analysis of structural finite element model, thus provide strong technical support for aeroplane structure design.

Accompanying drawing explanation

Fig. 1 is unmanned plane mode shape figure;

Fig. 2 is unmanned plane model skeleton and body axis system schematic diagram;

Fig. 3 is unmanned plane fuel tank load node location schematic diagram;

Fig. 4 is unmanned plane non-structural trim mass unit illustraton of model;

Fig. 5 is unmanned plane relative reference point schematic diagram;

Process flow diagram of the present invention during Fig. 6.

In accompanying drawing, 1. fuel tank load node, 2. fuel tank load node location, 3. relative reference point.

Embodiment

The present embodiment is by being described in detail technical scheme of the present invention the non-structural mass trim process of certain type unmanned plane under permanent overload.

The present embodiment, specifically for unmanned plane cad data, overload factor and aerodynamic loading that certain user is given, completes the force analysis design process of this unmanned plane under free flight state by non-structural mass Calculate Ways.Detailed process comprises the following steps:

Step 1, the division of finite element unstrctured grid.According to the unmanned plane cad data that user is given, Hypermesh software is adopted to carry out the division of finite element unstrctured grid to unmanned plane CAD geometric model.As shown in Figure 1, inner skeleton as shown in Figure 2 for unmanned plane geometric shape.This unmanned plane is divided into fuselage, inner wing, outer wing three sections.Fuselage is long is 3.893m, and the main load-carrying member of inner wing comprises 3 webs and 5 ribs; The main load-carrying member of outer wing comprises 3 webs and 16 ribs.Wing major parameter is as follows: length is 15.000m, and root chord length is 2.791m, and wing tip chord length is 0.900m, and leading edge sweep is 28 °, and trailing sweep is 24 °, and wing is without torsion angle, and skin thickness is 0.002m.In described unmanned plane geometric model, all beam rafter bars, rib rafter bar, reinforcement and long purlin all use the equal straight beam element simulation of two nodes, have 12334 unit.Its central sill rafter bar, rib rafter bar are " L " type beam element, and reinforcement and long purlin use rectangular beam unit.All coverings, web, rib web and frame web all use shell unit to simulate, and shell unit has 63864.The RBE2 unit simulation in Nastran software is adopted in each joint of unmanned plane.Whole unmanned plane has node 59802, unit 76199.

Step 2, inputs the unmanned plane material parameter that user specifies in Hypermesh software.This unmanned plane adopts 5 kinds of materials altogether: engine nozzle place uses exotic material 30CrMnSi; Floor stringer rafter bar and web adopt 7050 aluminum alloy materials; Inner wing covering, outer wing covering, web and fuselage skin use symmetrically laminated composites; Remainder material all uses 2024 aluminium alloys.Each material properties as table 1, shown in 2.In table 2, E ₁for 1-direction Young modulus, E ₂for 2-direction Young modulus, μ ₁₂for 1-2 plane Poisson ratio, G ₁₂for 1-2 plane shear modulus, G ₁₃for 1-3 plane shear modulus, G ₂₃for 2-3 plane shear modulus, ρ is density.

Metal material performance in table 1 model

Step 3, imports Patran software by the wing finite element model file set up.

Step 4, sets up lumped mass point.Two lumped mass points are established at fuel tank load node 1 place.These two lumped mass points are for simulating the effect of oil tank fuel load to aircaft configuration.In described unmanned plane, fuel tank is positioned at frame sections.In unmanned plane Finite element design, fuel oil adopts lumped mass unit to replace usually, by the effect of web by described fuel oil dynamic changes process to fuselage.In this example, according to design, two fuel tank load node locations 2 are respectively (1781.0,43.7799,400.0) and (1781.0,43.7799 ,-400.0), as shown in Figure 3.

