CN102254066A - Collaborative optimization design method for curved surface shape and pore shape in pored thin-wall curved shell structure - Google Patents

Abstract

The invention discloses a collaborative optimization design method for a curved surface shape and a pore shape in a pored thin-wall curved shell structure, aiming at solving the technical problems that collaborative optimization design of the curved surface shape and the pore shape thereon cannot be performed by using the existing design method. In a technical scheme provided by the invention, two design variables, namely a curved surface design variable relevant to the curved surface shape and a pore shape design variable relevant to the pore shape, are defined at the same time, the pore shape design variable is defined in an curved surface internal parameter mapping domain changing along with the change of the curved surface shape, so that a pore shape curve is effectively guaranteed to be always in the parameter mapping domain, and the collaborative optimization design of the curved surface shape and the pore shape thereon is realized at the same time when the structural completeness is guaranteed. After the design flow in the method provided by the invention is adopted for the collaborative optimization design of the curved surface shape and the pore shape thereon, the maximal equivalent stress of a pored thin-wall hyperbolic-rotation curved shell structure finite element model under the restraint of initial volume is decreased to 18.690-24.181kPa from 135.199-360.649kPa at an initial period, and the decreasing amplitude reaches 82.1-94.8%.

Description

The curve form of Thin Walled Curved shell structure with holes and void shape cooperate optimization method for designing

Technical field

The present invention relates to a kind of curve form and void shape cooperate optimization method for designing, the curve form of Thin Walled Curved shell structure particularly with holes and void shape cooperate optimization method for designing.Be applicable to any Thin Walled Curved shell structure with holes in space.

Background technology

In Aeronautics and Astronautics, navigation and the construction work, there is a large amount of thin-wall curved-surface structures.For loss of weight, maintenance, exhaust in addition attractive in appearance on needs, have various holes on these thin-wall curved-surfaces usually.The introducing of hole will inevitably destroy the integrality of structure, changes the load path of structure, thereby causes that the hole circumferential stress is concentrated, a series of problems of degradation under the structure fatigue life.

Document 1 " Form Finding of Shells by Structural Optimization.Bletzinger KU and Ramm E, Engineering with computers.1993; 9:27-35. " a kind of method for designing disclosed, the parameter of curved surface is optimized design as design variable, realized the Shape optimization designs of free form surface.

Document 2 " A parametric mapping method for curve shape optimization on 3D panel structures.Zhang WH; Wang D and Yang JG, International Journal for Numerical Methods in Engineering.2010; 84:485-504. " a kind of method of parameter maps is disclosed, can realize the void shape optimal design on the thin-wall curved-surface structure with holes.This Optimization Design at first is defined in the void shape design variable on the parameter plane, adopt the method for parameter fitting on parameter plane, to generate hole, plane perimeter curve again, utilize the mapping relations between space curved surface and the parameter plane at last, on the mapping making the return trip empty of the point on a parameter plane curved-surface structure.Like this, can effectively control the shape of space hole, and guarantee that by mapping relations any point of space hole boundary curve is positioned on the given thin-wall curved-surface structure all the time by the void shape design variable on the parameter plane.

But all do not propose in the above-mentioned document to consider the curve form of curved surface with holes simultaneously and the method for void shape cooperate optimization design on it.And practical application mean camber shape and the void shape on it all have certain designability, need to consider curve form and the cooperate optimization effect of void shape on it.In the cooperate optimization process, if directly the hole shape design variable is defined in the parameter maps territory of the fixed in shape that provides in the document 2, just can't reflect the curved surface change information, may cause the surface mesh deformity, influence the finite element solving precision, even can't carry out finite element solving.In addition, common control vertex coordinate with hole perimeter matched curve is defined as the hole shape design variable in the document 2, and the variation of shining upon the territory like this can cause the bound of hole shape design variable also to change.So, can not simply curve form optimization method in the document 1 and the void shape optimization method on the thin-wall curved-surface with holes in the document 2 directly be combined the cooperate optimization design of carrying out curve form and the void shape on it.

Summary of the invention

Do not consider curved-surface structure mean camber shape with holes in the prior art simultaneously and the designability of void shape on it, and can't be simply the void shape optimization method of previous surface Shape Optimization and curved surface with holes be directly combined and carry out curve form and the design of the void shape cooperate optimization on it.In order to solve this technical matters, the invention provides a kind of curve form and void shape cooperate optimization method for designing of Thin Walled Curved shell structure with holes, this method defines the curved design variable relevant with curve form and hole shape design variable two kind design variables relevant with void shape simultaneously, the hole shape design variable is defined in the curved surface inner parameter mapping territory that changes with the curve form variation, thereby can guarantee the precision of finite element solving effectively, and it is the hole shape design variable is regular to [0,1] on the interval, can upgrade the hole shape position according to the change dynamics of curved design variable like this, can guarantee that the hole shape curve is positioned at the parameter maps territory all the time, thereby when guaranteeing structural intergrity, can realize the cooperate optimization design of curve form and the void shape on it.

