CN101719187B - Hole optimizing design method for porous thin wall rotating curved surface structure - Google Patents

Abstract

The invention discloses a hole optimizing design method for a porous thin wall rotating curved surface structure, which is used for hole optimizing design on any thin wall rotating curved surface. The method comprises the following steps of: establishing a rotating bus equation and establishing a parameter equation of the given rotating curved surface; confirming the position of a hole core on the s-t plane according to the parameter equation of the given rotating curved surface and establishing a parameter equation of a hole peripheral curve; establishing a finite element model of a three-dimensional porous thin wall rotating curved surface structure in finite element analyzing software by a mapping relation between the s-t plane and a space coordinate system by adopting a shell unit; applying a boundary condition and a load on the basis of the finite element model, establishing a mechanical model of the porous thin wall rotating curved surface structure and selecting an optimization algorithm to carry out optimizing design. A space hole is equivalently simplified into a plane hole optimizing design problem by a parameter mapping method for defining a design variable on the parameter plane inside the curved surface, and the problem of the hole optimizing design on the rotating curved surface is solved.

Description

The hole optimizing design method of thin wall rotating curved surface structure with holes

Technical field

The present invention relates to a kind of hole optimizing design method of void shape Optimization Design, particularly thin wall rotating curved surface structure with holes, be applicable to the hole optimal design on any thin wall rotating curved surface.

Background technology

In the design of aerospace flight vehicle chain drive, there is the engineering example of the hole optimal design on the thin wall rotating curved surface structures such as a large amount of service hatches, fabrication hole, cooling holes.The existence of hole, problem such as can cause that unavoidably the hole circumferential stress is concentrated directly has influence on serviceable life of structure.In addition, choosing of hole size is directly related with the weight of structure, and be particularly important for aerospace structure loss of weight.

Generally be at first to adopt methods such as matched curve, analytic equation to set up the geometric parameter equation of hole boundary curve in the hole optimal design process, secondly the reference mark coordinate of selected parameter equation is as design variable, by revising the position at these reference mark, optimize the matched curve on hole border.

Provide employing B-spline curves match hole week curve in the document 1 " Shape optimal design using B-splines.Braibant V and Fleury; C.Computer methods inapplied mechanics and engineering; 1984; 44:247-267. ", carried out the hole shape optimal design method.

Provide employing nurbs curve match hole week curve in the document 2 " The coupling of geometric descriptions and finite elements using NURBS-A study inshape optimization.Schramm U and Pilkey WD.Finite elements in analysis and design; 1993; 15:11-34. ", carried out the hole shape optimal design method.For the hole design problem on the plane, this method can realize.But for space problem, even the modification at reference mark guarantees to be positioned on the given space curved surface all the time, but corresponding matched curve still can't guarantee also to be positioned on the given curved surface.

Provided in the document 3 " On the optimum shape of fillets in plates subjected to multiple in-plane loading cases.Kristensen ES and Madsen NF.International journal for numerical methods in engineering; 1976; 10:1007-1019. " and adopted different holes all curve analytic equations combination parameter, carried out the hole shape optimal design method as design variable.For the hole design problem on the plane, this method is easier.But for space problem, hole week curvilinear motion is very complicated, and the general difficult analytical expression that directly adopts is expressed.

Summary of the invention

In the prior art, exist the matched curve of hole boundary curve control vertex can't guarantee to be positioned at all the time on the given curved surface for the hole optimal design on the curved surface, the variation of control vertex can't control effectively that the hole boundary curve changes and all curves of spatial hole are difficult to the problem of Analytical Expression.In order to solve this technical matters, the present invention proposes a kind of hole optimizing design method of thin wall rotating curved surface structure with holes, design variable is defined in parameter maps method on the curved surface inner parameter plane, with space hole optimal design problem equivalent-simplification is plane hole optimal design problem, can solve the hole optimal design problem on the surface of revolution.

The technical solution adopted for the present invention to solve the technical problems is: a kind of hole optimizing design method of thin wall rotating curved surface structure with holes is characterized in comprising the steps:

(a) set up the rotation bus equation, determine under the polar coordinate system relation between any point radial coordinate and axial coordinate on the surfaces of revolution; If the z axle is a turning axle, the rotation bus is positioned on the y-z plane, and R represents under the polar coordinate system radial coordinate of any point on the surfaces of revolution;

It is as follows to adopt Analytical Expression to set up rotation bus equation expression formula:

$\left\{\begin{array}{c}F(y,z)=0\\ x=0\end{array}\right.---\left(1\right)$

Then the relation between R and the z is determined by (2) formula

F(sign(y)R(z)，z)＝0 (2)

The rotation bus equation expression formula that adopts the parameter fitting mode to set up is as follows:

$\left\{\begin{array}{c}y=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{N}_i\left(v\right)\·y_i\\ z=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{N}_i\left(v\right)\·z_i\end{array}\right.0\≤v\≤1---\left(3\right)$