Step 5, sets up non-structural trim mass unit.Set up a mass unit in the lower end of the fuselage plane of symmetry, this mass unit x-is consistent to coordinate with the x-of fuel tank load node 1 to position, and this mass unit is designated as non-structural trim mass unit.By determining the mass property of this non-structural trim mass unit, to reach the self-equilibrating of unmanned plane structural loads under the immovable condition of unmanned plane overload.In this example, the coordinate of described non-structural trim mass unit is (1781.0 ,-643.78,0.0).In finite element initial analysis, described non-structural trim mass unit quality is zero, and is connected on two lumped mass cell nodes of foundation in step 4 by the RBE3 unit in Nastran software, the namely load joint of fuel tank, as shown in Figure 4.Described RBE3 unit is the linkage unit in Nastran software, and effect realizes load from non-structural trim mass unit to the transmission of fuel tank load node 1.

Step 6, obtains initial stiffness matrix K, initial mass battle array M and aerodynamic loading array { F}.In Patran software, input the aerodynamic loading of the given unmanned plane of user, and be committed to initial stiffness matrix K, initial mass battle array M and aerodynamic loading array { F} that Nastran software calculates also derived type structure.

Step 7, solves the panel load array { P} of unmanned plane finite element structure model.{ F} solves the panel load array { P} of unmanned plane finite element structure model for the initial mass battle array M derived according to Nastran software and the given aerodynamic loading of user.Panel load array P} by external action aerodynamic loading F} and architecture quality inertial load G} two is formed, mass inertia load G} by designer according to the loading factor n under current flight state _ypropose.Make the node total number in unmanned plane finite element model be n, then the vector acceleration of each node is expressed as:

$a={\[a_1^T,\mathrm{...},a_i^T,\mathrm{...},a_n^T\]}^T,i=1,\mathrm{...},n$

In formula, a _i=[0a _y0000] ^t, a _y=n _yg, a _yfor the accekeration in unmanned plane lift direction, g is acceleration of gravity, i.e. g=-9800mm/s ².In this example, unmanned plane flies at the uniform velocity flat, n _y=1.So the inertial load of unmanned plane is expressed as:

G＝Ma

By above formula obtain unmanned plane finite element structure model panel load array P} is:

{P}＝{F}-{G}

Step 8, chooses relative reference point.Choose a finite element node as relative reference point 3 at fuselage plane of symmetry lower end, relative reference point x-is consistent to coordinate with the x-of fuel tank load node to position, is designated as r-collection.The coordinate of described relative reference point 3 is (1781.0 ,-449.964,0.0), and position as shown in Figure 5.If translation displacements and the corner displacement of relative reference point are constrained to zero.Relative reference point 3 represents that the deformation displacement of other nodes in structural model is all relative to this relative reference point, and the deformational displacement of this relative reference point is zero.Because unmanned plane stiffness matrix under free flight state is unusual, therefore the displacement of unmanned plane this node under structural loads effect comprises 3 translation rigid body displacements and 3 rotary rigid body displacements.The choosing difference and can't have an impact to internodal relative displacement and aircraft mechanical characteristic of reference point.

Step 9: piecemeal process is carried out to stiffness matrix.The complete set of node of definition unmanned plane finite element model is that a-integrates, relative reference point as r-collection, and is remembered that a-concentrates and do not comprised set of node that r-integrates as l-collection, is called residue set of node.Then the Partitioning Expression of A of the stiffness matrix K of unmanned plane structure is

$K=K_{aa}=\left[\begin{array}{cc}{K}_{rr}& K_{rl}\\ K_{lr}& K_{ll}\end{array}\right]$

Here K _aathe stiffness matrix that a-collection is relevant, K _rrthe stiffness matrix that r-collection is relevant, K _llthe stiffness matrix that l-collection is relevant, K _lrthe Coupling stiffness matrix of l-collection and r-collection, K _rlit is the Coupling stiffness matrix of r-collection and l-collection.

