CN102417158A - Shell membrane model for forecasting bending and folding characteristics of inflatable membrane beam - Google Patents

Abstract

The invention which provides a shell membrane model for forecasting the bending and folding characteristics of an inflatable membrane beam relates to the technical field of structure mechanics and the structural buckling analysis of membranes. The shell membrane model is established according to the following steps: 1, establishing a membrane model for forecasting the bending and folding characteristics of the inflatable membrane beam; 2, introducing a critical compression stress to establish a thin shell model for forecasting the bending and folding characteristics of the inflatable membrane beam; 3, determining a natural configuration and a prestressed reference configuration according to the bearing characteristic of the inflatable beam; and 4, introducing an inflation pressure effect and a correction coefficient under the prestressed reference configuration to establish a shell model for forecasting the bending and folding characteristics of the inflatable membrane beam to reduce the overestimate of a predicted value of the shell membrane model, and jointly introducing a critical compression stress formula considering the inflation pressure effect to obtain the shell membrane model for forecasting the bending and folding characteristics of the inflatable beam of the membrane. The shell membrane model of the invention is used to forecast the bending and folding characteristics of the inflatable membrane beam.

Description

The shell membrane model that is used for film inflation beam cockle prediction of Characteristics

Technical field

The present invention relates to the technical field that a kind of membrane structure mechanics and buckling structure are analyzed.

Background technology

Film inflation beam is the primary load bearing parts of large-scale spacecraft membrane structure (like developing space inflation antenna and solar sail etc.), bears the main force status of end bending load when being its work.Because the wall thickness of film inflation beam is thin (micron order) very, thus be easy to cripling to occur under the bending load effect near its stiff end, even have under the situation of pressure effect also can its axially and hoop produce a plurality of folds.Inflation beam end moment of flexure corresponding when fold produces is critical rugosity moment of flexure; Fold can be expanded rapidly along the axial and hoop of film inflation beam along with the increase of moment of flexure simultaneously; When fold almost spreads all over whole hoop; Film inflation beam will lose bearing capacity, and this moment, corresponding inflation beam end moment of flexure was the inefficacy moment of flexure, and the cockle prediction of Characteristics is the key problem that film inflation joist support force characteristic is analyzed.

At present, film inflation beam cockle prediction of Characteristics model mainly contains two big types, and one type is thin-skin model, and another kind of is the shell model.Thin-skin model is thought of as pure film with the beam wall material, thinks that stiff end produced fold when inflation beam axial stress was zero, and fold structural failure when spreading all over whole hoop.The shell model is thought of as shell with the beam wall material, thinks that it can resist small compression stress, when inflation beam axial stress reaches critical compressive stress, fold occurs, and fold structural failure when spreading all over whole hoop.The shell model is through the superimposed forecast that realizes film inflation beam cockle characteristic of the moment of flexure of moment of flexure that the shell compression stress is partly born and thin-skin model forecast.

Thin-skin model and shell model are all supposed structural failure when fold spreads all over whole inflation beam hoop; This is not inconsistent with actual experimental result fully; Cause film formula part in thin-skin model or the shell model to the too high estimation of structure; And two models all do not have accurately to consider expansion of structure distortion under the effect of the blowing pressure effect, and therefore, existing thin-skin model and shell model all can not accurately forecast the cockle characteristic of film inflation beam.

Summary of the invention

The objective of the invention is in order to solve the problem that existing film is inflated the beam cockle too high estimated prediction value of prediction of Characteristics model and do not considered the blowing pressure effect, propose a kind of shell membrane model that is used for film inflation beam cockle prediction of Characteristics.

Establishment step of the present invention is following:

Step 1: the thin-skin model of setting up film inflation beam cockle prediction of Characteristics: suppose that at first film inflation beam beam wall material is pure film, unite the thin-skin model that specific fold condition is set up film inflation beam cockle prediction of Characteristics;

Step 2: introduce the shell model that critical compressive stress is set up film inflation beam cockle prediction of Characteristics: introduce elastic thin shell critical compressive stress form, set up the shell model of film inflation beam cockle prediction of Characteristics on the thin-skin model that will be added to by the moment of flexure of its generation;

Step 3: confirm nature configuration and prestressing force reference configuration according to inflation beam stress characteristic: the mechanical characteristic according to film inflation beam confirms to set up the required prestressing force reference configuration of shell membrane model, and on this configuration, introduces the dilatancy that the blowing pressure effect considers that film inflation beam produces because of inflation;

Step 4: under the prestressing force reference configuration, introduce the blowing pressure effect and correction factor; Set up the shell membrane model of film inflation beam cockle prediction of Characteristics: introduce correction factor and act on film formula in the shell model of considering the blowing pressure effect; To reduce its too high estimation, unite and introduce the shell membrane model that the critical compressive stress formula of considering the blowing pressure effect obtains film inflation beam cockle prediction of Characteristics predicted value.