Then the relation between R and the z is determined by (4) formula

R(z)＝|y(v(z))| (4)

(b) set up the parametric equation of given surface of revolution:

$\left\{\begin{array}{c}x=R\left(z\left(t\right)\right)\cos [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s/s_0]\\ y=R\left(z\left(t\right)\right)\sin [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s/s_0]\\ z=H_0+(H_1-H_0)t/t_0\end{array}\right.(0\&le;s\&le;{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">\; <figure-callout\; id="0"\; label="s"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">s</figure-callout>\; </figure-callout>}}_0,0\&le;t\&le;t_0)---\left(5\right)$

In the formula, θ ₀With θ ₁Be the initial and termination point of rotation dough sheet, H ₀With H ₁Minimum and maximum axial coordinate for the surfaces of revolution; The surfaces of revolution is mapped as the long s that is ₀, height is t ₀The rectangular area;

(c) determine the position of the hole heart according to formula (5), be set to the initial point of s-t plane local coordinate system on the s-t plane;

(d) set up the parametric equation of hole week curve:

$\left\{\begin{array}{c}s=s\left(u\right)\\ t=t\left(u\right)\end{array}\right.0\&le;u\&le;1---\left(6\right)$

The hole week curve parametric equation that adopts fit Plane reference mark mode to determine:

$\left\{\begin{array}{c}s=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;s_i\\ t=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;t_i\end{array}\right.0\&le;u\&le;1---\left(7\right)$

Wherein, N _i(u) be the basis function of fit equation;

Then the parametric equation of all curves in the structural hole of space curved surface is:

$\left\{\begin{array}{c}x=R\left(z\left(t\left(u\right)\right)\right)\cos ({\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s\left(u\right)/s_0)\\ y=R\left(z\left(t\left(u\right)\right)\right)\sin ({\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s\left(u\right)/s_0)\\ z=H_0+(H_1-H_0)t\left(u\right)/{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">t</figure-callout>}}_0\end{array}\right.0\&le;u\&le;1---\left(8\right)$

(e), adopt shell unit in finite element analysis software, to set up the finite element model of three-dimensional thin wall rotating curved surface structure with holes by the mapping relations between s-t plane and the space coordinates;

(f) on the basis of finite element model, apply boundary condition and load, set up the mechanical model of thin wall rotating curved surface structure with holes;

(g) according to design feature and stand under load form, determine that design variable distributes, symmetrical structure adopts 1/2nd hole shapes to set design variable, and the disymmetry structure adopts 1/4th hole shapes to set design variable;

(h) choosing hole week maximum equivalent minimum is optimization aim, and structural volume is set design variable initial value and variation range as constraint function, sets up the Optimization Model of thin wall rotating curved surface structure hole optimal design problem with holes;

(i) choose optimized Algorithm and be optimized design.

The present invention's beneficial effect compared to existing technology is: after adopting the inventive method, the maximum equivalent of the thin wall cylindrical patch structural finite element model of equal volume is reduced to 164.050MPa by initial 328.072MPa among the embodiment 1; The maximum equivalent of the thin-walled conical surface chip architecture finite element model of equal volume is reduced to 187.170MPa by initial 248.123MPa among the embodiment 2; The maximum equivalent of the thin-walled of equal volume rotation hyperboloid of one sheet structural finite element model is reduced to 199.455MPa by initial 470.082MPa among the embodiment 3; The maximum equivalent of the thin-walled ellipse of revolution curved-surface structure finite element model of equal volume is reduced to 31.295MPa by initial 108.814MPa among the embodiment 4; Thin-walled ellipse of revolution curved-surface structure finite element structure loss of weight 10.65% among the embodiment 5, and maximum equivalent is reduced to 49.961MPa by initial 108.814MPa; Adopt the thin wall rotating curved surface structure of spline curve fitting plane hole shape satisfying under the prerequisite of volume requirement among the embodiment 6, the maximum equivalent of its finite element model is reduced to 87.446MPa by initial 175.974MPa; The maximum equivalent of the thin wall rotating curved surface structure finite element model of the employing B-spline curves fit Plane hole shape of equal volume is reduced to 90.944MPa by initial 161.328MPa among the embodiment 7; The maximum equivalent of the thin wall rotating curved surface structure finite element model of the employing nurbs curve fit Plane hole shape of equal volume is reduced to 90.478MPa by initial 177.113MPa among the embodiment 8; Squirrel-cage elastic support structure among the embodiment 9, when adopting the traditional rectangular slotted eye to carry out finite element analysis, the unit maximum equivalent of its finite element model is 170.201MPa, and the stiffness coefficient of structure is 32561.2N/mm, and the sleeve area is 32561.2mm ²By the Shape optimization designs of slotted eye on it, under the prerequisite that satisfies the requirement of the rigidity of structure and weight, the unit maximum equivalent of the squirrel-cage elastic support structure after the optimization is reduced to 115.077MPa, and the range of decrease is 32.4%.