The technical solution adopted for the present invention to solve the technical problems is: a kind of curve form of Thin Walled Curved shell structure with holes and void shape cooperate optimization method for designing are characterized in comprising the steps:

(a), in the Ω of parameter maps territory, set up the parametric equation of curved-surface structure mean camber with holes according to the features of shape of curved surface:

$\left\{\begin{array}{c}x=x(\mathrm{\ξ},\mathrm{\η})\\ y=y(\mathrm{\ξ},\mathrm{\η})\\ z=z(\mathrm{\ξ},\mathrm{\η})\end{array}\right.\mathrm{\ξ}\≥0,\mathrm{\η}\≥0;(\mathrm{\ξ},\mathrm{\η})\∈\mathrm{\Ω}.---\left(1\right)$

Set up the method in parameter maps territory: for three limit curved surfaces, corresponding triangle parameter maps territory, a limit in triangle mapping territory are on the parameter coordinate axis, and a summit is initial point, and two summits are respectively (ξ in addition ₀, 0), (ξ ₁, η ₀); Corresponding three undetermined parameter: ξ in plane parameter mapping territory of three limit curved surfaces ₀, ξ ₁And η ₀For four limit curved surfaces, corresponding rectangle parameter maps territory, its two limits are on the parameter coordinate axis, and a summit is initial point, and at this moment three summits in addition in parameter maps territory are respectively (ξ ₀, 0), (ξ ₀, η ₀), (0, η ₀); Corresponding two undetermined parameter: the ξ in the parameter maps territory of four limit curved surfaces ₀And η ₀For complex-curved, it is divided into the combination of a plurality of three limit curved surfaces and four limit curved surfaces, by operations such as translation, rotation, symmetries the parameter maps territory of a plurality of triangle parameter maps territory, a plurality of rectangle parameter maps territories or other shapes is made up again, form mapping relations with corresponding piecemeal curved surface;

(b) determine the curved surface parameter according to the bent edge lengths of curved surface;

For three limit curved surfaces, set its three curved surface length of sides and be respectively L ₁, H ₁And H ₂, and corresponding with base, right edge and limit, left side in the triangle mapping territory respectively; Then the triangle parameter maps field parameter of three limit curved surfaces is determined by following formula:

$\left\{\begin{array}{c}{\mathrm{\ξ}}_0=\mathrm{\λ}{L}_1\\ {\mathrm{\ξ}}_1=\frac{\mathrm{\λ}{H}_2{L}_1}{H_1+H_2}\\ {\mathrm{\η}}_0=0.5\mathrm{\λ}(H_1+H_2)\end{array}\right.---\left(2\right)$

For four limit curved surfaces, suppose that its four curved surface length of sides are respectively L ₁, H ₁, L ₂And H ₂, and corresponding with base, right edge, top margin and limit, left side in the rectangle mapping territory respectively; Then the rectangle parameter maps field parameter of four limit curved surfaces is determined by following formula:

$\left\{\begin{array}{c}{\mathrm{\ξ}}_0=0.5\mathrm{\λ}(L_1+L_2)\\ {\mathrm{\η}}_0=0.5\mathrm{\λ}(H_1+H_2)\end{array}\right.---\left(3\right)$

In the formula, λ is the length ratio coefficient greater than 0;

(c) select only relevant with curve form parameter as the curved design variable in the parametric equation formula (1) of curved surface, the parametric equation that adopts approximating method to generate curved-surface structure is:

$\left\{\begin{array}{c}x=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{N}_i(\mathrm{\ξ},\mathrm{\η})\·x_i\\ y=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{N}_i(\mathrm{\ξ},\mathrm{\η})\·y_i\\ z=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{N}_i(\mathrm{\ξ},\mathrm{\η})\·z_i\end{array}\right.,(\mathrm{\ξ},\mathrm{\η})\∈\mathrm{\Ω}.---\left(4\right)$

In the formula, ξ and η are the parameter of curved surface, N _i(ξ η) is the match basis function of i control vertex, (x _i, y _i, z _i) be the spatial control point coordinate of curved surface;

(d) be the parametric equation of setting up hole, plane perimeter curve on ξ-η plane at the curved surface intrinsic coordinates:

$\left\{\begin{array}{c}\mathrm{\ξ}=\mathrm{\ξ}\left(u\right)\\ \mathrm{\η}=\mathrm{\η}\left(u\right)\end{array}\right.,0\≤u\≤1---\left(5\right)$

In the formula, u is the parameter of hole week curve;

(e) in the parametric equation of hole, plane week curve, select only relevant parameter as the hole shape design variable, adopt the parametric equation of hole, the plane perimeter curve of approximating method generation to be with hole week curve shape:

$\left\{\begin{array}{c}\mathrm{\ξ}=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{B}_j\left(u\right)\·s_j\\ \mathrm{\η}=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{B}_j\left(u\right)\·t_j\end{array}\right.,0\≤u\≤1---\left(6\right)$

In the formula, B _j(u) be the match basis function of j control vertex, (s _j, t _j) be the reference mark coordinate of hole, plane perimeter curve, b _kIt is the symbol of k hole shape design variable;

(f) with selected hole shape design variable b _kCarry out normalization process, obtain corresponding regular hole shape design variable α _k:

${\mathrm{\α}}_k=\frac{b_k-b_k^{\min }}{b_k^{\max }-b_k^{\min }}\∈\left[\mathrm{0,1}\right]---\left(7\right)$

In the formula, b _k ^MaxAnd b _k ^MinBe respectively k hole shape design variable b _kThe upper and lower bound that changes, α _kBe corresponding k regular hole shape design variable, the variation range of k is from 1 number to the hole shape design variable;

(g) like this, the parametric equation of spatial hole perimeter curve is:

$\left\{\begin{array}{c}x=x(\mathrm{\ξ}\left(u\right),\mathrm{\η}\left(u\right))\\ y=y(\mathrm{\ξ}\left(u\right),\mathrm{\η}\left(u\right))\\ z=z(\mathrm{\ξ}\left(u\right),\mathrm{\η}\left(u\right))\end{array}\right.,0\≤u\≤1---\left(8\right)$