Step 10: determine the restriction relation in unmanned plane structural model between a-collection and r-collection and bunching load column.By Guyan bunching principle, determine the restriction relation in unmanned plane structural model between a-collection and r-collection and bunching load column.The key obtaining this relation is the finite element equation solving a no-load effect, and the structure finite element equation of Gua-Ji is write as following block form:

$\left[\begin{array}{cc}{K}_{rr}& K_{rl}\\ K_{lr}& K_{ll}\end{array}\right]\left\{\begin{array}{c}{u}_r\\ u_l\end{array}\right\}=\left\{\begin{array}{c}0\\ 0\end{array}\right\}$

In formula, u _rthe motion vector of reference mode r-collection, u _lit is the motion vector of reference mode l-collection.Second piece of system of equations of sub solving method above formula obtains:

[K _lr]{u _r}+[K _ll]{u _l}＝0

{u _l}＝-[K _ll] ^-1[K _lr]{u _r}＝[G _lr]{u _r}

In formula, [G _lr] be the restriction matrix between l-collection and r-collection.So, obtain the restriction relation [G between a-collection and r-collection _ar]:

$\left\{u_a\right\}=\left\{\begin{array}{c}{u}_r\\ u_l\end{array}\right\}=\left[\begin{array}{c}{I}_{rr}\\ G_{lr}\end{array}\right]\left\{u_r\right\}=\[G_{ar}\]\left\{u_r\right\}---\left(1\right)$

Step 11, sets up and reduces load column { P _r.[G is retrained by the r-collection obtained and a-collection rigid body displacement _ar], obtain reducing load column { P _r}:

{P _r}＝[G _ar] ^T{P _a}＝[G _ar] ^T{P}(2)

The present invention is only the loading imbalance situation on permanent overload and gravity direction for unmanned plane at gravity direction.For the state of flight that this is common, unmanned plane x-to direction and z-stressed to direction be zero, and because unmanned plane is only by the load effect of gravity direction, therefore rigid body unmanned plane is zero around the moment of torsion that vertical direction rotates.Therefore the non-equilibrium load { P of rigid body unmanned plane after obtaining bunching _rconcrete form is:

{P _r}＝[0P _n0M ₁0M ₃] ^T(3)

Here, P _nfor unmanned plane is along gravity direction load, M ₁for unmanned plane is along moment of flexure suffered by x-axle, M ₃for unmanned plane is along moment of flexure suffered by z-axle.In this example, unmanned plane aerodynamic loading is substituted into (2) formula, obtains reducing load column { P _rbe

{P _r}＝[01.86×10 ⁵07.30×10 ⁵08.79×10 ⁶] ^T(4)

Step 12: determine r-collection trim Mass matrix by r-collection generalized load.The trim Mass matrix of r-collection is made to be r-collection node acceleration a _r=[0a _y0000] ^t, constant for ensureing the overload of structure, namely unmanned plane load act as zero about relative reference point.The then inertial load of r-collection trim quality and the unbalanced load { P of unmanned plane structure _rzero is act as, by reducing load column { P in step 11 about r-collection _rthe rigid block element that can obtain r-collection is

$\[M_{rr}^I\]\left\{a_r\right\}+\left\{P_r\right\}=0$

Therefore

$\[M_{rr}^I\]\left\{a_r\right\}=-\left\{p_r\right\}={\left[\begin{array}{cccccc}0& -P_n& 0& -M_1& 0& -M_3\end{array}\right]}^T---\left(5\right)$

Namely a feasible r-collection trim Mass matrix solution can be provided by above formula:

$\[M_{rr}^I\]==\left[\begin{array}{cccccc}-P_n/a_y& 0& 0& 0& 0& 0\\ 0& -P_n/a_y& 0& -M_1/a_y& 0& -M_3/a_y\\ 0& 0& -P_n/a_y& 0& 0& 0\\ 0& -M_1/a_y& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& -M_3/a_y& 0& 0& 0& 0\end{array}\right]---\left(6\right)$

Namely generalized mass increment battle array can ensure the unchangeability of unmanned plane overload under flight load function, and shows that the increment of trim quality should be-P _n/ a _y.