The present invention is further described below in conjunction with drawings and Examples.

Description of drawings

Fig. 1 (a) is that application example 1 of the present invention is optimized the pre-structure synoptic diagram, and Fig. 1 (b) is that example 1 is optimized the back structural representation.

Fig. 2 (a) is that application example 2 of the present invention is optimized the pre-structure synoptic diagram, and Fig. 2 (b) is that example 2 is optimized the back structural representation.

Fig. 3 (a) is that application example 3 of the present invention is optimized the pre-structure synoptic diagram, and Fig. 3 (b) is that example 3 is optimized the back structural representation.

Fig. 4 (a) is that application example 4 of the present invention is optimized the pre-structure synoptic diagram, and Fig. 4 (b) is that example 4 is optimized the back structural representation.

Fig. 5 (a) is that application example 5 of the present invention is optimized the pre-structure synoptic diagram, and Fig. 5 (b) is that example 5 is optimized the back structural representation.

Fig. 6 (a) is that application example 6 of the present invention is optimized the pre-structure synoptic diagram, and Fig. 6 (b) is that example 6 is optimized the back structural representation.

Fig. 7 (a) is that application example 7 of the present invention is optimized the pre-structure synoptic diagram, and Fig. 7 (b) is that example 7 is optimized the back structural representation.

Fig. 8 (a) is that application example 8 of the present invention is optimized the pre-structure synoptic diagram, and Fig. 8 (b) is that example 8 is optimized the back structural representation.

Fig. 9 (a) is traditional squirrel-cage elastic support structural representation of application example 9 correspondences of the present invention, and Fig. 9 (b) is that example 9 is optimized the pre-structure synoptic diagram, and Fig. 9 (c) is that example 9 is optimized the back structural representation.

Embodiment

Following examples are with reference to Fig. 1～Fig. 9.

Embodiment 1: the void shape optimal design on the thin wall cylindrical patch.

The hole of an axial length near circumferential width arranged on the thin wall cylindrical patch structure, and its basic parameter is as shown in table 1.

Table 1

1) bus equation of thin wall cylindrical patch curved-surface structure is:

$\left\{\begin{array}{c}x=0\\ y=0\end{array}\right.---\left(9\right)$

Then under the polar coordinate system on the surfaces of revolution relation between any point radial coordinate R and the axial coordinate z satisfy:

R(z)＝R ₀ (10)

2) set up the parametric equation of given cylinder patch

$\left\{\begin{array}{c}x=R\left(z\left(t\right)\right)\cos [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s/s_0]\\ y=R\left(z\left(t\right)\right)\sin [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s/s_0]\\ z=H_0+(H_1-H_0)t/t_0\end{array}\right.(0\&le;s\&le;{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">\; <figure-callout\; id="0"\; label="s"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">s</figure-callout>\; </figure-callout>}}_0,0\&le;t\&le;t_0)---\left(11\right)$

In the formula, θ ₀=0, θ ₁=2.5, H ₀=0, H ₁=1000mm, s ₀=1, t ₀=1.

3) the hole heart is (0.5,0.5) at the coordinate on s-t plane, is set to the initial point of s-t plane local coordinate system.

4) adopt oval hole shape in the curved surface inner plane coordinate system, the hole boundary curve is determined by elliptic equation:

$\left\{\begin{array}{c}s=0.5+r_1\cos \left(2\mathrm{\&pi;u}\right)\\ t=0.5+r_2\sin \left(2\mathrm{\&pi;u}\right)\end{array}\right.0\&le;u\&le;1---\left(12\right)$

Wherein, r ₁With r ₂Be respectively elipse hole along s to t to the axle radius.

Then the parametric equation of all curves in the structural hole of space curved surface is:

$\left\{\begin{array}{c}x={\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">R</figure-callout>}}_0\cos ({\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)(0.5+r_1\cos \left(2\mathrm{\&pi;u}\right))/s_0)\\ y={\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">R</figure-callout>}}_0\sin ({\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)(0.5+r_1\cos \left(2\mathrm{\&pi;u}\right))/s_0)\\ z={\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">H</figure-callout>}}_0+(H_1-H_0)(0.5+r_2\sin \left(2\mathrm{\&pi;u}\right)){/\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">t</figure-callout>}}_0\end{array}\right.0\&le;u\&le;1---\left(13\right)$

5) adopt shell unit in commercial finite element analysis software ANSYS, at first to set up the finite element model of thin wall cylindrical patch structure with holes.

6) the 5th) an axial end of coordinate minimum in the fixed sturcture on the basis of the finite element model set up in the step, apply uniform axial tension at the structure other end, the axial tension sum is 100kN, sets up the mechanical model of thin wall cylindrical curved-surface structure with holes.