The present invention has following beneficial effect: the present invention is with the advantages of thin-skin model and shell model; Through under the prestressing force reference configuration, introducing correction factor and considering the blowing pressure effect; Can be accurately and forecast critical rugosity moment of flexure and the inefficacy moment of flexure of film inflation beam effectively, for the load prediction of Characteristics and the fold of subsequent thin film inflation beam are controlled the information more accurately that provides.The present invention is the shell membrane model that is used to forecast film inflation beam cockle characteristic; It has taken into account the advantage of thin-skin model and shell model simultaneously; Take into full account the too high estimation of the blowing pressure effect and original forecasting model, fundamentally solved the problem that single thin-skin model and shell model can't accurately forecast film inflation beam cockle characteristic.

Description of drawings

Fig. 1 is the flow chart that is used for the shell membrane model of film inflation beam cockle prediction of Characteristics; Fig. 2 is the block mold sketch map of film inflation beam, and Fig. 3 is the arbitrary section sketch map of film inflation beam, and Fig. 4 is the arbitrary section stress envelope of film inflation beam; (among Fig. 2 and Fig. 3: x representes the horizontal direction coordinate of film inflation beam arbitrary section; Y representes the vertical direction coordinate of film inflation beam arbitrary section, and z representes the axis direction coordinate of film inflation beam, z ₀Be the axial length of film inflation beam, θ _wBe the fold angle, W is a folded region).

The specific embodiment

The specific embodiment one: combine Fig. 1～Fig. 4 that this embodiment is described, this embodiment is set up through following steps:

Step 1: the thin-skin model of setting up film inflation beam cockle prediction of Characteristics: suppose that at first film inflation beam beam wall material is pure film, unite the thin-skin model that specific fold condition is set up film inflation beam cockle prediction of Characteristics;

Step 2: introduce the shell model that critical compressive stress is set up film inflation beam cockle prediction of Characteristics: introduce elastic thin shell critical compressive stress form, set up the shell model of film inflation beam cockle prediction of Characteristics on the thin-skin model that will be added to by the moment of flexure of its generation;

Step 3: confirm nature configuration and prestressing force reference configuration according to inflation beam stress characteristic: the mechanical characteristic according to film inflation beam confirms to set up the required prestressing force reference configuration of shell membrane model, and on this configuration, introduces the dilatancy that the blowing pressure effect considers that film inflation beam produces because of inflation;

Step 4: under the prestressing force reference configuration, introduce the blowing pressure effect and correction factor; Set up the shell membrane model of film inflation beam cockle prediction of Characteristics: introduce correction factor and act on film formula in the shell model of considering the blowing pressure effect; To reduce its too high estimation, unite and introduce the shell membrane model that the critical compressive stress formula of considering the blowing pressure effect obtains film inflation beam cockle prediction of Characteristics predicted value.

The specific embodiment two: combine Fig. 1 that this embodiment is described, this embodiment is described further embodiment one, the foundation of the thin-skin model of the cockle prediction of Characteristics of film inflation beam in the step 1 of this embodiment:

At first, the equilibrium equation of structural capacity by formula one is set up:

Formula one $p=\frac{\mathrm{Rt}{\∫}_0^{2\mathrm{\π}}{\mathrm{\σ}}_1\mathrm{D\θ}}{\mathrm{\π}{r}^2};$

Wherein, p is a blowing pressure, and r is the circular section radius of film inflation beam, and t is the wall thickness of film inflation beam, σ ₁Be the axial stress of film inflation beam,

The equilibrium equation of structure moment is:

Formula two $M=-r^{2}t{\∫}_0^{2\mathrm{\π}}{\mathrm{\σ}}_1\mathrm{Cos}\mathrm{\θ\; D\θ};$

Wherein, M is the moment of flexure that film inflation joist support receives, and θ is the hoop angle,

The axial stress form of film inflation beam is:

Formula three ${\mathrm{\σ}}_1=\left\{\begin{array}{cc}E(-\mathrm{Kr}\mathrm{Cos}\mathrm{\θ}+C_1)+v\frac{\mathrm{Pr}}{t};& {\mathrm{\θ}}_w\≤\mathrm{\θ}\≤2\mathrm{\π}-{\mathrm{\θ}}_w\\ 0;& -{\mathrm{\θ}}_w\≤\mathrm{\θ}\≤{\mathrm{\θ}}_w\end{array}\right.;$

Wherein, E is the elastic modelling quantity of film material, and v is a Poisson's ratio, and k is the curvature of film inflation beam, C ₁For with the undetermined constant of fold strain-dependent,

For thin-skin model, fold generation condition is:

Formula four σ ₁=0; θ=θ _w

Wherein, θ _wBe the fold angle, undetermined constant C can be confirmed thus in the hoop angle of corresponding film inflation beam when promptly fold produced ₁:

Formula five $C_1=\mathrm{Kr}\mathrm{Cos}{\mathrm{\θ}}_w-v\frac{\mathrm{Pr}}{\mathrm{Et}};$

With obtaining in the formula five substitution formula three:

Formula six ${\mathrm{\σ}}_1=\left\{\begin{array}{cc}\mathrm{Ekr}(\mathrm{Cos}{\mathrm{\θ}}_w-\mathrm{Cos}\mathrm{\θ});& {\mathrm{\θ}}_w\≤\mathrm{\θ}\≤2\mathrm{\π}-{\mathrm{\θ}}_w\\ 0;& -{\mathrm{\θ}}_w\≤\mathrm{\θ}\≤{\mathrm{\θ}}_w\end{array}\right.;$

Wherein ,-θ _w≤θ≤θ _wCorresponding plication region, θ _w≤θ≤2 π-θ _wCorresponding non-plication region,

Formula six is updated to the power and the torque equilibrium equation that can obtain thin-skin model in formula one and the formula two:

Formula seven $\left\{\begin{array}{c}p=\frac{2{\mathrm{Kr}}^2\mathrm{Et}[\mathrm{Sin}{\mathrm{\θ}}_w+(\mathrm{\π}-{\mathrm{\θ}}_w)\mathrm{Cos}{\mathrm{\θ}}_w]}{\mathrm{\π}{r}^2}\\ M={\mathrm{Kr}}^3\mathrm{Et}(\mathrm{\π}-{\mathrm{\θ}}_w+\frac{1}{2}\mathrm{Sin}2{\mathrm{\θ}}_w)\end{array}\right.;$

Can further obtain by formula seven:

Formula eight $\frac{M}{p}=\frac{\mathrm{\π}{r}^3(\mathrm{\π}-{\mathrm{\θ}}_w+\frac{1}{2}\mathrm{Sin}2{\mathrm{\θ}}_w)}{2[\mathrm{Sin}{\mathrm{\θ}}_w+(\mathrm{\π}-{\mathrm{\θ}}_w)\mathrm{Cos}{\mathrm{\θ}}_w]};$

For thin-skin model, (θ when it produces fold _w=0) moment of flexure is critical rugosity moment M _M-w:

Formula nine $M_{m-w}=\frac{\mathrm{P\π}{r}^3}{2};$

For thin-skin model, (θ when fold spreads all over whole hoop _w=π) structure-bearing characteristic inefficacy, the inefficacy moment M of counter structure at this moment _M-f:

Formula ten M _M-f=p π r ³

The specific embodiment three: this embodiment is described further embodiment one, and the step 2 of this embodiment is introduced critical compressive stress on the basis of step 1, and then sets up the shell model of film inflation beam cockle prediction of Characteristics:

Consider that film inflation beam beam wall material is an elastic thin shell, its condition that produces fold is:

Formula 11 σ ₁=-σ _Crθ=θ _w

Wherein, σ _CrBe the critical compressive stress of shell, confirm the undetermined constant C of shell model thus ₁For:

Formula 12 $C_1=\mathrm{Kr}\mathrm{Cos}{\mathrm{\θ}}_w-v\frac{\mathrm{Pr}}{\mathrm{Et}}-\frac{{\mathrm{\σ}}_{\mathrm{Cr}}}{E};$

Formula 12 is updated to the axial stress that obtains the shell model in the formula three:

Formula 13 ${\mathrm{\σ}}_1=\left\{\begin{array}{cc}\mathrm{Ekr}(\mathrm{Cos}{\mathrm{\θ}}_w-\mathrm{Cos}\mathrm{\θ})-{\mathrm{\σ}}_{\mathrm{Cr}};& {\mathrm{\θ}}_w\≤\mathrm{\θ}\≤2\mathrm{\π}-{\mathrm{\θ}}_w\\ -{\mathrm{\σ}}_{\mathrm{Cr}};& -{\mathrm{\θ}}_w\≤\mathrm{\θ}\≤{\mathrm{\θ}}_w\end{array}\right.;$

Formula 13 is updated to the power and the torque equilibrium equation form that obtain the shell model in formula one and the formula two is:

Formula 14 $\left\{\begin{array}{c}p=\frac{2{\mathrm{Kr}}^2\mathrm{Et}[\mathrm{Sin}{\mathrm{\θ}}_w+(\mathrm{\π}-{\mathrm{\θ}}_w)\mathrm{Cos}{\mathrm{\θ}}_w]-2\mathrm{\π\; Tr}{\mathrm{\σ}}_{\mathrm{Cr}}}{\mathrm{\π}{r}^2}\\ M={\mathrm{Kr}}^3\mathrm{Et}(\mathrm{\π}-{\mathrm{\θ}}_w+\frac{1}{2}\mathrm{Sin}2{\mathrm{\θ}}_w)\end{array}\right.;$

Can further obtain by formula 14:

Formula 15 $\frac{M}{p}=\frac{\mathrm{\π}{r}^3(\mathrm{\π}-{\mathrm{\θ}}_w+\frac{1}{2}\mathrm{Sin}2{\mathrm{\θ}}_w)}{2[\mathrm{Sin}{\mathrm{\θ}}_w+(\mathrm{\π}-{\mathrm{\θ}}_w)\mathrm{Cos}{\mathrm{\θ}}_w]-2\mathrm{\π\; Tr}{\mathrm{\σ}}_{\mathrm{Cr}}};$

Work as θ _w, confirm the critical rugosity moment of flexure N of shell model at=0 o'clock _S-w:

Formula 16 $M_{s-w}=\frac{\mathrm{P\π}{r}^3}{2}+{\mathrm{\π\; r}}^{2}t{\mathrm{\σ}}_{\mathrm{Cr}};$

Work as θ _wDuring=π, confirm the inefficacy moment M of shell model _S-f:

Formula 17 M _S-f=p π r ³+ 2 π r ²T σ _Cr

For the shell model, its critical compressive stress σ _CrFor:

Formula 18 ${\mathrm{\σ}}_{\mathrm{Cr}}=\frac{\sqrt{2}}{9}\frac{\mathrm{Et}}{r\sqrt{1-v^2}}.$

The specific embodiment four: this embodiment is described further embodiment one, and for film inflation Liang Eryan, its stand under load process is divided into two stages in the step 3 of this embodiment; First stage is the inner inflatable dilatancy stage, and second stage is that structure is born the outer deformation stage that carries, this two stages corresponding respectively two kinds with reference to configuration; First kind of reference is configured as the nature configuration; First stage is the nature configuration, and film inflation beam is the nature of zero the blowing pressure under this configuration, and second kind of reference is configured as the prestressing force reference configuration; Second stage is the prestressing force reference configuration; The corresponding film inflation of this configuration beam receives the dilatancy state of inner non-zero the blowing pressure effect, and the cockle specificity analysis of film inflation beam must be based upon on the prestressing force reference configuration and carry out, to consider the blowing pressure effect.

The specific embodiment five: this embodiment is described further embodiment one, and the consideration of the blowing pressure effect realizes through calculating film inflation beam pressurising dilatancy on the prestressing force reference configuration in the step 4 of this embodiment:

Based on elastic theory, the length Z on the prestressing force configuration that circular section film inflation beam pressurising The deformation calculation obtains _i, section radius r _iAnd thickness t _iFor:

Formula 19 $Z_i=Z_0(1+\frac{1-2v}{2}\frac{\mathrm{Pr}}{\mathrm{Et}});$

Formula 20 $r_i=r(1+\frac{2-v}{2}\frac{\mathrm{Pr}}{\mathrm{Et}});$

Formula 21 $t_i=t(1-\frac{3v}{2}\frac{\mathrm{Pr}}{\mathrm{Et}});$

The shell membrane model of film inflation beam cockle prediction of Characteristics is considered the advantage of film and shell model simultaneously, and is based upon on the prestressing force reference configuration, formula 18 is brought into the forecasting model that obtains considering the blowing pressure effect in the formula 17:

Formula 22 ${M_{s-f}}^i=\mathrm{P\π}{r_i}^3+\frac{2\sqrt{2}}{9}\frac{\mathrm{E\π}{r}_i{t_i}^2}{\sqrt{1-v^2}}.$

The specific embodiment six: this embodiment is described further embodiment five, and this embodiment can be found that by thin-skin model formula nine, ten or shell model formation 16,17 two models judge that the condition of structural failure all is θ _w=π has only promptly that structure just lost efficacy when inflation beam hoop spreads all over fold fully, and this and actual experiment result do not meet fully, and cause the problem of film being inflated the too high forecast of beam cockle characteristic; Experiment finds that structural failure is actual to be occurred in early than θ _wThe moment of=π, i.e. fold angle θ during ultimate failure _F-w＜π.

Because thin-skin model is the major part that causes too high estimation, so the modifying factor α that introduces less than 1 acts on the film formula of thin-skin model or shell model, make the shell membrane model prediction more near actual, the forecasting model of revising on the prestressing force configuration of back is:

Formula 23 ${M_{s-f}}^{i*}=\mathrm{\α}\·\mathrm{P\π}{r_i}^3+\frac{2\sqrt{2}}{9}\frac{\mathrm{E\π}{r}_i{t}_i^2}{\sqrt{1-v^2}}.$

The specific embodiment seven: this embodiment is described further embodiment six, and the critical compressive stress in the forecasting model of this embodiment need be introduced the effect of the blowing pressure,

Formula 18 is critical compressive stress formula that the shell model is not considered the blowing pressure effect, and the critical compressive stress formula of introducing the shell membrane model that obtains considering the blowing pressure effect after the blowing pressure is:

Formula 24 ${\mathrm{\σ}}_{\mathrm{Sm}-\mathrm{Cr}}=\frac{\sqrt{2}}{9}\frac{{\mathrm{Et}}_i}{r_i}\sqrt{\frac{1}{1-v^2}+4\frac{p}{E}{\left(\frac{r_i}{t_i}\right)}^2};$

Formula 22 is updated to the inefficacy moment of flexure that obtains the shell membrane model in the formula 21 is:

Formula 25 $M_{\mathrm{Sm}-f}=\mathrm{\α}\·\mathrm{P\π}{r_i}^3+\frac{2\sqrt{2}}{9}\mathrm{E\π}{r}_i{t_i}^2\sqrt{\frac{1}{1-v^2}+4\frac{p}{E}{\left(\frac{r_i}{t_i}\right)}^2};$

α p π r in the formula 23 _i ³Critical rugosity moment of flexure forecasting model M for the shell membrane model _Sm-w, that is:

Formula 26 M _Sm-w=α p π r _i ³

Shell membrane model prediction result of the present invention compares with existing film inflation beam cockle prediction of Characteristics model prediction result and sees table 1, and material, structure and the load parameter of film inflation beam are seen table 2,

Table 1 shell membrane model and existing model and experimental result contrast

Can find out significantly that from table 1 result of shell membrane Model Calculation of the present invention and experimental result are the most approaching.

Table 2 material, structure and load parameter

Claims (7)

1. one kind is used for the shell membrane model that film is inflated beam cockle prediction of Characteristics, and it is characterized in that: its establishment step is following:

Step 1: the thin-skin model of setting up film inflation beam cockle prediction of Characteristics: suppose that at first film inflation beam beam wall material is pure film, unite the thin-skin model that specific fold condition is set up film inflation beam cockle prediction of Characteristics;

Step 2: introduce the shell model that critical compressive stress is set up film inflation beam cockle prediction of Characteristics: introduce elastic thin shell critical compressive stress form, set up the shell model of film inflation beam cockle prediction of Characteristics on the thin-skin model that will be added to by the moment of flexure of its generation;

Step 3: confirm nature configuration and prestressing force reference configuration according to inflation beam stress characteristic: the mechanical characteristic according to film inflation beam confirms to set up the required prestressing force reference configuration of shell membrane model, and on this configuration, introduces the dilatancy that the blowing pressure effect considers that film inflation beam produces because of inflation;

Step 4: under the prestressing force reference configuration, introduce the blowing pressure effect and correction factor; Set up the shell membrane model of film inflation beam cockle prediction of Characteristics: introduce correction factor and act on film formula in the shell model of considering the blowing pressure effect; To reduce its too high estimation, unite and introduce the shell membrane model that the critical compressive stress formula of considering the blowing pressure effect obtains film inflation beam cockle prediction of Characteristics predicted value.