By (4) formula and a _y(6) formula of substitution can about r-collection trim Mass matrix

$\[M_{rr}^I\]=\left[\begin{array}{cccccc}18.98& 0& 0& 0& 0& 0\\ 0& 18.98& 0& 74.48& 0& 896.9\\ 0& 0& 18.98& 0& 0& 0\\ 0& 74.48& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 896.9& 0& 0& 0& 0\end{array}\right]$

Need particularly point out, in the methods of the invention, the node location of relative reference point 3 is fixing, thus causes non-trim Mass matrix to be broad sense.In fact also exist in space a bit, adopt traditional Mass matrix at that point, first three namely only in diagonal entry has value, and size is-P _n/ a _y, namely can be embodied as M ₁and M ₃balance.Make this position relative to the x of relative reference point r to distance for r _x, z is r to distance _z, then

r _x＝M ₃/P _n，r _z＝M ₁/P _n

Described r _xwith r _zafter being mainly used in structure optimization, locus adjustment is carried out for cargo structures such as fuel tanks, by the adjustment to its center of gravity, to eliminate in optimizing process because size upgrades the impact of the unmanned plane centre of gravity place change brought.According to learn that unmanned plane is under current configuration, need increase quality of loads is 18.98Kg, and this mass cg be 47.25mm, z to apart from being 3.92mm relative to relative reference point x to distance.

Step 13: determine the Rigid Constraints relation between relative reference point r-collection and non-structural trim mass unit node.Note relative reference point is r point, and non-structural trim mass unit node is s point.The corner of relative reference point and non-structural trim mass unit node is respectively θ _rand θ _s, displacement is respectively d _rand d _s.The displacement of non-structural trim mass unit node and the displacement of corner relative reference point and corner are expressed as:

d _r＝d _s+θ _s×r _sr

θ _r＝θ _s

In formula, r _srfor by the vector of node s to node r.Then the displacement of non-structural trim mass unit node and the expression matrix of corner and relative reference point displacement and corner close and are:

$u_r=\left[\begin{array}{cccccc}1& 0& 0& 0& d_z& -d_y\\ 0& 1& 0& -d_z& 0& d_x\\ 0& 0& 1& d_y& -d_x& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]u_s=G_{rs}{u}_s---\left(7\right)$

Wherein, u _r=[d _r, θ _r] ^t, u _s=[d _s, θ _s] ^t, d _x, d _y, d _zfor vector r _srat the component in x, y, z direction, G _rsfor the Rigid Constraints relational matrix between relative reference point and non-structural trim mass unit node.By relative reference point coordinate (1781.0,-643.78,0.0) and non-structural trim mass unit node coordinate (1781.0 ,-448.96,0.0) substitute into the Rigid Constraints relation G that (7) formula obtains between relative reference point and non-structural trim mass unit node _rs

$G_{rs}=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& -193.82\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 193.82& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$

Rapid 14, determine the trim Mass matrix of non-structural trim mass unit.By the trim Mass matrix of non-structural trim mass unit in the r-collection trim Mass matrix equivalent transformation to step 5 in step 12.The displacement of non-structural trim mass unit and acceleration is made to be respectively u _sand a _s, trim Mass matrix is M _s.Then non-structural trim mass unit inertial force institute work W in corresponding displacement _sfor

$W_s=u_s^T{M}_s{a}_s$

In like manner can obtain inertial load institute work W in corresponding displacement of r-collection trim Mass matrix _rfor

$W_r=u_r^T{M}_{rr}^I{a}_r=u_s^T{G}_{rs}^T{M}_{rr}^I{G}_{rs}{a}_s$

Due to both equivalency transform energy coincidence, i.e. W _s=W _r.Therefore

$M_s=G_{rs}^T{M}_{rr}^I{G}_{rs}---\left(8\right)$

Rigid Constraints relation G between the r-collection that step 13 is obtained and non-structural trim mass unit node _rs, (8) formula of substitution can access non-structural trim mass unit mass property M _s

$\[M_s\]==\left[\begin{array}{cccccc}18.98& 0& 0& 0& 0& -3679\\ 0& 18.98& 0& 74.48& 0& 896.9\\ 0& 0& 18.98& 3679& 0& 0\\ 0& 74.48& 3679& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ -3679& 896.9& 0& 0& 0& 0\end{array}\right]$

M in above formula _sbe the trim Mass matrix of added non-structural mass point in structural model, it should be noted that this quality trim increment battle array is broad sense, not only comprise quality information, further comprises moment of inertia information.M _sreflect the inertial force for guarantee unmanned plane overload under flight load function is constant and need increase and moment, this is because in design process, the barycenter change that structural configuration Parameters variation causes is indefinite, and the setting of non-structural trim quality point is determined, namely the trim of inertial load is not only the trim of mass force, also needs the trim of moment.