Wherein promptly comprise the curved design variable relevant, comprise again and the relevant hole shape design variable of hole week curve shape with the space curved surface shape;

When space curved surface and hole, plane perimeter curve all are that the parametric equation of spatial hole perimeter curve is when adopting the match mode to generate:

$\left\{\begin{array}{c}x=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{N}_i(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{B}_j\left(u\right)\·{\mathrm{\ξ}}_j,\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{B}_j\left(u\right)\·{\mathrm{\η}}_j)\·x_i\\ y=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{N}_i(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{B}_j\left(u\right)\·{\mathrm{\ξ}}_j,\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{B}_j\left(u\right)\·{\mathrm{\η}}_j)\·y_i\\ z=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{N}_i(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{B}_j\left(u\right)\·{\mathrm{\ξ}}_j,\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{B}_j\left(u\right)\·{\mathrm{\η}}_j)\·z_i\end{array}\right.,0\≤u\≤1.---\left(9\right)$

In the formula, spatial control summit (x _i, y _i, z _i) as the curved design variable of control curved surface shape, the control vertex (ξ on the parameter plane _j, η _j) as the hole shape design variable of control punch week curve shape;

(h) directly in the parameter maps territory, divide finite element grid, utilize plane curve-space curve again, dual mapping relations between plane domain-curved-surface structure, respectively discrete nodes on the perimeter curve of hole, plane and the discrete nodes in the parameter maps territory are mapped on the curved surface with holes, and, adopt shell unit to generate finite element grid on the curved surface with holes according to the topological structure of discrete nodes in the parameter maps territory;

(i) set material properties, and on the curved surface finite element model by applying boundary condition and load, set up the mechanical model of thin-wall curved-surface structure with holes;

(j) initial value and the variation range of setting curved design variable, the hole shape design variable is curved design variable and regular hole shape design variable, the initial value of selected regular hole shape design variable; Compages stress distribution, weight are set up the Optimization Model of thin-wall curved-surface structure curve form with holes and void shape cooperate optimization design problem, choose usually that hole week maximum equivalent is minimum to be optimization aim, and surface area is as constraint function;

(k) adopt and to be optimized design based on the optimized Algorithm of gradient or intelligent optimization algorithm and to find the solution.

The present invention's beneficial effect compared to existing technology is: because this method defines the curved design variable relevant with curve form and hole shape design variable two kind design variables relevant with void shape simultaneously, the hole shape design variable is defined in the curved surface inner parameter mapping territory that changes with the curve form variation, thereby guaranteed the precision of finite element solving effectively, and it is the hole shape design variable is regular to [0,1] on the interval, can upgrade the hole shape position according to the change dynamics of curved design variable like this, guaranteed that the hole shape curve is positioned at the parameter maps territory all the time, thereby when guaranteeing structural intergrity, realized the cooperate optimization design of curve form and the void shape on it.After the design cycle of employing the inventive method is carried out curve form and the design of the void shape cooperate optimization on it, the maximum equivalent that Thin-wall Hyperbolic with holes under the initial volume constraint is rotated bent shell structure finite element model is reduced to 18.690～24.181kPa by 135.199 initial～360.649kPa, decreases by 82.1～94.8%.

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

Description of drawings

Fig. 1 is the synoptic diagram in rectangle mapping territory.

Fig. 2 is the synoptic diagram in triangle mapping territory.

Fig. 3 is the size synoptic diagram of the thin-walled semielliptical shell structure among the embodiment 1.

Fig. 4 is the bus size synoptic diagram that the Thin-wall Hyperbolic among the embodiment 2 is rotated bent shell structure.

Embodiment

Following examples are with reference to Fig. 1～Fig. 4.

Embodiment 1: the curve form of semielliptical shell with holes and void shape cooperate optimization design on it.

The hole of 4 circulation symmetries is arranged on the semielliptical shell structure with holes, and its material and dimensional parameters are: Young modulus E=210GPa, and Poisson ratio μ=0.3, density is ρ=8.0 * 10 ^-6Kg/mm ³, curved surface thickness T=2mm.

(a) semielliptical shell structure with holes is three limit curved surfaces, and itself and triangle mapping territory are set up mapping relations, can set up the parametric equation with the thin-walled semielliptical shell single cell structure of a hole:

$\left\{\begin{array}{c}x=a_1\cos \left(\frac{\mathrm{\π\η}}{2{\mathrm{\η}}_0}\right)\cos \left(\frac{\mathrm{\π}({\mathrm{\η}}_0\mathrm{\ξ}-{\mathrm{\ξ}}_1\mathrm{\η})}{2({\mathrm{\η}}_0-\mathrm{\η}){\mathrm{\ξ}}_0}\right)\\ y=a_1\cos \left(\frac{\mathrm{\π\η}}{2{\mathrm{\η}}_0}\right)\sin \left(\frac{\mathrm{\π}({\mathrm{\η}}_0\mathrm{\ξ}-{\mathrm{\ξ}}_1\mathrm{\η})}{2({\mathrm{\η}}_0-\mathrm{\η}){\mathrm{\ξ}}_0.}\right),\frac{{\mathrm{\ξ}}_1\mathrm{\η}}{{\mathrm{\η}}_0}\≤\mathrm{\ξ}\≤{\mathrm{\ξ}}_0-\frac{({\mathrm{\ξ}}_0-{\mathrm{\ξ}}_1)\mathrm{\η}}{{\mathrm{\η}}_0},0\≤\mathrm{\η}\≤{\mathrm{\η}}_0.\\ z=a_2\sin \left(\frac{\mathrm{\π\η}}{2{\mathrm{\η}}_0}\right)\end{array}\right.---\left(1\right)$

In the formula, a ₁And a ₂Be respectively the axial radii and circumferential radius of semielliptical shell.At this moment, ξ ₀, ξ ₁And η ₀Three undetermined parameters for the parameter maps territory.

