CN103544347A - Finite element analyzing method for inflatable unfolding fabric working process - Google Patents

Abstract

The invention discloses a finite element analyzing method for an inflatable unfolding fabric working process. The finite element analyzing method comprises the following steps of performing reverse folding modeling on a fabric to obtain a folded model on the basis of an indirect deformation principle; performing inflatable unfolding calculation on the folded model by using a finite element method; and realizing finite element simulation on the inflatable unfolding fabric working process. The reverse folding modeling comprises the main steps of (1) establishing a finite element grid model of the fabric which is in a completely unfolding state; (2) selecting a deformation strategy on the finite element grid model; (3) performing interpolation offset on the basis of an indirect deformation principle, and enabling nodes in a deformation area to respond to constrained point offset; and (4) detecting the quality of grids to obtain a fabric grid model which is folded. According to the finite element analyzing method, the fabric model which is in the complete unfolding state is reversely deformed to be in the folded state by using the indirect deformation principle for the first time, modeling of the fabric can be carried out under the condition that the appearance of the fabric is complicated or a folding mode is complicated, and numerical simulation of a complicated folded fabric unfolding process can be realized.

Description

A kind of finite element method of the inflating expanded fabric course of work

Technical field

The present invention relates to a kind of finite element method of the inflating expanded fabric course of work, belong to aviation lifesaving's technical field.

Background technology

Inflating expanded fabric (as parachute, air bag), due to the advantage that its storage space is little, cost is low, work efficiency is high, is widely used in the fields such as Aeronautics and Astronautics.Inflating expanded fabric strong nonlinearity work characteristics of acute variation under airflow function has determined that its deployment lifting process becomes most critical and a most dangerous link.Therefore the course of work of the inflating expanded fabric of the inflating expanded fabric of complexity or employing special marked fold mode being carried out to finite element analysis, is the technical matters of needing solution badly.But fabric folded modeling is the problem that first finite element analysis of the inflating expanded fabric course of work will solve.Current existing grid method for folding needs a large amount of experiences, directly calculates the position coordinates of folding line or fold, is only applicable to the modeling of simple folding fabric.For some more complicated inflation fabrics or other special marked fold mode modelings, almost cannot realize by classic method.

Summary of the invention

Technical matters to be solved by this invention be in background technology, relate to how to the inflating expanded fabric of complexity or adopt the course of work of the inflating expanded fabric of special marked fold mode to carry out finite element analysis, a kind of inflating expanded fabric course of work finite element method is proposed.

The present invention for achieving the above object, adopts following technical scheme:

A kind of finite element method of the inflating expanded fabric course of work, first based on indirect deformation principle, carry out the reverse folding modeling of fabric and obtain folding model, next adopts Finite Element Method to carry out inflating expanded calculating to folding model, realizes the course of work finite element simulation of complicated inflating expanded fabric; Wherein said reverse folding modeling process is as follows:

Step 1: use shell unit to carry out grid division to deployed condition fabric, set up the fabric finite element grid model under complete deployed condition;

Step 2: select distortion strategy, specify the grid cell of restraint joint, spatial offset, deformed region and be out of shape borderline node on fabric finite element grid model;

Step 3: the grid node in deformed region is carried out to the interpolation skew based on indirect deformation principle, make the node response obligatory point skew in deformed region;

Step 4: element quality detects;

Mesh quality after distortion is detected, if mesh quality is defective, reselect distortion strategy, repeating step two is to step 3, until the mesh quality after distortion reaches requirement again.

As the further prioritization scheme of finite element method of a kind of inflating expanded fabric course of work of the present invention, described Finite Element Method is for controlling the solid coupling process of volumetric method or stream.

As the further prioritization scheme of finite element method of a kind of inflating expanded fabric course of work of the present invention, described shell unit is triangular element or quadrilateral units.

As the further prioritization scheme of finite element method of a kind of inflating expanded fabric course of work of the present invention, the detailed process of step 2 and step 3 is:

According to actual folding mode, on definition grid model, certain node, as obligatory point P, and obtains being offset rear obligatory point P according to spatial offset ^*, deformed region grid node Q is configured to a triangle Δ PP ^*q, establishes Δ PP ^*q place plane and the deformed region border l Q that intersects at a point _c, adopt Q _c, P ^*, a new triangle Δ PP of these 3 of P structure ^*q _c;

At above-mentioned P point, P ^*point and Q _cthe triangle Δ PP that point forms ^*q _c, Q sets up an office _pfor a Q is at straight line Q _cthe projection of P, calculates the skew weight t of deformed region grid node Q, and computing formula is:

t=|Q _p(x,y,z)-P(x,y,z)|/|Q _c(x,y,z)-P(x,y,z)| （1）

According to skew weight, t calculates a Q at straight line

upper corresponding point coordinate:

$Q_p^{*}(x,y,z)=t\·Q_c(x,y,z)+(1-t)\·P^{*}(x,y,z)---\left(2\right)$

And final volume coordinate after grid node Q distortion is:

$Q^{*}(x,y,z)=Q_p^{*}(x,y,z)+|Q(x,y,z)-Q_p(x,y,z)|\·n---\left(3\right)$

Wherein, vector Q _p(x, y, z) represents some Q _pvolume coordinate, P (x, y, z), Q _c(x, y, z), P ^*(x, y, z), Q ^*(x, y, z),

q _p(x, y, z) represents respectively some P, some Q _c, some P ^*, some Q ^*, point

point Q _pvolume coordinate; N is a little

the normal vector at place;

If there is multiple constraint point P _n, the side-play amount of independent calculation level Q under each obligatory point impact, finally averages calculating to all side-play amounts.

As the further prioritization scheme of finite element method of a kind of inflating expanded fabric course of work of the present invention, described intersection point Q _ccoordinate by element sides interpolation, obtain.

As the further prioritization scheme of finite element method of a kind of inflating expanded fabric course of work of the present invention, in step 4, be that the mesh quality after adopting Jacobian to distortion detects.

The further prioritization scheme of finite element method as a kind of inflating expanded fabric course of work of the present invention, also comprise step 5: to being not suitable for adopting the part of the reverse folding modeling based on indirect distortion, should adopt additive method to process, as coordinate transformation method, the solid coupling process of stream.

The further prioritization scheme of finite element method as a kind of inflating expanded fabric course of work of the present invention, also comprises step 6: the error that adopts correction stress to produce indirect distortion is revised, and is specially:

Using the grid of deployed condition as with reference to grid, and grid after folding is as map grids, relatively the difference between two nested grids, calculates correction stress, on grid after folding, apply correction stress, guarantee that folding model is identical with expansion model after inflating expanded.

The present invention adopts above technical scheme, and the advantage compared with prior art having is:

The present invention abandons the thought of original direct calculating folding line or fold node coordinate completely, but adopt means indirectly to obtain the position of folding line or fold: definition deformed region, obligatory point and spatial offset, suppose that obligatory point is offset, and also there is certain displacement in all the other adjacent nodes under " pullling " of obligatory point, and distance restraint point is nearer, be offset greatlyr, grid model can be deformed into folded state from deployed condition completely so.The present invention has realized the course of work finite element simulation of complicated inflating expanded fabric just based on this indirectly folding idea about modeling, overcome the shortcoming that existing folding modeling method cannot adapt to complex folds modeling completely, by calculating, find, the present invention meets requirement of engineering completely, can save actual loading test test, for inflation Fabric Design provides reference.

Accompanying drawing explanation

Fig. 1 is air bag model overall schematic.

Fig. 2 is bonnet geometry model and burst schematic diagram.

Fig. 3 is gas cell netting lattice model schematic diagram.

Fig. 4 is the schematic diagram of containment surfaces.

Fig. 5 is the partial enlarged drawing of Fig. 4.

Fig. 6 is multiple constraint point definition schematic diagram.

Fig. 7 is that distortion defines schematic diagram indirectly.

Fig. 8 is distorted area node offset method schematic diagram.

Fig. 9 is one of element deformation schematic diagram.

Figure 10 is two of element deformation schematic diagram.

Figure 11 is three of element deformation schematic diagram.

Figure 12 is four of element deformation schematic diagram.

Figure 13 is Nang body middle part first paragraph deformation pattern.

Figure 14 is Nang body middle part second segment deformation pattern.

Figure 15 is the 3rd section of deformation pattern in Nang body middle part.

Figure 16 is that utricule middle part cell node Z-direction coordinate carries out ratio and dwindles schematic diagram.

Figure 17 is the downward translation schematic diagram of utricule head unit node Z-direction coordinate.

Figure 18 is final folding model schematic diagram.

Figure 19 is folding model outside drawing while being full of.

Number in the figure is explained: 1-distorted area, 2-non-deformation zone, 3-distorted area border l, 4-containment surfaces.

Figure 20 is holistic approach process flow diagram of the present invention.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in further detail.

First, shown in Figure 20, the finite element method overall flow of the inflating expanded fabric course of work of the present invention is as follows:

First based on indirect deformation principle, carry out the reverse folding modeling of fabric and obtain folding model, specific as follows:

Step 1: use shell unit (as triangular element or quadrilateral units etc.) to carry out grid division to deployed condition fabric, set up the fabric finite element grid model under complete deployed condition.