Step 15: give non-structural trim mass unit qualitative attribute, and complete finite element analysis.Give non-structural trim mass unit qualitative attribute, and complete finite element analysis.The M of gained will be calculated by step 14 _sgive non-structural trim mass unit, namely can complete corresponding nodal displacement and stress distribution analysis further by NASTRAN solver.

By the effect of this non-structural trim mass unit, can obtain the unmanned plane structural finite element model of a self-equilibrating, be namely zero at relative reference point place support reaction.The present invention, when not changing overload, obtains the unmanned plane structure of a self-equilibrating by the trim of non-structural mass, this finite element numerical simulation for unmanned plane is vital.If adopt traditional displacement constraint method or inertia release rule that finite element analogy can be made to obtain irrational numerical solution.

In the present embodiment, step 7 ~ 14 mainly complete unbalanced load and the analysis of non-structural trim mass unit mass property, by the introducing of non-structural trim mass unit, entirety keeps the constant of unmanned plane mass property in the design process, the centre of gravity place comprising the quality size of unmanned plane and unmanned plane is constant, thus ensure that, under the effect of specific external load, the overload of unmanned plane is constant.This technology meets engineering design demand, and implementation process form is simple, automatically can realize the mass property analysis of non-structural trim mass unit easily by writing computer program, thus greatly accelerates the analysis of optimizing design of unmanned plane finite element.This technology overcomes the unreasonable analysis result of displacement constraint method and the introducing of inertia method for releasing, is efficient unmanned plane structural design, and unmanned plane Optimal Structure Designing especially efficiently, provides good technical support.

Claims (4)

1. the non-structural mass Calculate Ways of aircraft under permanent overload, it is characterized in that, detailed process is:

Step 1, limits first unstrctured grid to divide: according to the unmanned plane cad data that user is given, adopts Hypermesh software to carry out the division of finite element unstrctured grid to unmanned plane CAD geometric model;

Step 2, inputs the parameter of each part material of unmanned plane in Hypermesh software: the parameter of each part material of described unmanned plane comprises: Young modulus E, and unit is MPa; Shear modulus G, unit is MPa; Poisson ratio μ and density p, unit is Kg/mm ³; And composite plys one-way tape material property; Described composite plys one-way tape material property comprises 1-direction Young modulus E ₁, 2-direction Young modulus E ₂, 1-2 plane Poisson ratio μ ₁₂,-2 plane shear modulus G ₁₂, 1-3 plane shear modulus G ₁₃, 2-3 plane shear modulus G ₂₃and density p;

Step 3, imports Patran software by establishing later wing finite element model file;

Step 4, sets up lumped mass point: establish two lumped mass points at fuel tank load Nodes, to simulate the effect of oil tank fuel load to aircaft configuration; In described unmanned plane, fuel tank is positioned at frame sections; In aircraft Finite element design, fuel oil adopts lumped mass unit to replace usually, by the effect of web by its dynamic changes process to fuselage;

Step 5, sets up mass unit: set up a mass unit in the lower end of the fuselage plane of symmetry; This mass unit x-is consistent to coordinate with the x-of fuel tank load node to position, is designated as non-structural trim mass unit; In finite element initial analysis, the quality settings of non-structural trim mass unit is zero, and is connected on two lumped mass cell nodes of foundation in step 4 by the RBE3 unit in Nastran software;

Step 6, obtain initial stiffness matrix K, initial mass battle array M and aerodynamic loading array { F}: the aerodynamic loading inputting the given unmanned plane of user in Patran software, final generation Nastran software can perform BDF model file, and is committed to initial stiffness matrix K, initial mass battle array M and aerodynamic loading array { F} that Nastran software calculates also derived type structure;