7) the major and minor axis radius coordinate that adopts elliptical aperture is as two design variables, i.e. r in the formula (11) ₁With r ₂

8) choosing hole week maximum equivalent minimum is optimization aim, and cylinder patch area is limited to 0.8m as constraint function in the constraint ², set r ₁With r ₂Variation range be [0.2,0.8], set up the Optimization Model of thin wall cylindrical curved-surface structure hole shape optimal design problem with holes;

9) in general optimum design platform Boss-Quattro, choose the GCMMA optimized Algorithm and be optimized design.

The maximum equivalent and the patch area of this structural finite element model are as shown in table 2 before and after optimizing.

Table 2

Embodiment 2: the void shape optimal design on the thin-walled conic dough sheet.

A hole is arranged on the thin-walled conical surface chip architecture, and its basic parameter is as shown in table 3.

Table 3

1) bus equation of thin-walled conical surface structure is:

$\left\{\begin{array}{c}x=0\\ z=\frac{H}{R_{\max }-R_{\min }}(y-R_{\min })\end{array}\right.---\left(14\right)$

Then under the polar coordinate system on the surfaces of revolution relation between any point radial coordinate R and the axial coordinate z satisfy:

$R\left(z\right)=R_{\min }+(R_{\max }-R_{\min })\frac{z}{H}---\left(15\right)$

2) set up the parametric equation of given conical surface:

$\left\{\begin{array}{c}x=R\left(z\left(t\right)\right)\cos [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s/s_0]\\ y=R\left(z\left(t\right)\right)\sin [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s/s_0]\\ z={\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">H</figure-callout>}}_0+(H_1-H_0)t/t_0\end{array}\right.(0\&le;s\&le;s_0,0\&le;t\&le;t_0)---\left(16\right)$

In the formula, θ ₀=0, θ ₁=1.0472, H ₀=0, H ₁=90mm.

3) the hole heart is (0.4683,0.5) at the coordinate on s-t plane, is set to the initial point of s-t plane local coordinate system.

4) the hole boundary curve in the curved surface inner plane coordinate system determines that by the reference mark of Cubic Spline Functions Fitting design variable decision the match form is as follows:

$\left\{\begin{array}{c}s=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;s_i\\ t=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;{\mathrm{<figure-callout\; id="0"\; label="t\; i"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">t</figure-callout>}}_i\end{array}\right.0\&le;u\&le;1---\left(17\right)$

5) adopt shell unit in commercial finite element analysis software ANSYS, to set up the finite element model of thin-walled conical surface chip architecture with holes.

6) the 5th) an axial end of coordinate maximum in the fixed sturcture on the basis of the finite element model set up in the step, applying summation at the structure other end is the uniform axial tension of 1kN, sets up the mechanical model of thin-walled conical surface structure with holes;

7) consider that structure and stand under load all have the characteristics of axial symmetry, adopt 1/2nd hole shapes to set design variable.According to the less features of shape of hole length and width gap, adopt polar coordinates definition hole shape design variable.The 3rd) go on foot in the s-t plane local pole coordinate system of determining, the utmost point electrical path length of quartern half cycle polar angle place control vertex is set to design variable, totally five design variables.

8) choosing hole week maximum equivalent minimum is optimization aim; Conical surface sheet area is limited to 6150mm as constraint function in the constraint ²The initial value of setting utmost point footpath design variable is 0.2, and variation range is [0.05,0.35]; Set up the Optimization Model of thin-walled conical surface chip architecture hole shape optimal design problem with holes.

9) in general optimum design platform Boss-Quattro, choose the GCMMA optimized Algorithm and be optimized design.

The maximum equivalent and the patch area of this structural finite element model are as shown in table 4 before and after optimizing.

Table 4

Embodiment 3: the void shape optimal design on the thin-walled rotation hyperboloid of one sheet.

The hole that has 12 circulations to be symmetrically distributed on the thin-walled rotation hyperboloid of one sheet structure, basic parameter is as shown in table 5.

Table 5

1) bus equation of thin-walled rotation hyperboloid of one sheet structure is:

$\left\{\begin{array}{c}\frac{y^2}{b^2}-\frac{z^2}{c^2}=1\\ x=0\end{array}\right.---\left(18\right)$

Then under the polar coordinate system on the surfaces of revolution relation between any point radial coordinate R and the axial coordinate z satisfy:

$R\left(z\right)=b\sqrt{1+\frac{z^2}{c^2}}=200\sqrt{1+\frac{z^2}{{150}^2}}---\left(19\right)$

2) set up the parametric equation of this rotation hyperboloid of one sheet:

$\left\{\begin{array}{c}x=R\left(z\left(t\right)\right)\cos [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s/s_0]\\ y=R\left(z\left(t\right)\right)\sin [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s/s_0]\\ z={\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">H</figure-callout>}}_0+(H_1-H_0)t/t_0\end{array}\right.(0\&le;s\&le;s_0,0\&le;t\&le;t_0)---\left(20\right)$

In the formula, θ ₀=0, θ ₁=0.5236, H ₀=-300, H ₁=200mm, s ₀=0.2261, t ₀=1.