2. according to the said shell membrane model that is used for film inflation beam cockle prediction of Characteristics of claim 1, it is characterized in that: the process of setting up of the thin-skin model of the cockle prediction of Characteristics of film inflation beam is in the step 1:

At first, the equilibrium equation of structural capacity by formula one is set up:

Formula one $p=\frac{\mathrm{Rt}{\∫}_0^{2\mathrm{\π}}{\mathrm{\σ}}_1\mathrm{D\θ}}{\mathrm{\π}{r}^2};$

Wherein, p is a blowing pressure, and r is the circular section radius of film inflation beam, and t is the wall thickness of film inflation beam, σ ₁Be the axial stress of film inflation beam,

The equilibrium equation of structure moment is:

Formula two $M=-r^{2}t{\∫}_0^{2\mathrm{\π}}{\mathrm{\σ}}_1\mathrm{Cos}\mathrm{\θ\; D\θ};$

Wherein, M is the moment of flexure that film inflation joist support receives, and θ is the hoop angle,

The axial stress form of film inflation beam is:

Formula three ${\mathrm{\σ}}_1=\left\{\begin{array}{cc}E(-\mathrm{Kr}\mathrm{Cos}\mathrm{\θ}+C_1)+v\frac{\mathrm{Pr}}{t};& {\mathrm{\θ}}_w\≤\mathrm{\θ}\≤2\mathrm{\π}-{\mathrm{\θ}}_w\\ 0;& -{\mathrm{\θ}}_w\≤\mathrm{\θ}\≤{\mathrm{\θ}}_w\end{array}\right.;$

Wherein, E is the elastic modelling quantity of film material, and v is a Poisson's ratio, and k is the curvature of film inflation beam, C ₁For with the undetermined constant of fold strain-dependent,

For thin-skin model, fold generation condition is:

Formula four σ ₁=0; θ=θ _w

Wherein, θ _wBe the fold angle, undetermined constant C can be confirmed thus in the hoop angle of corresponding film inflation beam when promptly fold produced ₁:

Formula five $C_1=\mathrm{Kr}\mathrm{Cos}{\mathrm{\θ}}_w-v\frac{\mathrm{Pr}}{\mathrm{Et}};$

With obtaining in the formula five substitution formula three:

Formula six ${\mathrm{\σ}}_1=\left\{\begin{array}{cc}\mathrm{Ekr}(\mathrm{Cos}{\mathrm{\θ}}_w-\mathrm{Cos}\mathrm{\θ});& {\mathrm{\θ}}_w\≤\mathrm{\θ}\≤2\mathrm{\π}-{\mathrm{\θ}}_w\\ 0;& -{\mathrm{\θ}}_w\≤\mathrm{\θ}\≤{\mathrm{\θ}}_w\end{array}\right.;$

Wherein ,-θ _w≤θ≤θ _wCorresponding plication region, θ _w≤θ≤2 π-θ _wCorresponding non-plication region,

Formula six is updated to the power and the torque equilibrium equation that can obtain thin-skin model in formula one and the formula two:

Formula seven $\left\{\begin{array}{c}p=\frac{2{\mathrm{Kr}}^2\mathrm{Et}[\mathrm{Sin}{\mathrm{\θ}}_w+(\mathrm{\π}-{\mathrm{\θ}}_w)\mathrm{Cos}{\mathrm{\θ}}_w]}{\mathrm{\π}{r}^2}\\ M={\mathrm{Kr}}^3\mathrm{Et}(\mathrm{\π}-{\mathrm{\θ}}_w+\frac{1}{2}\mathrm{Sin}2{\mathrm{\θ}}_w)\end{array}\right.;$

Can further obtain by formula seven:

Formula eight $\frac{M}{p}=\frac{\mathrm{\π}{r}^3(\mathrm{\π}-{\mathrm{\θ}}_w+\frac{1}{2}\mathrm{Sin}2{\mathrm{\θ}}_w)}{2[\mathrm{Sin}{\mathrm{\θ}}_w+(\mathrm{\π}-{\mathrm{\θ}}_w)\mathrm{Cos}{\mathrm{\θ}}_w]};$