Step 2: select distortion strategy, specify the grid cell of restraint joint, spatial offset, deformed region and be out of shape borderline node on fabric finite element grid model.

Step 3: the grid node in deformed region is carried out to the interpolation skew based on indirect deformation principle, make the node response obligatory point skew in deformed region.

Step 4: element quality detects; Mesh quality after distortion is detected to (as adopted Jacobian), if mesh quality is defective, reselect distortion strategy, repeating step two is to step 3, until the mesh quality after distortion reaches requirement again.

Step 5: to being not suitable for adopting the part of the reverse folding modeling based on indirect distortion, adopt additive method to process, additive method comprises coordinate transformation method, the solid coupling process of stream.

Step 6: the error that adopts correction stress to produce indirect distortion is revised, and is specially:

Using the grid of deployed condition as with reference to grid, and grid after folding is as map grids, relatively the difference between two nested grids, calculates correction stress, on grid after folding, apply correction stress, guarantee that folding model is identical with expansion model after inflating expanded.

Secondly, adopt Finite Element Method (as controlled the solid coupling process of volumetric method or stream) to carry out inflating expanded calculating to folding model, realize the course of work finite element simulation of complicated inflating expanded fabric.

For proving feasibility of the present invention, using certain extraordinary air bag (shown in Fig. 1) as example, enforcement of the present invention is discussed in detail:

The first step: use shell unit to carry out grid division to deployed condition fabric, set up fabric finite element grid model and the geometric surface for retraining under complete deployed condition;

First, from point-line-face, set up geometric model, wherein afterbody is directly set up the geometric model of folded state according to engine request, and stage casing utricule carries out burst processing and set up folding line (Fig. 2); Finally adopt triangle and tetragonal mixed mesh geometric model (Fig. 3), can certainly all use triangular mesh or quadrilateral mesh.

Secondly, in order to make cell node that accurately distortion skew occur, prevent initial intert or overlapping, the present invention takes full distortion indirectly to all nodes in deformation domain.Folding according to reality, adopt the order of point-line-face to set up containment surfaces, containment surfaces and above-mentioned geometric model intert (Fig. 4) mutually, make each burst containment surfaces and geometry bursts in Fig. 2 corresponding (Fig. 5) one by one.

Second step: select distortion strategy, specify the grid cell of restraint joint, spatial offset, deformed region and be out of shape borderline node on fabric finite element grid model;

Unit shown in Fig. 6 is made as to deformed region, by camber line

upper each point, as obligatory point, is established each obligatory point and is projected to successively line l by former putting in order _1*2*, wherein, P sets up an office ₁be projected to a P ₁ ^*position, some P ₂be projected to a P ₂ ^*position, and all the other each points keep equidistantly projecting to straight line relevant position, so just can specify a plurality of restraint joints and spatial offset thereof simultaneously.

The 3rd step: the grid node in deformed region is carried out to the interpolation skew based on indirect deformation principle, make the node response obligatory point skew in deformed region;

Change to fabric unit node space coordinate, is not the FEM (finite element) calculation adopting based on the principle of virtual work, but finite element grid figureization is processed.If the obligatory point defining in second step is offset, and also there is certain displacement in all the other adjacent nodes under " pullling " of obligatory point, and distance restraint point is nearer, be offset greatlyr, grid model can be deformed into folded state from deployed condition completely so.

On definition grid model, certain node, as obligatory point P, and obtains being offset rear obligatory point P according to spatial offset ^*, deformed region grid node Q is configured to a triangle Δ PP ^*q(Fig. 7), establish Δ PP ^*q place plane and the deformed region border l Q that intersects at a point _c, adopt Q _c, P ^*, a new triangle Δ PP of these 3 of P structure ^*q _c(Fig. 8);

At above-mentioned P point, P ^*point and Q _cthe triangle Δ PP that point forms ^*q _c, Q sets up an office _pfor a Q is at straight line Q _cthe projection of P, calculates the skew weight t of deformed region grid node Q, and computing formula is:

t=|Q _p(x,y,z)-P(x,y,z)|/|Q _c(x,y,z)-P(x,y,z)| （1）

According to skew weight, t calculates a Q at straight line upper corresponding point

coordinate:

$Q_p^{*}(x,y,z)=t\·Q_c(x,y,z)+(1-t)\·P^{*}(x,y,z)---\left(2\right)$

And final volume coordinate after grid node Q distortion is:

$Q^{*}(x,y,z)=Q_p^{*}(x,y,z)+|Q(x,y,z)-Q_p(x,y,z)|\·n---\left(3\right)$

Wherein, vector Q _p(x, y, z) represents some Q _pvolume coordinate, P (x, y, z), Q _c(x, y, z), P ^*(x, y, z), Q ^*(x, y, z), q _p(x, y, z) represents respectively some P, some Q _c, some P ^*, some Q ^*, point

point Q _pvolume coordinate; N is a little

the normal vector at place;

In above-mentioned second step, the present invention has defined P simultaneously ₁, P ₂and a plurality of obligatory points of point-to-point transmission and spatial offset (Fig. 6) thereof, side-play amount based on the first independent calculation level Q of said method under each obligatory point impact, then all side-play amounts are averaged to calculating, just can determine the side-play amount that a Q is final, by this calculating, realized camber line

processing.

Adopt and use the same method to camber line process (after processing, element deformation as shown in Figure 9).

Sideline, obligatory point place after distortion, as new border, is reset to deformed region according to new border.To camber line

take identical processing mode (after distortion as shown in figure 10), the obligatory point on former camber line after distortion is defined as to border, continue camber line

process (after distortion as shown in figure 11).

From Figure 11, can find, after the distortion of a series of node space, the node of deformed region overlaps completely with the limit of containment surfaces, but due to error, also has part of nodes not and containment surfaces is well fitted.Finally by not completely the node of laminating be projected to containment surfaces (after distortion as shown in figure 12).

The 4th step: element quality detects;

To being out of shape rear unit, carry out quality testing, unit is imported in HYPERMESH software and detected, Jacobian determinant (Jacobian) is detected, find that all unit inspection values are all greater than 0.4, in the reasonable scope.If detected value is too small or occur negative value, reselect distortion strategy, as reselect obligatory point, deformed region etc., again repeat second step to the three steps.

The 5th step: to being not suitable for adopting the part of the reverse folding modeling based on indirect distortion, adopt additive method to fold modeling.

Pass through said method, the present invention has realized the most folding modeling of this air bag (Figure 13-Figure 15), but it is folding not carry out the compression of whole height direction, same head is also not yet realized folding, for the model shown in Figure 15, said method is no longer applicable, but can adopt other existing methods to process.

(the method can reference: Zhang J H to use coordinate transformation method, Ma C S, Bai Y L, et al.Airbag mapped mesh auto-flattening method.Tsinghua Science and Technology, 2005,10 (3): 387-390.), the Z-direction coordinate of all nodes of middle part utricule is carried out to ratio and dwindle (Figure 16); By head unit node along the downward translation of Z-direction (Figure 17).

Finally, adopt existing based on FSI(Fluid Structure Interaction, the solid coupling of stream) method is compressed calculating to utricule head (the method can be with reference to CHENG Han, YU Li, YIN Zhuwei.A New Method of Complicated Folded Fabric Modeling.Journal of Harbin Institute of Technology, 2012,19 (2): 43-46.), finally obtain the air bag model of complete folded state as shown in figure 18.

The 6th step: the error that adopts correction stress to produce indirect distortion is revised;

Hereto, model deformation in Fig. 3 is to the model in Figure 18, mesh topology does not change, therefore using the grid model in Fig. 3 as with reference to grid, and folding grid model in Figure 18 is as map grids, the difference that compares both, calculate correction stress, when inflating expanded calculating, correction stress is applied on grid model as initial mechanical border, thereby guaranteeing folding model, identical with material object after inflating expanded (method can reference: Cheng Han, Yu Li, Zhang Xinhua etc. the folding modeling method of parachute of revising based on IMM. computer-aided design (CAD) and graphics journal, 2013, 25 (5): 751-757.).

(computing method can reference: Yu Li finally folding model to be carried out to inflating expanded calculating, Cheng Han, Liu Xiong. the solid Coupled Numerical Simulation of airbag aeration process streams. the journal .2010 of Nanjing Aero-Space University, 42 (4): 472-476.), model after expansion as shown in figure 19, and by utricule (Figure 19) size after reverse modeling inflation and the contrast of design utricule (Fig. 1) size, can find utricule and exact shape basically identical (in Table 1).

Design load and moulded dimension contrast after table 1 inflation

Utricule structure height	Design load	Model
			Hemispherical head (m)	0.3	0.312
Cylindric middle part (m)	1.5	1.511
			Coniform afterbody (m)	1	0.994

Inflating expanded fabric course of work finite element method of the present invention, adopt first distortion indirectly to realize the folding modeling of flexible fabric, the model adopting when modeling meets engineering reality, reliable results, can obtain folding model effectively accurately, the inflating expanded finite element numerical simulation of complex folds fabric is calculated becomes possibility, can save actual loading test test, for inflation Fabric Design provides reference.