3) the hole heart is (0.1130,0.5) at the coordinate on s-t plane, is set to the initial point of s-t plane local coordinate system;

4) the hole boundary curve in the curved surface inner plane coordinate system determines that by the reference mark on the Cubic Spline Functions Fitting s-t parameter plane match form is as follows:

$\left\{\begin{array}{c}s=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;s_i\\ t=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;{\mathrm{<figure-callout\; id="0"\; label="t\; i"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">t</figure-callout>}}_i\end{array}\right.0\&le;u\&le;1---\left(21\right)$

The parametric equation that then rotates curve of structural hole week of the hyperboloid of one sheet is:

$\left\{\begin{array}{c}x=b\sqrt{1+{(z\left(t\left(u\right)\right)/c)}^2}\cos [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;s_i/s_0]\\ y=b\sqrt{1+{(z\left(t\left(u\right)\right)/c)}^2}\sin [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;s_i/s_0]\\ z={\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">H</figure-callout>}}_0+\frac{H_1-H_0}{{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">t</figure-callout>}}_0}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;t_i\end{array}\right.(0\&le;u\&le;1)---\left(22\right)$

Wherein, N _i(u) be the basis function of cubic spline function.

5) adopt shell unit in commercial finite element analysis software ANSYS, at first to set up the single cell model that the thin-walled with holes that contains a hole rotates the hyperboloid of one sheet, generate complete finite element model by array processing again.

6) the 5th) an axial end of coordinate minimum in the fixed sturcture on the basis of the finite element model set up in the step, apply uniform axial tension at the structure other end, the axial tension summation is 10kN, sets up the mechanical model of thin-walled rotation hyperboloid of one sheet structure with holes.

7) consider that structure and stand under load all have the characteristics of axial symmetry, adopt 1/2nd hole shapes to set design variable.According to the bigger features of shape of hole length and width gap, adopt Cartesian coordinates definition hole shape design variable.The 3rd) go on foot in the s-t plane local coordinate system of determining, the t that chooses two hole curve control points that t makes progress to the coordinate absolute value as t to first and second design variable, and with t forward and t negative sense difference trisection, the corresponding t of each Along ent to the coordinate absolute value, is made as s respectively to first design variable to the, five design variables by t to coordinate order from big to small to the s of the hole curve control point of coordinate correspondence.Choose seven design variables altogether.

8) choosing hole week maximum equivalent minimum is optimization aim; The area of the rotation hyperboloid of one sheet is limited to 0.93m as constraint function in the constraint ²Setting t is 0.3 to the design variable initial value, and s is 0.06 to the initial value of design variable, and t is [0.1,0.6] to the variation range of design variable, and s is [0.02,0.10] to the variation range of design variable; Set up the Optimization Model of thin-walled rotation hyperboloid of one sheet structure hole shape optimal design problem with holes.

9) in general optimum design platform Boss-Quattro, choose the GCMMA optimized Algorithm and be optimized design.

The maximum equivalent and the surface area of this structural finite element model are as shown in table 6 before and after optimizing.

Table 6

Embodiment 4: the void shape optimal design on the thin-walled ellipse of revolution curved-surface structure.

3/8ths thin-walled ellipse of revolution curved-surface structures are evenly distributed with 12 holes on it, basic parameter is as shown in table 7.

Table 7

1) bus equation of thin-walled ellipse of revolution curved-surface structure is:

$\left\{\begin{array}{c}\frac{y^2}{b^2}+\frac{z^2}{c^2}=1\\ x=0\end{array}\right.---\left(23\right)$

Then under the polar coordinate system on the surfaces of revolution relation between any point radial coordinate R and the axial coordinate z satisfy:

$R\left(z\right)=b\sqrt{1-\frac{z^2}{c^2}}=300\sqrt{1-\frac{z^2}{{400}^2}}---\left(24\right)$

2) set up the parametric equation of this ellipse of revolution curved surface

$\left\{\begin{array}{c}x=R\left(z\left(t\right)\right)\cos [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s/s_0]\\ y=R\left(z\left(t\right)\right)\sin [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s/s_0]\\ z={\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">H</figure-callout>}}_0+(H_1-H_0)t/t_0\end{array}\right.(0\&le;s\&le;s_0,0\&le;t\&le;t_0)---\left(25\right)$

In the formula, θ ₀=0, θ ₁=0.5236, H ₀=0, H ₁=300mm, s ₀=0.4353, t ₀=1.