For thin-skin model, (θ when it produces fold _w=0) moment of flexure is critical rugosity moment M _M-w,

Formula nine $M_{m-w}=\frac{\mathrm{P\π}{r}^3}{2};$

For thin-skin model, (θ when fold spreads all over whole hoop _w=π) structure-bearing characteristic inefficacy, the inefficacy moment M of counter structure at this moment _M-f

Formula ten M _M-f=p π r ³

3. according to the said shell membrane model that is used for film inflation beam cockle prediction of Characteristics of claim 1; It is characterized in that: step 2 is on the basis of step 1; Introduce critical compressive stress, and then set up the shell model of film inflation beam cockle prediction of Characteristics, detailed process is:

Consider that film inflation beam beam wall material is an elastic thin shell, its condition that produces fold is:

Formula 11 σ ₁=-σ _Crθ=θ _w

Wherein, σ _CrBe the critical compressive stress of shell, confirm the undetermined constant C of shell model thus ₁For:

Formula 12 $C_1=\mathrm{Kr}\mathrm{Cos}{\mathrm{\θ}}_w-v\frac{\mathrm{Pr}}{\mathrm{Et}}-\frac{{\mathrm{\σ}}_{\mathrm{Cr}}}{E};$

Formula 12 is updated to the axial stress that obtains the shell model in the formula three:

Formula 13 ${\mathrm{\σ}}_1=\left\{\begin{array}{cc}\mathrm{Ekr}(\mathrm{Cos}{\mathrm{\θ}}_w-\mathrm{Cos}\mathrm{\θ})-{\mathrm{\σ}}_{\mathrm{Cr}};& {\mathrm{\θ}}_w\≤\mathrm{\θ}\≤2\mathrm{\π}-{\mathrm{\θ}}_w\\ -{\mathrm{\σ}}_{\mathrm{Cr}};& -{\mathrm{\θ}}_w\≤\mathrm{\θ}\≤{\mathrm{\θ}}_w\end{array}\right.;$

Formula 13 is updated to the power and the torque equilibrium equation form that obtain the shell model in formula one and the formula two is:

Formula 14 $\left\{\begin{array}{c}p=\frac{2{\mathrm{Kr}}^2\mathrm{Et}[\mathrm{Sin}{\mathrm{\θ}}_w+(\mathrm{\π}-{\mathrm{\θ}}_w)\mathrm{Cos}{\mathrm{\θ}}_w]-2\mathrm{\π\; Tr}{\mathrm{\σ}}_{\mathrm{Cr}}}{\mathrm{\π}{r}^2}\\ M={\mathrm{Kr}}^3\mathrm{Et}(\mathrm{\π}-{\mathrm{\θ}}_w+\frac{1}{2}\mathrm{Sin}2{\mathrm{\θ}}_w)\end{array}\right.;$

Can further obtain by formula 14:

Formula 15 $\frac{M}{p}=\frac{\mathrm{\π}{r}^3(\mathrm{\π}-{\mathrm{\θ}}_w+\frac{1}{2}\mathrm{Sin}2{\mathrm{\θ}}_w)}{2[\mathrm{Sin}{\mathrm{\θ}}_w+(\mathrm{\π}-{\mathrm{\θ}}_w)\mathrm{Cos}{\mathrm{\θ}}_w]-2\mathrm{\π\; Tr}{\mathrm{\σ}}_{\mathrm{Cr}}};$

Work as θ _w, confirm the critical rugosity moment M of shell model at=0 o'clock _S-w:

Formula 16 $M_{s-w}=\frac{\mathrm{P\π}{r}^3}{2}+{\mathrm{\π\; r}}^{2}t{\mathrm{\σ}}_{\mathrm{Cr}};$

Work as θ _wDuring=π, confirm the inefficacy moment M of shell model _S-f:

Formula 17 M _S-f=p π r ³+ 2 π r ²T σ _Cr

For the shell model, its critical compressive stress σ _CrFor:

Formula 18 ${\mathrm{\σ}}_{\mathrm{Cr}}=\frac{\sqrt{2}}{9}\frac{\mathrm{Et}}{r\sqrt{1-v^2}}.$

4. according to the said shell membrane model that is used for film inflation beam cockle prediction of Characteristics of claim 1; It is characterized in that: in step 3, inflate Liang Eryan for film; Its stand under load process is divided into two stages, and first stage is the inner inflatable dilatancy stage, and second stage is that structure is born the outer deformation stage that carries; First stage is the nature configuration; Film inflation beam is the nature of zero the blowing pressure under this configuration, and second stage is the prestressing force reference configuration, and the corresponding film inflation of this configuration beam receives the dilatancy state of inner non-zero the blowing pressure effect; The cockle specificity analysis of film inflation beam must be based upon on the prestressing force reference configuration and carry out, to consider the blowing pressure effect.

