CN102799737B - Design method of high-precision pneumatic membrane structure - Google Patents

Abstract

The invention relates to a design method of a high-precision pneumatic membrane structure, and belongs to the field of morphological analysis of pneumatic membrane structures (antenna, airship and pneumatic wing). The method aims to effectively solve the problem of large error between the appearance and the design appearance caused by pneumatic deformation of the pneumatic membrane structure. The method comprises the steps of establishing a pneumatic membrane structure model, dividing grids, setting a boundary condition, applying pneumatic pressure and solving, processing node data and updating a model, stamping and solving the new model again, and determining whether root-mean-square meets the precision requirement, if not, returning and calculating, and otherwise, outputting configuration. The design method is used for designing the pneumatic membrane structure.

Description

The method for designing of high precision air-supported membrane structure

Technical field

The present invention relates to air-supported membrane structure (antenna, dirigible and the inflation wing etc.) morphological analysis field, be specifically related to a kind of method for designing of high precision air-supported membrane structure.

Background technology

After referring to and be filled with air in the film article made from macromolecular material, air-supported membrane structure forms the structure with certain load performance configuration.Due to it, to have quality light, and the plurality of advantages such as folding Zhan Bi great and load-carrying efficiency height show out its advantage in aerospace field application, as inflation airship, and paraballon and inflatable wing etc.But these inflatable structures, in the time of normal work, have certain accuracy requirement to its profile, and the accuracy requirement of the inflation wing and paraballon is the highest, is secondly inflation airship, so need to analyze its initial configuration.The pressurising distortion of air-supported membrane structure, it is the large deformation nonlinear problem of allusion quotation shape, if directly analyze or process with the air-supported membrane structure size of designing, after loading, can produce distortion, so just there is larger error and then affect computational accuracy and usability with our configuration of design, so initial configuration while being necessary to find it and do not load according to air-supported membrane structure target configuration, and common bidimensional initial configuration analysis can not meet harsh accuracy requirement, need to be from three-dimensional perspective, air-supported membrane structure is carried out to the analysis of omnidirectional three-dimensional initial configuration.A kind of according to target three-dimensional configuration like this, the problem of finding air-supported membrane structure initial configuration is one " inverse problem " in mechanics, needs special method to study.In the present invention, find the three-dimensional initial configuration of air-supported membrane structure by reverse iteration and be defined as the three-dimensional initial configuration analysis of air-supported membrane structure to guarantee the method after air-supported membrane structure inflation loads with designed function profile this.In addition, the three-dimensional initial configuration analysis of air-supported membrane structure, to later stage air-supported membrane structure surface flattening, cutting, the forming processes such as splicing have great significance.

Summary of the invention

The object of this invention is to provide a kind of method for designing of high precision air-supported membrane structure, in order to effectively reduce air-supported membrane structure because inflation large deformation causes its profile and the problem that designs error excessive between shape.

The present invention solves the problems of the technologies described above the technical scheme of taking to be: said method comprising the steps of:

Step 1, set up model: utilize solid model under virtual condition, to set up inflatable structure model, and provide design shape and allow the error size ζ existing;

Step 2, grid division: first define material properties, then with triangle thin shell element, inflatable structure is carried out discrete;

Step 3, boundary condition loading solve: boundary condition is set, applies after edge load, model is carried out to pressurising expansion and calculate, stiff end, the material of solid model and the border load applying are as input quantity;

The pressurising expansion nonlinear computation of step 3 one, air-supported membrane structure:

Supposing has m node by discrete air-supported membrane structure for after finite element model, the object N of every step optimization contrast _i(X _i, Y _i, Z _i) be i(0<i≤m) target location coordinate of individual node, node i is at X, Y, the displacement of tri-directions of Z is respectively u _i, v _i, and w _i, these information that pressurising is expanded are the input quantities of this method;

Step 3 two, node optimization iteration: model data is processed,

while being the optimization of j step, after the node coordinate of i node loads and analyzes, the displacement of three directions of node i is respectively

position and the destination node coordinate of distortion posterior nodal point are subtracted each other, obtain the deviation of three directions of this point, be defined as

can be expressed as:

$\left.\begin{array}{c}{p}_{\mathrm{xi}}^j=(x_i^j+u_i^j)-X_i\\ p_{\mathrm{yi}}^j=(y_i^j+v_i^j)-Y_i\\ p_{\mathrm{zi}}^j=(z_i^j+w_i^j)-Z_i\end{array}\right\}---\left(1\right)$

Wherein X _i, Y _i, Z _ithe coordinate of the target location of node i, according to the deviation of target location, to the model node of j step

revise, obtain the model node of j+1 step

wherein there is following relation:

$\left.\begin{array}{c}{x}_i^{j+1}=x_i^j-p_{\mathrm{xi}}^j\\ y_i^{j+1}=y_i^j-p_{\mathrm{yi}}^j\\ z_i^{j+1}=z_i^j-p_{\mathrm{zi}}^j\end{array}\right\}---\left(2\right)$