3) the hole heart is (0.2177,0.5) at the coordinate on s-t plane, is set to the initial point of s-t plane local coordinate system;

4) the hole boundary curve in the curved surface inner plane coordinate system determines that by the reference mark on the Cubic Spline Functions Fitting s-t parameter plane match form is as follows:

$\left\{\begin{array}{c}s=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;s_i\\ t=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;{\mathrm{<figure-callout\; id="0"\; label="t\; i"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">t</figure-callout>}}_i\end{array}\right.0\&le;u\&le;1---\left(26\right)$

Then the parametric equation of all curves in the hole on the ellipse of revolution curved-surface structure is:

$\left\{\begin{array}{c}x=b\sqrt{1-{(z\left(t\left(u\right)\right)/c)}^2}\cos [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;s_i/s_0]\\ y=b\sqrt{1-{(z\left(t\left(u\right)\right)/c)}^2}\sin [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;s_i/s_0]\\ z={\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">H</figure-callout>}}_0+\frac{H_1-H_0}{{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">t</figure-callout>}}_0}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;t_i\end{array}\right.(0\&le;u\&le;1)---\left(27\right)$

Wherein, N _i(u) be the basis function of cubic spline function.

5) adopt shell unit in commercial finite element analysis software ANSYS, at first to set up the single cell model of the thin-walled ellipse of revolution curved surface with holes that contains a hole, generate complete finite element model by array processing again.

6) the 5th) an axial end of coordinate minimum in the fixed sturcture on the basis of the finite element model set up in the step, acceleration of gravity is set, set up the mechanical model of the thin-walled ellipse of revolution curved-surface structure with holes that bears deadweight.

7) consider that structure and stand under load all have the characteristics of axial symmetry, adopt 1/2nd hole shapes to set design variable.According to the bigger features of shape of hole length and width gap, adopt Cartesian coordinates definition hole shape design variable.The 3rd) go on foot in the s-t plane local coordinate system of determining, the t that chooses two hole curve control points that t makes progress to the coordinate absolute value as t to first and second design variable, and with t forward and t negative sense difference trisection, the corresponding t of each Along ent to the coordinate absolute value, is made as s respectively to first design variable to the, five design variables by t to coordinate order from big to small to the s of the hole curve control point of coordinate correspondence.Choose seven design variables altogether.

8) choosing hole week maximum equivalent minimum is optimization aim; The area of ellipse of revolution curved surface is limited to 0.3775m as constraint function in the constraint ²Setting t is 0.3 to the design variable initial value, and s is 0.06 to the initial value of design variable, and t is [0.05,0.40] to the variation range of design variable, and s is [0.05,0.20] to the variation range of design variable; Set up the Optimization Model of thin-walled ellipse of revolution curved-surface structure hole shape optimal design problem with holes.

9) in general optimum design platform Boss-Quattro, choose the GCMMA optimized Algorithm and be optimized design.

The maximum equivalent and the surface area of this structural finite element model are as shown in table 8 before and after optimizing.

Table 8

Embodiment 5: loss of weight is a target, and stress is the void shape optimal design on the thin-walled ellipse of revolution curved-surface structure of constraint.

With the thin-walled ellipse of revolution curved-surface structure among the embodiment 4, concrete steps among void shape Optimization Design such as the embodiment four on it, unique different be to choose the surface area minimum as optimization aim, hole week equivalent stress is a constraint function, is limited to 50MPa in the constraint.

The maximum equivalent and the surface area of this structural finite element model are as shown in table 9 before and after optimizing.

Table 9

Embodiment 6: the void shape optimal design that adopts the splines match on the thin wall rotating curved surface structure.

Be distributed with the hole of circulation symmetry on the thin wall rotating curved surface structure, these hole axial lengths are obviously greater than axial width, and its basic parameter is as shown in table 10.

Table 10

1) bus equation of thin wall rotating curved surface structure adopts Cubic Spline Functions Fitting, and fit equation satisfies (3) formula.N=6 wherein, reference mark coordinate (y _i, z _i) (i=1,2 ..., 6) be respectively (0,0), (70,0), (60,24), (50,48), (80,72), (90,96), the area of space of wherein back 4 formation is the mapping territory.Then under the polar coordinate system on the surfaces of revolution relation between any point radial coordinate R and the axial coordinate z satisfy following formula:

R(z)＝|y(v(z))| (28)

2) set up the parametric equation of given surface of revolution:

$\left\{\begin{array}{c}x=R\left(z\left(t\right)\right)\cos [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s/s_0]\\ y=R\left(z\left(t\right)\right)\sin [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s/s_0]\\ z={\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">H</figure-callout>}}_0+(H_1-H_0)t/t_0\end{array}\right.(0\&le;s\&le;s_0,0\&le;t\&le;t_0)---\left(29\right)$

In the formula, θ ₀=0, θ ₁=0.5236, H ₀=0, H ₁=96mm, s ₀=0.1852, t ₀=1.