Claims (9)

1. the finite element method of an inflating expanded fabric course of work, it is characterized in that: first based on indirect deformation principle, carry out the reverse folding modeling of fabric and obtain folding model, next adopts Finite Element Method to carry out inflating expanded calculating to folding model, realizes the course of work finite element simulation of complicated inflating expanded fabric; Wherein said reverse folding modeling process is as follows:

Step 1: use shell unit to carry out grid division to deployed condition fabric, set up the fabric finite element grid model under complete deployed condition;

Step 2: select distortion strategy, specify the grid cell of restraint joint, spatial offset, deformed region and be out of shape borderline node on fabric finite element grid model;

Step 3: the grid node in deformed region is carried out to the interpolation skew based on indirect deformation principle, make the node response obligatory point skew in deformed region;

Step 4: element quality detects;

Mesh quality after distortion is detected, if mesh quality is defective, reselect distortion strategy, repeating step two is to step 3, until the mesh quality after distortion reaches requirement again.

2. the finite element method of a kind of inflating expanded fabric course of work according to claim 1, is characterized in that: described Finite Element Method is for controlling the solid coupling process of volumetric method or stream.

3. the finite element method of a kind of inflating expanded fabric course of work according to claim 1, is characterized in that: described shell unit is triangular element or quadrilateral units.

4. the finite element method of a kind of inflating expanded fabric course of work according to claim 1, is characterized in that: the detailed process of step 2 and step 3 is:

According to actual folding mode, on definition grid model, certain node, as obligatory point P, and obtains being offset rear obligatory point P according to spatial offset ^*, deformed region grid node Q is configured to a triangle Δ PP ^*q, establishes Δ PP ^*q place plane and the deformed region border l Q that intersects at a point _c, adopt Q _c, P ^*, a new triangle Δ PP of these 3 of P structure ^*q _c;

At above-mentioned P point, P ^*point and Q _cthe triangle Δ PP that point forms ^*q _c, Q sets up an office _pfor a Q is at straight line Q _cthe projection of P, calculates the skew weight t of deformed region grid node Q, and computing formula is:

t=|Q _p(x,y,z)-P(x,y,z)|/|Q _c(x,y,z)-P(x,y,z)| （1）

According to skew weight, t calculates a Q at straight line

upper corresponding point

coordinate:

$Q_p^{*}(x,y,z)=t\·Q_c(x,y,z)+(1-t)\·P^{*}(x,y,z)---\left(2\right)$

And final volume coordinate after grid node Q distortion is:

$Q^{*}(x,y,z)=Q_p^{*}(x,y,z)+|Q(x,y,z)-Q_p(x,y,z)|\·n---\left(3\right)$

Wherein, vector Q _p(x, y, z) represents some Q _pvolume coordinate, P (x, y, z), Q _c(x, y, z), P ^*(x, y, z), Q ^*(x, y, z), q _p(x, y, z) represents respectively some P, some Q _c, some P ^*, some Q ^*, point

point Q _pvolume coordinate; N is a little the normal vector at place.

5. the finite element method of a kind of inflating expanded fabric course of work according to claim 4, is characterized in that: if there is multiple constraint point P _n, the side-play amount of independent calculation level Q under each obligatory point impact, finally averages calculating to all side-play amounts.

6. the finite element method of a kind of inflating expanded fabric course of work according to claim 4, is characterized in that: described intersection point Q _ccoordinate by element sides interpolation, obtain.

7. the finite element method of a kind of inflating expanded fabric course of work according to claim 1, is characterized in that: in step 4, be to adopt Jacobian to detect the mesh quality after being out of shape.

8. the finite element method of a kind of inflating expanded fabric course of work according to claim 1, it is characterized in that: also comprise step 5: to being not suitable for adopting the part of the reverse folding modeling based on indirect distortion, employing additive method is processed, and additive method comprises coordinate transformation method, the solid coupling process of stream.

9. the finite element method of a kind of inflating expanded fabric course of work according to claim 1, is characterized in that: also comprise step 6: adopt and revise the error that stress produces indirect distortion and revise, be specially:

Using the grid of deployed condition as with reference to grid, and grid after folding is as map grids, relatively the difference between two nested grids, calculates correction stress, on grid after folding, apply correction stress, guarantee that folding model is identical with expansion model after inflating expanded.

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