Thereby set up and curved surface corresponding parameter mapping territory Ω at the first quartile of ξ-η parameter plane.

Here provide a kind of method of setting up the parameter maps territory: for three limit curved surfaces, corresponding triangle parameter maps territory, a limit in triangle mapping territory are on the parameter coordinate axis, and a summit is initial point, and two summits are respectively (ξ in addition ₀, 0), (ξ ₁, η ₀).So, corresponding three undetermined parameter: ξ in plane parameter mapping territory of three limit curved surfaces ₀, ξ ₁And η ₀For four limit curved surfaces, corresponding rectangle parameter maps territory, its two limits are on the parameter coordinate axis, and a summit is initial point, and at this moment three summits in addition in parameter maps territory are respectively (ξ ₀, 0), (ξ ₀, η ₀), (0, η ₀).So, corresponding two undetermined parameter: the ξ in the parameter maps territory of four limit curved surfaces ₀And η ₀For complex-curved, it can be divided into the combination of a plurality of three limit curved surfaces and four limit curved surfaces, by operations such as translation, rotation, symmetries the parameter maps territory of a plurality of triangle parameter maps territory, a plurality of rectangle parameter maps territories or other shapes is made up again, form mapping relations with corresponding piecemeal curved surface.

(b) the length ratio coefficient lambda is made as 1, then triangle parameter maps territory corresponding parameters ξ ₀, ξ ₁And η ₀Value satisfy:

$\left\{\begin{array}{c}{\mathrm{\ξ}}_0=0.5\mathrm{\π}{a}_1\\ {\mathrm{\ξ}}_1=0.5{\mathrm{\ξ}}_0\\ {\mathrm{\η}}_0=0.25\mathrm{\π}(1.5(a_1+a_2)-\sqrt{a_1{a}_2})\end{array}\right.---\left(2\right)$

(c) at this moment, choose the only relevant parameter a of parametric equation formula (1) of curved surface with curve form ₁And a ₂As the curved design variable.

(d) be to adopt the mode of cubic B-spline match to set up the parametric equation of hole, plane perimeter curve on ξ-η plane at the curved surface intrinsic coordinates, wherein u is the parameter of hole week curve:

$\left\{\begin{array}{c}\mathrm{\ξ}=\underset{j=1}{\overset{8}{\mathrm{\Σ}}}{C}_j\left(u\right)\·s_j\\ \mathrm{\η}=\underset{j=1}{\overset{8}{\mathrm{\Σ}}}{C}_j\left(u\right)\·t_j\end{array}\right.,0\≤u\≤1---\left(3\right)$

In the formula, C _j(u) be the cubic B-spline match basis function of j control vertex, (s _j, t _j) be the reference mark coordinate of hole, plane perimeter curve.

(e) in the parametric equation of hole, plane week curve, (s _j, t _j) be the reference mark coordinate of hole, plane perimeter curve, only relevant with hole week curve shape.Hole shape is set to symmetrical hole shape among this embodiment, the hole heart is arranged on the center (ξ in parameter maps territory ₀/ 2, η ₀/ 2), as the local coordinate system that defines the hole shape design variable.The via hole heart is provided with 1 vertical control vertex respectively along ξ axle forward and negative sense, and these two vertical control vertexs in local coordinate system only η to coordinate t ₁And t ₅Can change, along the direction parallel 3 horizontal control vertexs are set with the η axle, wherein the η of first horizontal control vertex in local coordinate system is half of first vertical control vertex corresponding coordinate to coordinate, and second η of horizontal control vertex in local coordinate system is η to coordinate ₀The/2, three η of horizontal control vertex in local coordinate system is half of second vertical control vertex corresponding coordinate to coordinate, then these three horizontal control vertexs only ξ to coordinate s _j(j=2,3,4) can change.The η of vertical control vertex is only relevant with hole week curve shape to coordinate to the ξ of coordinate and horizontal control vertex, with its absolute value b _k(k=1,2 ... 5) be made as the hole shape design variable, and these five hole shape design variables satisfy:

$\left\{\begin{array}{c}0\≤b_j=t_j\≤\frac{{\mathrm{\η}}_0}{2},j=\mathrm{1,5}\\ 0\≤b_2=s_2\≤\frac{{\mathrm{\ξ}}_0}{4}(1-\frac{b_1}{{\mathrm{\η}}_0})\\ 0\≤b_3=s_3\≤\frac{{\mathrm{\ξ}}_0}{4}\\ 0\≤b_4=s_4\≤\frac{{\mathrm{\ξ}}_0}{4}(1+\frac{b_5}{{\mathrm{\η}}_0}).\end{array}\right.---\left(4\right)$

(f) with selected hole shape design variable b _k(k=1,2 ... 5) carry out normalization process, can obtain corresponding regular hole shape design variable α _k(k=1,2 ... 5):