3) the hole heart is (0.0926,0.5) at the coordinate on s-t plane, is set to the initial point of s-t plane local coordinate system;

4) the hole boundary curve in the curved surface inner plane coordinate system determines that by the reference mark on the Cubic Spline Functions Fitting s-t parameter plane match form is as follows:

$\left\{\begin{array}{c}s=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;s_i\\ t=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;{\mathrm{<figure-callout\; id="0"\; label="t\; i"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">t</figure-callout>}}_i\end{array}\right.0\&le;u\&le;1---\left(30\right)$

Then the parametric equation of all curves in the hole on this thin-wall curved-surface structure is:

$\left\{\begin{array}{c}x=R\left(z\left(t\left(u\right)\right)\right)\cos [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;s_i/s_0]\\ y=R\left(z\left(t\left(u\right)\right)\right)\sin [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;s_i/s_0]\\ z={\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">H</figure-callout>}}_0+\frac{H_1-H_0}{{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">t</figure-callout>}}_0}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;t_i/t_0\end{array}\right.(0\&le;u\&le;1)---\left(31\right)$

Wherein, N _i(u) be the basis function of cubic spline function.

5) adopt shell unit in commercial finite element analysis software ANSYS, at first to set up the single cell model of the thin wall rotating curved surface structure with holes that contains a hole, generate complete finite element model by array processing again;

6) the 5th) end of fixed sturcture axial coordinate maximum on the basis of the finite element model set up in the step, acceleration of gravity is set, set up the mechanical model of thin wall rotating curved surface structure with holes;

7) consider that structure and stand under load all have the characteristics of axial symmetry, adopt 1/2nd hole shapes to set design variable.According to the bigger features of shape of hole length and width gap, adopt Cartesian coordinates definition hole shape design variable.The 3rd) go on foot in the s-t plane local coordinate system of determining, the t that chooses two hole curve control points that t makes progress to the coordinate absolute value as t to first and second design variable, and with t forward and t negative sense difference trisection, the corresponding t of each Along ent to the coordinate absolute value, is made as s respectively to first design variable to the, five design variables by t to coordinate order from big to small to the s of the hole curve control point of coordinate correspondence.Choose seven design variables altogether.

8) choosing hole week maximum equivalent minimum is optimization aim; The surface area of rotating curved surface structure is limited to 1.19m as constraint function in the constraint ²Setting t is 0.25 to the design variable initial value, and s is 0.05 to the initial value of design variable, and t is [0.1,0.4] to the variation range of design variable, and s is [0.01,0.08] to the variation range of design variable; Set up the Optimization Model of thin wall cylindrical curved-surface structure hole shape optimal design problem with holes.

9) in general optimum design platform Boss-Quattro, choose the GCMMA optimized Algorithm and be optimized design.

The maximum equivalent and the surface area of this structural finite element model are as shown in table 11 before and after optimizing.

Table 11

Embodiment 7: adopt on the thin wall rotating curved surface B-spline function match the void shape optimal design.

With the thin wall rotating curved surface structure among the embodiment 6, concrete steps among void shape Optimization Design such as the embodiment 5 on it uniquely are not all the 4th) adopt the reference mark on the cubic B-spline function match s-t parameter plane in the step, and then definite hole boundary curve.

The maximum equivalent and the surface area of this structural finite element model are as shown in table 12 before and after optimizing.

Table 12

Embodiment 8: adopt on the thin wall rotating curved surface structure match of NURBS function the void shape optimal design.

With the thin wall rotating curved surface structure among the embodiment 6, concrete steps among void shape Optimization Design such as the embodiment 5 on it, uniquely be not all the 4th) adopt the reference mark on the NURBS function match s-t parameter planes in the step three times, and then definite hole boundary curve, wherein t is made as 10 to the weight factor of the corresponding control vertex of design variable, and the weight factor of other control vertex is made as 1.

The maximum equivalent and the cylinder surface area of this structural finite element model are as shown in table 13 before and after optimizing.

Table 13

Embodiment 9: the slotted eye Shape optimization designs on actual engineering structure-squirrel-cage elastic support.

The cocycle of a squirrel-cage elastic support structure is symmetrically distributed with 24 slotted eyes, and its basic parameter is as shown in table 14.

Table 14

1) squirrel-cage elastic support curved-surface structure sleeve is a column structure, and its bus equation satisfies following formula

$\left\{\begin{array}{c}x=0\\ y=0\end{array}\right.---\left(32\right)$

Then under the polar coordinate system on the surfaces of revolution relation between any point radial coordinate R and the axial coordinate z satisfy:

R(z)＝R ₀ (33)

2) set up the parametric equation of given cylinder patch

$\left\{\begin{array}{c}x=R\left(z\left(t\right)\right)\cos [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s/s_0]\\ y=R\left(z\left(t\right)\right)\sin [{\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)s/s_0]\\ z={\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">H</figure-callout>}}_0+(H_1-H_0)t/t_0\end{array}\right.(0\&le;s\&le;s_0,0\&le;t\&le;t_0)---\left(34\right)$

In the formula, θ ₀=0, θ ₁=0.2618rad, H ₀=15mm, H ₁=105mm, s ₀=0.1745, t ₀=1.