Formula (2) also just represents Nodes Three-dimensional iterative relation;

Step 3 three, precision δ calculate: node i can be expressed as at the offset deviation of the rear position of j step distortion and destination node location:

$U_i^j=\sqrt{{\left(p_{\mathrm{xi}}^j\right)}^2+{\left(p_{\mathrm{yi}}^j\right)}^2+{\left(p_{\mathrm{zi}}^j\right)}^2}---\left(3\right)$

The root-mean-square value δ of the offset deviation of such j step model can be expressed as:

$\mathrm{\&delta;}=\sqrt{\frac{\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left(U_i^j\right)}^2}{m}}---\left(4\right)$

Step 3 four, CYCLIC LOADING iterative: the model having upgraded is re-started to loading and solve calculating, and then the action of recurring formula (2) and formula (3) step, until a certain step δ≤ζ just stops carrying out iterative computation.

The present invention has following beneficial effect: basic thought of the present invention is to be configured as initial shape with target, applies real material parameter and load and edge-restraint condition and carries out reverse iterative analysis.By analyzing, the geometrical configuration and the target shape that obtain after distortion are contrasted, if shape error (root-mean-square value δ) does not meet the demands, revise initial geometrical configuration, reanalyse, so, after iteration several times, can be met the result of accuracy requirement;

The present invention adopts real material parameter to carry out initial configuration analytical calculation, and the result calculating is like this more scientific more reliable.The analysis of part initial configuration is at a dimension coordinate, or analyze under bidimensional coordinate surface.And method of the present invention is under 3 d space coordinate system, consider that three direction coordinates carry out the analysis of inverse iteration initial configuration simultaneously, the precision that therefore the present invention calculates is higher, more approach truth.

Accompanying drawing explanation

Fig. 1 is the inflation wing model of studying in embodiment; Fig. 2 is a pressurising deformation pattern; Fig. 3 is that in embodiment, every step root-mean-square value changes; Fig. 4 is the contrast between initial configuration and the target shape of optimum results in embodiment.

Embodiment

Embodiment one: the method for present embodiment comprises the following steps: said method comprising the steps of:

Step 1, set up model: utilize solid model under virtual condition, to set up inflatable structure model, and provide design shape and allow the error size ζ existing;

Step 2, grid division: first define material properties, then with triangle thin shell element, inflatable structure is carried out discrete;

Step 3, boundary condition loading solve: boundary condition is set, applies after edge load, model is carried out to pressurising expansion and calculate, stiff end, the material of solid model and the border load applying are as input quantity;

The pressurising expansion nonlinear computation of step 3 one, air-supported membrane structure:

Supposing has m node by discrete air-supported membrane structure for after finite element model, the object N of every step optimization contrast _i(X _i, Y _i, Z _i) be i(0<i≤m) target location coordinate of individual node, node i is at X, Y, the displacement of tri-directions of Z is respectively u _i, v _i, and w _i, these information that pressurising is expanded are the input quantities of this method;

Step 3 two, node optimization iteration: model data is processed,

while being the optimization of j step, after the node coordinate of i node loads and analyzes, the displacement of three directions of node i is respectively

position and the destination node coordinate of distortion posterior nodal point are subtracted each other, obtain the deviation of three directions of this point, be defined as

can be expressed as:

$\left.\begin{array}{c}{p}_{\mathrm{xi}}^j=(x_i^j+u_i^j)-X_i\\ p_{\mathrm{yi}}^j=(y_i^j+v_i^j)-Y_i\\ p_{\mathrm{zi}}^j=(z_i^j+w_i^j)-Z_i\end{array}\right\}---\left(1\right)$

Wherein X _i, Y _i, Z _ithe coordinate of the target location of node i, according to the deviation of target location, to the model node of j step

revise, obtain the model node of j+1 step

wherein there is following relation:

$\left.\begin{array}{c}{x}_i^{j+1}=x_i^j-p_{\mathrm{xi}}^j\\ y_i^{j+1}=y_i^j-p_{\mathrm{yi}}^j\\ z_i^{j+1}=z_i^j-p_{\mathrm{zi}}^j\end{array}\right\}---\left(2\right)$

Formula (2) also just represents Nodes Three-dimensional iterative relation;

Step 3 three, precision δ calculate: node i can be expressed as at the offset deviation of the rear position of j step distortion and destination node location:

$U_i^j=\sqrt{{\left(p_{\mathrm{xi}}^j\right)}^2+{\left(p_{\mathrm{yi}}^j\right)}^2+{\left(p_{\mathrm{zi}}^j\right)}^2}---\left(3\right)$

The root-mean-square value δ of the offset deviation of such j step model can be expressed as:

$\mathrm{\&delta;}=\sqrt{\frac{\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left(U_i^j\right)}^2}{m}}---\left(4\right)$

Step 3 four, CYCLIC LOADING iterative: the model having upgraded is re-started to loading and solve calculating, and then the action of recurring formula (2) and formula (3) step, until a certain step δ≤ζ just stops carrying out iterative computation.