$\left\{\begin{array}{c}0\&le;{\mathrm{\&alpha;}}_j=\frac{2{\mathrm{<figure-callout\; id="0"\; label="b\; j\; v"\; filenames="HSA00000528950300011.png"\; state="\{\{state\}\}">b</figure-callout>}}_j}{v_{}}\&le;1,j=\mathrm{1,5}\\ 0\&le;{\mathrm{\&alpha;}}_2=\frac{4v_0{b}_2}{u_0(v_0-b_1)}\&le;1\\ 0\&le;{\mathrm{\&alpha;}}_3=\frac{{4b}_3}{{\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="HSA00000528950300011.png"\; state="\{\{state\}\}">u</figure-callout>}}_0}\&le;1\\ 0\&le;{\mathrm{\&alpha;}}_4=\frac{{4v}_0{b}_4}{u_0({\mathrm{<figure-callout\; id="0"\; label="v"\; filenames="HSA00000528950300011.png"\; state="\{\{state\}\}">v</figure-callout>}}_0+b_5)}\&le;1.\end{array}\right.---\left(5\right)$

(g) like this, the parametric equation of spatial hole perimeter curve is:

$\left\{\begin{array}{c}x=a_1\cos (\frac{\mathrm{\&pi;}}{2{\mathrm{\&eta;}}_0}\underset{j=1}{\overset{8}{\mathrm{\&Sigma;}}}{C}_j\left(u\right)\&CenterDot;t_j)\cos \left(\frac{\mathrm{\&pi;}({\mathrm{\&eta;}}_0{\mathrm{\&Sigma;}}_{j=1}^8{C}_j\left(u\right)\&CenterDot;s_j-{\mathrm{\&xi;}}_1{\mathrm{\&Sigma;}}_{j=1}^8{C}_j\left(u\right)\&CenterDot;t_j)}{2{\mathrm{\&xi;}}_0({\mathrm{\&eta;}}_0-{\mathrm{\&Sigma;}}_{j=1}^8{C}_j\left(u\right)\&CenterDot;t_j)}\right)\\ y=a_1\cos (\frac{\mathrm{\&pi;}}{2{\mathrm{\&eta;}}_0}\underset{j=1}{\overset{8}{\mathrm{\&Sigma;}}}{C}_j\left(u\right)\&CenterDot;t_j)\sin \left(\frac{\mathrm{\&pi;}({\mathrm{\&eta;}}_0{\mathrm{\&Sigma;}}_{j=1}^8{C}_j\left(u\right)\&CenterDot;s_j-{\mathrm{\&xi;}}_1{\mathrm{\&Sigma;}}_{j=1}^8{C}_j\left(u\right)\&CenterDot;t_j)}{2{\mathrm{\&xi;}}_0({\mathrm{\&eta;}}_0-{\mathrm{\&Sigma;}}_{j=1}^8{C}_j\left(u\right)\&CenterDot;t_j)}\right)\\ z=a_2\sin (\frac{\mathrm{\&pi;}}{2{\mathrm{\&eta;}}_0}\underset{j=1}{\overset{8}{\mathrm{\&Sigma;}}}{C}_j\left(u\right)\&CenterDot;t_j)\end{array}\right.,0\&le;u\&le;1.---\left(6\right)$

Wherein promptly comprise the curved design variable relevant, comprise again and the relevant hole shape design variable of hole week curve shape with the space curved surface shape.

(h) directly divide finite element grid in the parameter maps territory, utilize plane curve-space curve again, dual mapping relations between plane domain-curved-surface structure, respectively discrete nodes on the perimeter curve of hole, plane and the discrete nodes in the parameter maps territory are mapped on the curved surface with holes, and according to the topological structure of discrete nodes in the parameter maps territory, adopt shell unit to generate the finite element grid of semielliptical shell single cell structure with holes, and generate the finite element grid of total by the circulation symmetry operation.

(i) set material properties, fixed belt hole semielliptical shell, and, set up its mechanical model along bearing z to semielliptical shell structure weight application load with holes.

(j) curved design variable a ₁And a ₂Initial value be 0.3m and variation range is [0.15m, 0.45m], the bound of hole shape design variable is that iteration is upgraded with the variation of curved design variable, and the design variable that adopts in the actual optimization is curved design variable and regular hole shape design variable, regular hole shape design variable α _k(k=1,2 ..., 5) initial value be 0.25; Choosing hole week maximum equivalent minimum is optimization aim, and surface area is smaller or equal to 0.4670m ²As constraint function, set up the Optimization Model of thin-walled semielliptical shell structure curve form with holes and void shape optimal design problem.

(k) adopting optimized Algorithm GCMMA based on gradient to be optimized design finds the solution.

Unit maximum equivalent, the surface area in this structure hole week are as shown in table 1 before and after optimizing.

Table 1

Embodiment 2: Thin-wall Hyperbolic with holes is rotated the curve form of bent shell structure and void shape cooperate optimization design on it.

Thin-wall Hyperbolic with holes is rotated the holes that 12 circulation symmetries are arranged on the bent shell structure, and its material parameter and bent thickness of the shell are identical with embodiment 1, its vertically, be z here to, the maximum height of forward is 0.2m, the maximum height of negative sense is 0.3m.