3) the hole heart is (0.0872,0.5) at the coordinate on s-t plane, is set to the initial point of s-t plane local coordinate system.

4) the hole boundary curve in the curved surface inner plane coordinate system determines that by the Cubic Spline Functions Fitting reference mark match form is as follows:

$\left\{\begin{array}{c}s=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;s_i\\ t=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i\left(u\right)\&CenterDot;{\mathrm{<figure-callout\; id="0"\; label="t\; i"\; filenames="H2009102544663E00012.png"\; state="\{\{state\}\}">t</figure-callout>}}_i\end{array}\right.0\&le;u\&le;1---\left(35\right)$

5) adopt shell unit in commercial finite element analysis software ANSYS, at first to set up the finite element model in thin-walled squirrel-cage elastic support curved-surface structure unit cell spatial mappings territory, in space coordinates, set up then lower limb unit cell finite element model on limit and the sleeve is installed, set up complete squirrel-cage elastic support finite element model by duplicating array processing at last.

6) the 5th) on the basis of the finite element model set up in the step the fixing installation limit of squirrel-cage elastic support, adopts the rigid body beam element to apply the radial load of 3kN at the sleeve cantilever end, sets up the mechanical model of thin-walled squirrel-cage elastic support structure with holes.

7) adopt 1/4th hole shapes to set design variable.According to the bigger features of shape of hole length and width gap, adopt Cartesian coordinates definition hole shape design variable.The 3rd) in the s-t plane local coordinate system determined of step, choose t hole curve control point t forward reference forward as t to design variable; With t forward trisection, press t to each Along ent t of coordinate sequential definition from big to small to the s of the hole curve control point of coordinate correspondence to the coordinate absolute value as s to first to the 3rd design variable.Choose four design variables altogether.

8) choosing hole week maximum equivalent minimum is optimization aim; Sleeve area and rigidity of structure coefficient are limited to 32561.2mm as constraint function in the constraint of sleeve area ², be limited to 21724.96N/mm in the constraint of stiffness coefficient; Set r ₁Variation range be [0.0333,0.0778], r ₂Variation range be [0.2889,0.3333]; Set up the Optimization Model of the hole shape optimal design problem of thin-walled squirrel-cage elastic support structure with holes.

9) in general optimum design platform Boss-Quattro, choose the GCMMA optimized Algorithm and be optimized design.

The maximum equivalent and the sleeve surface area of this structural finite element model are as shown in Table 15 before and after optimizing.

Table 15

Claims (1)

1. the hole optimizing design method of a thin wall rotating curved surface structure with holes is characterized in that may further comprise the steps:

(a) set up the rotation bus equation, determine under the polar coordinate system relation between any point radial coordinate and axial coordinate on the surfaces of revolution; If the z axle is a turning axle, the rotation bus is positioned on the y-z plane, and R represents under the polar coordinate system radial coordinate of any point on the surfaces of revolution;

It is as follows to adopt Analytical Expression to set up rotation bus equation expression formula:

Then the relation between R and the z is determined by (2) formula

F(sign(y)R(z)，z)＝0(2)

The rotation bus equation expression formula that adopts the parameter fitting mode to set up is as follows:

0≤v≤1(3)

Then the relation between R and the z is determined by (4) formula

R(z)＝|y(v(z))|(4)

(b) set up the parametric equation of given surface of revolution:

0≤s≤s ₀，0≤t≤t ₀(5)

In the formula, θ ₀With θ ₁Be the initial and termination point of rotation dough sheet, H ₀With H ₁Minimum and maximum axial coordinate for the surfaces of revolution; The surfaces of revolution is mapped as the long s that is ₀, height is t ₀The rectangular area;

(c) determine the position of the hole heart according to formula (5), be set to the initial point of s-t plane local coordinate system on the s-t plane;

(d) set up the parametric equation of hole week curve:

0≤u≤1(6)

The hole week curve parametric equation that adopts fit Plane reference mark mode to determine:

0≤u≤1(7)

Wherein, N _i(u) be the basis function of fit equation;

Then the parametric equation of all curves in the structural hole of space curved surface is:

(e), adopt shell unit in finite element analysis software, to set up the finite element model of three-dimensional thin wall rotating curved surface structure with holes by the mapping relations between s-t plane and the space coordinates;

(f) on the basis of finite element model, apply boundary condition and load, set up the mechanical model of thin wall rotating curved surface structure with holes;

(g) according to design feature and stand under load form, determine that design variable distributes, symmetrical structure adopts 1/2nd hole shapes to set design variable, and the disymmetry structure adopts 1/4th hole shapes to set design variable;

(h) choosing hole week maximum equivalent minimum is optimization aim, and structural volume is set design variable initial value and variation range as constraint function, sets up the Optimization Model of thin wall rotating curved surface structure hole optimal design problem with holes;

(i) choose optimized Algorithm and be optimized design.

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