Step 7, solve aircraft finite element structure model panel load array P}: the initial mass battle array M derived according to Nastran software and the given aerodynamic loading of user { F}, solves the panel load array { P} of aircraft finite element structure model; Load column P} comprise external action aerodynamic loading F} and architecture quality inertial load G}, mass inertia load G} by designer according to the loading factor n under current flight state _ypropose; Make the node total number in aircraft finite element model be n, then the vector acceleration of each node is expressed as:

$a={\[a_1^T,...,a_i^T,...,a_n^T\]}^T,i=1,...,n$

In formula, a _i=[0a _y0000] ^t, a _y=n _yg, a _yfor the accekeration in airplane ascensional force direction, g is acceleration of gravity; When aircraft is at the uniform velocity flat fly time, n _ywhen=1, the inertial load of aircraft is expressed as:

G＝Ma

By above formula obtain aircraft finite element structure model panel load array P} is:

{P}＝{F}-{G}

Step 8, chooses relative reference point: choose a finite element node as relative reference point at fuselage plane of symmetry lower end, be designated as r-collection; Relative reference point x-is consistent to coordinate with the x-of fuel tank load node to position, and coordinate is (1781.0 ,-449.964,0.0); If translation displacements and the corner displacement of relative reference point are constrained to zero;

Step 9: piecemeal process is carried out to stiffness matrix: the complete set of node of definition aircraft finite element model is a-collection, and reference mode is r-collection, and is concentrated by a-the set of node not comprising r-collection to be designated as l-collection, is called residue set of node; Then the stiffness matrix Partitioning Expression of A of aircaft configuration is

$K=K_{aa}=\left[\begin{array}{cc}{K}_{rr}& K_{rl}\\ K_{lr}& K_{ll}\end{array}\right]$

Described K _aathe stiffness matrix that a-collection is relevant, K _rrthe stiffness matrix that r-collection is relevant, K _llthe stiffness matrix that l-collection is relevant, K _lrthe Coupling stiffness matrix of l-collection and r-collection, K _rlit is the Coupling stiffness matrix of r-collection and l-collection;

Step 10: determine the restriction relation in aircaft configuration model between a-collection and r-collection and bunching load column: by Guyan bunching principle, determine the restriction relation in aircaft configuration model between a-collection and r-collection and bunching load column, obtain the restriction relation [G between a-collection and r-collection _ar]:

$\left\{u_a\right\}=\left\{\begin{array}{c}{u}_r\\ u_l\end{array}\right\}=\left[\begin{array}{c}{I}_{rr}\\ G_{lr}\end{array}\right]\left\{u_r\right\}=\[G_{ar}\]\left\{u_r\right\}---\left(1\right)$

Step 11, sets up and reduces load column { P _r}: retrain [G by the r-collection obtained and a-collection rigid body displacement _ar], obtain reducing load column { P _r}:

{P _r}＝[G _ar] ^T{P _a}＝[G _ar] ^T{P}(2)

Aircraft when gravity direction is the state of flight of loading imbalance on permanent overload and gravity direction, this aircraft x-direction of principal axis and the z-axis direction stressed be zero, obtain the non-equilibrium load { P of rigid body aircraft after bunching _rconcrete form is:

{P _r}＝[0P _n0M ₁0M ₃] ^T(3)

In formula, P _nfor aircraft is along gravity direction load, M ₁for aircraft is along moment of flexure suffered by x-axle, M ₃for aircraft is along moment of flexure suffered by z-axle;

Step 12: determine r-collection trim Mass matrix by r-collection generalized load: the trim Mass matrix making r-collection is [M _r ⁱ _r], r-collection node acceleration a _r=[0a _y0000] ^t, by reducing load column { P in step 11 _rthe rigid block element that obtains r-collection is

$\[M_{rr}^I\]\left\{a_r\right\}+\left\{P_r\right\}=0$

Therefore

$\[M_{rr}^I\]\left\{a_r\right\}=-\left\{P_r\right\}={\left[\begin{array}{cccccc}0& -P_n& 0& -M_1& 0& -M_3\end{array}\right]}^T---\left(5\right)$