(a) Thin-wall Hyperbolic line with holes rotates bent shell structure four limit curved surfaces, and itself and rectangle mapping territory are set up mapping relations, can set up the parametric equation with the thin-walled semielliptical shell single cell structure of a hole:

$\left\{\begin{array}{c}x=a_1\sqrt{1+\frac{z^2\left(u\right)}{a_2^2}}\cos ({\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)\frac{\mathrm{\&xi;}}{{\mathrm{\&xi;}}_0})\\ y=a_1\sqrt{1+\frac{z^2\left(u\right)}{a_2^2}}\sin ({\mathrm{\&theta;}}_0+({\mathrm{\&theta;}}_1-{\mathrm{\&theta;}}_0)\frac{\mathrm{\&xi;}}{{\mathrm{\&xi;}}_0})\\ z={\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="HSA00000528950300011.png"\; state="\{\{state\}\}">H</figure-callout>}}_0+(H_1-H_0)\frac{\mathrm{\&eta;}}{{\mathrm{\&eta;}}_0}\end{array}\right.,0\&le;\mathrm{\&xi;}\&le;{\mathrm{\&xi;}}_0,0\&le;\mathrm{\&eta;}\&le;{\mathrm{\&eta;}}_0.---\left(1\right)$

Wherein, a ₁And a ₂Be respectively the size Control parameter that hyperbolic curve rotates bent shell.At this moment, ξ ₀And η ₀Two undetermined parameters for the parameter maps territory.

Thereby set up and curved surface corresponding parameter mapping territory Ω at the first quartile of ξ-η parameter plane.

Here provide a kind of method of setting up the parameter maps territory: for three limit curved surfaces, corresponding triangle parameter maps territory, a limit in triangle mapping territory are on the parameter coordinate axis, and a summit is initial point, and two summits are respectively (ξ in addition ₀, 0), (ξ ₁, η ₀).So, corresponding three undetermined parameter: ξ in plane parameter mapping territory of three limit curved surfaces ₀, ξ ₁And η ₀For four limit curved surfaces, corresponding rectangle parameter maps territory, its two limits are on the parameter coordinate axis, and a summit is initial point, and at this moment three summits in addition in parameter maps territory are respectively (ξ ₀, 0), (ξ ₀, η ₀), (0, η ₀).So, corresponding two undetermined parameter: the ξ in the parameter maps territory of four limit curved surfaces ₀And η ₀For complex-curved, it can be divided into the combination of a plurality of three limit curved surfaces and four limit curved surfaces, by operations such as translation, rotation, symmetries the parameter maps territory of a plurality of triangle parameter maps territory, a plurality of rectangle parameter maps territories or other shapes is made up again, form mapping relations with corresponding piecemeal curved surface.

(b) the length ratio coefficient lambda is made as 1, then rectangle parameter maps territory corresponding parameters ξ ₀, ξ ₁And η ₀Value can be approximately:

$\left\{\begin{array}{c}{\mathrm{\&xi;}}_0=\frac{\mathrm{\&pi;}}{6(N+1)}\underset{i=0}{\overset{N}{\mathrm{\&Sigma;}}}{R}_i\\ {\mathrm{\&eta;}}_0=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\sqrt{{(z_j-z_{j-1})}^2+{(R_i-R_{i-1})}^2}\end{array}\right.---\left(2\right)$

Wherein, N is a bigger integer, is used for discrete this to rotate the bus of bent shell, realizes approximate to its length, and N gets 100 here.Parameter z _iAnd R _iBe this axial and radial coordinate that rotates i the discrete point of bus of bent shell, satisfy:

$\left\{\begin{array}{c}{z}_i={\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="HSA00000528950300011.png"\; state="\{\{state\}\}">H</figure-callout>}}_0+\frac{(H_1-H_0)}{N}i\\ R_i=a_1\sqrt{1+\frac{z_i^2}{a_2^2}}\end{array}\right.i=\mathrm{0,1,2},...,N.---\left(3\right)$

(c) at this moment, choose the only relevant parameter a of parametric equation formula (1) of curved surface with curve form ₁And a ₂Rotate the curved design variable of bent shell as hyperbolic curve.

(d) adopting the method identical with embodiment 1 is the parametric equation of setting up hole, plane perimeter curve on ξ-η plane at the curved surface intrinsic coordinates, and the number of match mode and control vertex is identical with embodiment 1.

(e) in the parametric equation of hole, plane week curve, (s _j, t _j) be the reference mark coordinate of hole, plane perimeter curve, only relevant with hole week curve shape.Among this embodiment the hole heart is arranged on the center (ξ in parameter maps territory ₀/ 2, η ₀/ 2), as the local coordinate system initial point of definition hole shape design variable, hole shape is set to the while along the ξ axle of local coordinate system and the hole shape of η axle bi-directional symmetrical, and local coordinate system adopts cartesian coordinate system.The via hole heart is provided with 1 vertical control vertex along ξ axle forward, and this vertical control vertex in local coordinate system only its η to coordinate t ₁Can change, along the positive dirction parallel with the η axle 4 horizontal control vertexs are set, its η in local coordinate system is respectively 0.75t to coordinate ₁, 0.5t ₁, 0.25t ₁With 0, and these four horizontal control vertexs in local coordinate system only its ξ can change to coordinate.The η of vertical control vertex of preamble definition is to coordinate t under the local coordinate system ₁With the ξ of horizontal control vertex to coordinate s _j(j=2,3,4,5) are only relevant with hole week curve shape, are made as hole shape design variable b _k(k=1,2 ..., 5), and these five hole shape design variables satisfy:

$\left\{\begin{array}{c}0\&le;b_1=t_1\&le;\frac{{\mathrm{\&eta;}}_0}{2}\\ 0\&le;b_j=s_j\&le;\frac{{\mathrm{\&xi;}}_0}{2},j=\mathrm{2,3,4,5}.\end{array}\right.---\left(4\right)$

(f) with selected hole shape design variable b _k(k=1,2 ..., 5) carry out normalization process, obtain corresponding regular hole shape design variable α _k(k=1,2 ..., 5):

$\left\{\begin{array}{c}0\&le;{\mathrm{\&alpha;}}_1=\frac{{2b}_1}{{\mathrm{\&eta;}}_0}\&le;1\\ 0\&le;{\mathrm{\&alpha;}}_j=\frac{{2b}_j}{{\mathrm{\&xi;}}_0}\&le;1,j=\mathrm{2,3}.\end{array}\right.---\left(5\right)$

(g) like this, promptly comprise the curved design variable relevant in the parametric equation of spatial hole perimeter curve, comprise again and the relevant hole shape design variable of hole week curve shape with the space curved surface shape.