5. according to the said shell membrane model that is used for film inflation beam cockle prediction of Characteristics of claim 1; It is characterized in that: the consideration of the blowing pressure effect realizes that through calculating film inflation beam pressurising dilatancy implementation procedure is on the prestressing force reference configuration in the step 4:

Based on elastic theory, the length Z on the prestressing force configuration that circular section film inflation beam pressurising The deformation calculation obtains _i, section radius r _iAnd thickness t _iFor:

Formula 19 $Z_i=Z_0(1+\frac{1-2v}{2}\frac{\mathrm{Pr}}{\mathrm{Et}});$

Formula 20 $r_i=r(1+\frac{2-v}{2}\frac{\mathrm{Pr}}{\mathrm{Et}});$

Formula 21 $t_i=t(1-\frac{3v}{2}\frac{\mathrm{Pr}}{\mathrm{Et}});$

The shell membrane model of film inflation beam cockle prediction of Characteristics is considered the advantage of film and shell model simultaneously, and is based upon on the prestressing force reference configuration, formula 18 is brought into the forecasting model that obtains considering the blowing pressure effect in the formula 17:

Formula 22 ${M_{s-f}}^i=\mathrm{P\π}{r_i}^3+\frac{2\sqrt{2}}{9}\frac{\mathrm{E\π}{r}_i{t_i}^2}{\sqrt{1-v^2}}.$

6. according to the said shell membrane model that is used for film inflation beam cockle prediction of Characteristics of claim 5, it is characterized in that: can find that by thin-skin model formula nine, ten or shell model formation 16,17 two models judge that the condition of structural failure all is θ _w=π has only promptly that structure just lost efficacy when inflation beam hoop spreads all over fold fully, and structural failure is actual to be occurred in early than θ _wThe moment of=π, i.e. fold angle θ during ultimate failure _F-w＜π,

Because thin-skin model is the major part that causes too high estimation, so the modifying factor α that introduces less than 1 acts on the film formula of thin-skin model or shell model, make the shell membrane model prediction more near actual, the forecasting model of revising on the prestressing force configuration of back is:

Formula 23 ${M_{s-f}}^{i*}=\mathrm{\α}\·\mathrm{P\π}{r_i}^3+\frac{2\sqrt{2}}{9}\frac{\mathrm{E\π}{r}_i{t}_i^2}{\sqrt{1-v^2}}.$

7. according to the said shell membrane model that is used for film inflation beam cockle prediction of Characteristics of claim 6, it is characterized in that: the critical compressive stress in the forecasting model need be introduced the effect of the blowing pressure,

Formula 18 is critical compressive stress formula that the shell model is not considered the blowing pressure effect, and the critical compressive stress formula of introducing the shell membrane model that obtains considering the blowing pressure effect after the blowing pressure is:

Formula 24 ${\mathrm{\σ}}_{\mathrm{Sm}-\mathrm{Cr}}=\frac{\sqrt{2}}{9}\frac{{\mathrm{Et}}_i}{r_i}\sqrt{\frac{1}{1-v^2}+4\frac{p}{E}{\left(\frac{r_i}{t_i}\right)}^2};$

Formula 22 is updated to the inefficacy moment of flexure that obtains the shell membrane model in the formula 21 is:

Formula 25 $M_{\mathrm{Sm}-f}=\mathrm{\α}\·\mathrm{P\π}{r_i}^3+\frac{2\sqrt{2}}{9}\mathrm{E\π}{r}_i{t_i}^2\sqrt{\frac{1}{1-v^2}+4\frac{p}{E}{\left(\frac{r_i}{t_i}\right)}^2};$

α p π r in the formula 23 _i ³Critical rugosity moment of flexure forecasting model M for the shell membrane model _Sm-w, that is:

Formula 26 M _Sm-w=α p π r _i ³

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