Providing r-collection trim Mass matrix by formula (5) is:

$\[M_{rr}^I\]=\left[\begin{array}{cccccc}-P_n/a_y& 0& 0& 0& 0& 0\\ 0& -P_n/a_y& 0& -M_1/a_y& 0& -M_3/a_y\\ 0& 0& -P_n/a_y& 0& 0& 0\\ 0& -M_1/a_y& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& -M_3/a_y& 0& 0& 0& 0\end{array}\right]---\left(6\right)$

Namely this Mass matrix can ensure the unchangeability of aircraft overload under flight load function, and shows that the increment of trim quality should be-P _n/ a _y;

Step 13: determine the Rigid Constraints relation between r-collection and non-structural trim mass unit node:

Note relative reference point is r point, and non-structural trim mass unit node is s point; The corner of relative reference point and non-structural trim mass unit node is respectively θ _rand θ _s, displacement is d _rand d _s; Then the displacement of non-structural trim mass unit node and the expression matrix of corner and relative reference point displacement and corner close and are:

$u_r=\left[\begin{array}{cccccc}1& 0& 0& 0& d_z& -d_y\\ 0& 1& 0& -d_z& 0& d_x\\ 0& 0& 1& d_y& -d_x& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]u_s=G_{rs}{u}_s---\left(7\right)$

Wherein, u _r=[d _r, θ _r] ^t, u _s=[d _s, θ _s] ^t, d _x, d _y, d _zfor vector r _srat the component in x, y, z direction, G _rsfor the Rigid Constraints relational matrix between relative reference point and non-structural trim mass unit node; The Rigid Constraints relation between r-collection and non-structural trim mass unit node can be determined by formula (7);

Rapid 14, determine the trim Mass matrix of non-structural trim mass unit: by the trim Mass matrix of non-structural trim mass unit in the r-collection broad sense trim Mass matrix equivalent transformation to step 5 in step 12; The displacement of non-structural trim mass unit and acceleration is made to be respectively u _sand a _s, trim Mass matrix is M _s,

$M_s=G_{rs}^T{M}_{rr}^I{G}_{rs}---\left(8\right)$

Step 15: give non-structural trim mass unit qualitative attribute, and complete finite element analysis: by M _sgive non-structural trim mass unit, namely can complete corresponding nodal displacement and stress distribution analysis further by Nastran solver; So far, the trim of aircraft non-structural mass under permanent overload is completed.

2. the non-structural mass Calculate Ways of aircraft under permanent overload as claimed in claim 1, it is characterized in that, during the effect of the lumped mass point simulation oil tank fuel load set up by fuel tank load Nodes in step 4 to aircaft configuration, fuel oil adopts lumped mass unit to replace usually, by the effect of web by its dynamic changes process to fuselage.

3. the non-structural mass Calculate Ways of aircraft under permanent overload as claimed in claim 1, it is characterized in that, the quality settings of the mass unit set up in fuselage plane of symmetry lower end in step 5 is zero, and is connected to by the RBE3 unit in Nastran software on two lumped mass cell nodes of foundation in step 4.

4. the non-structural mass Calculate Ways of aircraft under permanent overload as claimed in claim 1, is characterized in that, determining the restriction relation [G in described aircaft configuration model between a-collection and r-collection _ar] time, by solving the structure finite element equation of described a-collection:

$\left[\begin{array}{cc}{K}_{rr}& K_{rl}\\ K_{lr}& K_{ll}\end{array}\right]\left\{\begin{array}{c}{u}_r\\ u_l\end{array}\right\}=\left\{\begin{array}{c}0\\ 0\end{array}\right\}$

Obtain:

[K _lr]{u _r}+[K _ll]{u _l}＝0

{u _l}＝-[K _ll] ^-1[K _lr]{u _r}＝[G _lr]{u _r}

In formula, described [G _lr] be the restriction matrix between l-collection and r-collection; u _rthe motion vector of reference mode r-collection, u _lit is the motion vector of reference mode l-collection.