(h) directly divide finite element grid in the parameter maps territory, utilize plane curve-space curve again, dual mapping relations between plane domain-curved-surface structure, respectively discrete nodes on the perimeter curve of hole, plane and the discrete nodes in the parameter maps territory are mapped on the curved surface with holes, and according to the topological structure of discrete nodes in the parameter maps territory, adopt shell unit to generate the finite element grid that hyperbolic with holes is rotated bent shell single cell structure, and generate the finite element grid of total by the circulation symmetry operation.

(i) set material properties, fix an end of its axial coordinate minimum, and, set up its mechanical model at the negative uniform pulling force that axially applies 10kN in the end edge of its axial coordinate maximum.

(j) curved design variable a ₁And a ₂Initial value be made as 0.2m and 0.15m respectively, its variation range all is [0.05m, 0.4m], the bound of hole shape design variable is that iteration is upgraded with the variation of curved design variable, and the design variable that adopts in the actual optimization is curved design variable and regular hole shape design variable, regular hole shape design variable α _k(k=1,2 ..., 5) initial value be 0.25; Set up Thin-wall Hyperbolic with holes and rotate the Optimization Model of bent shell structure curve form and void shape optimal design problem, choosing hole week maximum equivalent minimum is optimization aim, and surface area is smaller or equal to 0.9701m ²As constraint function.

(k) adopting optimized Algorithm GCMMA based on gradient to be optimized design finds the solution.

Unit maximum equivalent, the surface area in this structure hole week are as shown in table 2 before and after optimizing.

Table 2

Claims (1)

1. the curve form of a Thin Walled Curved shell structure with holes and void shape cooperate optimization method for designing is characterized in that adopting following steps:

(a), in the Ω of parameter maps territory, set up the parametric equation of curved-surface structure mean camber with holes according to the features of shape of curved surface:

$\left\{\begin{array}{c}x=x(\mathrm{\&xi;},\mathrm{\&eta;})\\ y=y(\mathrm{\&xi;},\mathrm{\&eta;})\\ z=z(\mathrm{\&xi;},\mathrm{\&eta;})\end{array}\right.,\mathrm{\&xi;}\&GreaterEqual;0,\mathrm{\&eta;}\&GreaterEqual;0;(\mathrm{\&xi;},\mathrm{\&eta;})\&Element;\mathrm{\&Omega;}.---\left(1\right)$

Set up the method in parameter maps territory: for three limit curved surfaces, corresponding triangle parameter maps territory, a limit in triangle mapping territory are on the parameter coordinate axis, and a summit is initial point, and two summits are respectively (ξ in addition ₀, 0), (ξ ₁, η ₀); Corresponding three undetermined parameter: ξ in plane parameter mapping territory of three limit curved surfaces ₀, ξ ₁And η ₀For four limit curved surfaces, corresponding rectangle parameter maps territory, its two limits are on the parameter coordinate axis, and a summit is initial point, and at this moment three summits in addition in parameter maps territory are respectively (ξ ₀, 0), (ξ ₀, η ₀), (0, η ₀); Corresponding two undetermined parameter: the ξ in the parameter maps territory of four limit curved surfaces ₀And η ₀For complex-curved, it is divided into the combination of a plurality of three limit curved surfaces and four limit curved surfaces, by operations such as translation, rotation, symmetries the parameter maps territory of a plurality of triangle parameter maps territory, a plurality of rectangle parameter maps territories or other shapes is made up again, form mapping relations with corresponding piecemeal curved surface;

(b) determine the curved surface parameter according to the bent edge lengths of curved surface;

For three limit curved surfaces, set its three curved surface length of sides and be respectively L ₁, H ₁And H ₂, and corresponding with base, right edge and limit, left side in the triangle mapping territory respectively; Then the triangle parameter maps field parameter of three limit curved surfaces is determined by following formula:

$\left\{\begin{array}{c}{\mathrm{\&xi;}}_0=\mathrm{\&lambda;}{L}_1\\ {\mathrm{\&xi;}}_1=\frac{\mathrm{\&lambda;}{H}_2{L}_1}{H_1+H_2}\\ {\mathrm{\&eta;}}_0=0.5\mathrm{\&lambda;}(H_1+H_2)\end{array}\right.---\left(2\right)$

For four limit curved surfaces, suppose that its four curved surface length of sides are respectively L ₁, H ₁, L ₂And H ₂, and corresponding with base, right edge, top margin and limit, left side in the rectangle mapping territory respectively; Then the rectangle parameter maps field parameter of four limit curved surfaces is determined by following formula:

$\left\{\begin{array}{c}{\mathrm{\&xi;}}_0=0.5\mathrm{\&lambda;}(L_1+L_2)\\ {\mathrm{\&eta;}}_0=0.5\mathrm{\&lambda;}(H_1+H_2)\end{array}\right.---\left(3\right)$