Current initial configuration analysis, mainly to solve rope membrane structure in the configuration that is subject to load large deformation with regard to the problem solving, be under target configuration is determined and the present invention solves, push away initial shape according to load and deformation is counter, and this initial shape be very approaching with the target configuration of design after loading.

Conventional initial configuration analysis has all adopted the hypothesis of little modulus, and this hypothesis is inadaptable in initial conformal analysis of the present invention.

Embodiment two: the method for present embodiment also comprises step 4, Output rusults, result of calculation is carried out aftertreatment, derives root-mean-square value variation diagram, output initial configuration.Other implementation steps are identical with embodiment one.

Embodiment three: take inflatable wing structure as example, carry out initial configuration analytical calculation on ANSYS platform.Set up the inflation wing model shown in Fig. 1.

The thickness of material is 50 microns, modulus 3Gpa, Poisson ratio 0.3, charge pressure 100Kpa, with triangle thin shell element, model is carried out discrete, then carry out pressurising expand calculate, result is as shown in Figure 2.

Carry out afterwards the Optimized Iterative processing of node, after 10 steps are optimized, precision δ meets the demands as 9.2500E-05m again.The root-mean-square value that every step is optimized is as Fig. 3.

Optimize the initial shape that obtains and target shape to such as Fig. 4.

Claims (2)

1. a method for designing for high precision air-supported membrane structure, is characterized in that said method comprising the steps of:

Step 1, set up model: utilize solid model under virtual condition, to set up inflatable structure model, and provide design shape and allow the error size ζ existing;

Step 2, grid division: first define material properties, then with triangle thin shell element, inflatable structure is carried out discrete;

Step 3, boundary condition loading solve: boundary condition is set, applies after edge load, model is carried out to pressurising expansion and calculate, stiff end, the material of solid model and the border load applying are as input quantity;

The pressurising expansion nonlinear computation of step 3 one, air-supported membrane structure:

Supposing has m node by discrete air-supported membrane structure for after finite element model, the object N of every step optimization contrast _i(X _i, Y _i, Z _i) be i(0<i≤m) target location coordinate of individual node, node i is at X, Y, the displacement of tri-directions of Z is respectively u _i, v _i, and w _i, these information that pressurising is expanded are the input quantities of this method;

Step 3 two, node optimization iteration: model data is processed,

while being the optimization of j step, after the node coordinate of i node loads and analyzes, the displacement of three directions of node i is respectively

position and the destination node coordinate of distortion posterior nodal point are subtracted each other, obtain the deviation of three directions of this point, be defined as

can be expressed as:

$\left.\begin{array}{c}{p}_{\mathrm{xi}}^j=(x_i^j+u_i^j)-X_i\\ p_{\mathrm{yi}}^j=(y_i^j+v_i^j)-Y_i\\ p_{\mathrm{zi}}^j=(z_i^j+w_i^j)-Z_i\end{array}\right\}---\left(1\right)$

Wherein X _i, Y _i, Z _ithe coordinate of the target location of node i, according to the deviation of target location, to the model node of j step

revise, obtain the model node of j+1 step

wherein there is following relation:

$\left.\begin{array}{c}{x}_i^{j+1}=x_i^j-p_{\mathrm{xi}}^j\\ y_i^{j+1}=y_i^j-p_{\mathrm{yi}}^j\\ z_i^{j+1}=z_i^j-p_{\mathrm{zi}}^j\end{array}\right\}---\left(2\right)$

Formula (2) also just represents Nodes Three-dimensional iterative relation;

Step 3 three, precision δ calculate: node i can be expressed as at the offset deviation of the rear position of j step distortion and destination node location:

$U_i^j=\sqrt{{\left(p_{\mathrm{xi}}^j\right)}^2+{\left(p_{\mathrm{yi}}^j\right)}^2+{\left(p_{\mathrm{zi}}^j\right)}^2}---\left(3\right)$

The root-mean-square value δ of the offset deviation of such j step model can be expressed as:

$\mathrm{\&delta;}=\sqrt{\frac{\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left(U_i^j\right)}^2}{m}}---\left(4\right)$

Step 3 four, CYCLIC LOADING iterative: the model having upgraded is re-started to loading and solve calculating, and then the action of recurring formula (2) and formula (3) step, until a certain step δ≤ζ just stops carrying out iterative computation.

2. the method for designing of high precision air-supported membrane structure according to claim 1, is characterized in that described method also comprises step 4, Output rusults, and result of calculation is carried out aftertreatment, derives root-mean-square value variation diagram, output initial configuration.

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