In the formula, λ is the length ratio coefficient greater than 0;

(c) select only relevant with curve form parameter as the curved design variable in the parametric equation formula (1) of curved surface, the parametric equation that adopts approximating method to generate curved-surface structure is:

$\left\{\begin{array}{c}x=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i(\mathrm{\&xi;},\mathrm{\&eta;})\&CenterDot;x_i\\ y=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i(\mathrm{\&xi;},\mathrm{\&eta;})\&CenterDot;y_i\\ z=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i(\mathrm{\&xi;},\mathrm{\&eta;})\&CenterDot;z_i\end{array}\right.,(\mathrm{\&xi;},\mathrm{\&eta;})\&Element;\mathrm{\&Omega;}.---\left(4\right)$

In the formula, ξ and η are the parameter of curved surface, N _i(ξ η) is the match basis function of i control vertex, (x _i, y _i, z _i) be the spatial control point coordinate of curved surface;

(d) be the parametric equation of setting up hole, plane perimeter curve on ξ-η plane at the curved surface intrinsic coordinates:

$\left\{\begin{array}{c}\mathrm{\&xi;}=\mathrm{\&xi;}\left(u\right)\\ \mathrm{\&eta;}=\mathrm{\&eta;}\left(u\right)\end{array}\right.,0\&le;u\&le;1---\left(5\right)$

In the formula, u is the parameter of hole week curve;

(e) in the parametric equation of hole, plane week curve, select only relevant parameter as the hole shape design variable, adopt the parametric equation of hole, the plane perimeter curve of approximating method generation to be with hole week curve shape:

$\left\{\begin{array}{c}\mathrm{\&xi;}=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{B}_j\left(u\right)\&CenterDot;s_j\\ \mathrm{\&eta;}=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{B}_j\left(u\right)\&CenterDot;t_j\end{array}\right.,0\&le;u\&le;1---\left(6\right)$

In the formula, B _j(u) be the match basis function of j control vertex, (s _j, t _j) be the reference mark coordinate of hole, plane perimeter curve, b _kIt is the symbol of k hole shape design variable;

(f) with selected hole shape design variable b _kCarry out normalization process, obtain corresponding regular hole shape design variable α _k:

${\mathrm{\&alpha;}}_k=\frac{b_k-b_k^{\min }}{b_k^{\max }-b_k^{\min }}\&Element;\left[\mathrm{0,1}\right]---\left(7\right)$

In the formula, b _k ^MaxAnd b _k ^MinBe respectively k hole shape design variable b _kThe upper and lower bound that changes, α _kBe corresponding k regular hole shape design variable, the variation range of k is from 1 number to the hole shape design variable;

(g) like this, the parametric equation of spatial hole perimeter curve is:

$\left\{\begin{array}{c}x=x(\mathrm{\&xi;}\left(u\right),\mathrm{\&eta;}\left(u\right))\\ y=y(\mathrm{\&xi;}\left(u\right),\mathrm{\&eta;}\left(u\right))\\ z=z(\mathrm{\&xi;}\left(u\right),\mathrm{\&eta;}\left(u\right))\end{array}\right.,0\&le;u\&le;1---\left(8\right)$

Wherein promptly comprise the curved design variable relevant, comprise again and the relevant hole shape design variable of hole week curve shape with the space curved surface shape;

When space curved surface and hole, plane perimeter curve all are that the parametric equation of spatial hole perimeter curve is when adopting the match mode to generate:

$\left\{\begin{array}{c}x=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i(\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{B}_j\left(u\right)\&CenterDot;{\mathrm{\&xi;}}_j,\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{B}_j\left(u\right)\&CenterDot;{\mathrm{\&eta;}}_j)\&CenterDot;x_i\\ y=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i(\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{B}_j\left(u\right)\&CenterDot;{\mathrm{\&xi;}}_j,\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{B}_j\left(u\right)\&CenterDot;{\mathrm{\&eta;}}_j)\&CenterDot;y_i\\ z=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i(\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{B}_j\left(u\right)\&CenterDot;{\mathrm{\&xi;}}_j,\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{B}_j\left(u\right)\&CenterDot;{\mathrm{\&eta;}}_j)\&CenterDot;z_i\end{array}\right.,0\&le;u\&le;1.---\left(9\right)$

In the formula, spatial control summit (x _i, y _i, z _i) as the curved design variable of control curved surface shape, the control vertex (ξ on the parameter plane _j, η _j) as the hole shape design variable of control punch week curve shape;

(h) directly in the parameter maps territory, divide finite element grid, utilize plane curve-space curve again, dual mapping relations between plane domain-curved-surface structure, respectively discrete nodes on the perimeter curve of hole, plane and the discrete nodes in the parameter maps territory are mapped on the curved surface with holes, and, adopt shell unit to generate finite element grid on the curved surface with holes according to the topological structure of discrete nodes in the parameter maps territory;

(i) set material properties, and on the curved surface finite element model by applying boundary condition and load, set up the mechanical model of thin-wall curved-surface structure with holes;

(j) initial value and the variation range of setting curved design variable, the hole shape design variable is curved design variable and regular hole shape design variable, the initial value of selected regular hole shape design variable; Compages stress distribution, weight are set up the Optimization Model of thin-wall curved-surface structure curve form with holes and void shape cooperate optimization design problem, choose usually that hole week maximum equivalent is minimum to be optimization aim, and surface area is as constraint function;

(k) adopt and to be optimized design based on the optimized Algorithm of gradient or intelligent optimization algorithm and to find the solution.

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