CN105260567A - Three-dimensional box-type structure rib plate distribution bionic optimum design method - Google Patents

Abstract

The present invention relates to a kind of three-dimensional box-structure gusset distribution bionic optimum design method,Include the following steps: 1,First according to the outer dimension of design object,The geometrical model of design is established,2,According to the load boundary condition of design object,Select several elementary boundaries as " kind sub-line ",Movable gusset of the gusset being connected with " kind sub-line " as growth; Finite element analysis is carried out to total,And sensitivity analysis is designed to movable gusset; 3,Gusset growth: the mechanism grown up according to nature branching system,I.e. branch is always grown up along the direction for keeping whole system function optimal and speed; 4,Branching process; 5,Step 3 and 4 is repeated,Until the gusset total volume grown up reaches the scheduled total volume upper limit . The stiffened panel of three-dimensional box inside configuration is regarded as the branch grown up since one " kind sub-line " by this method, is made structure while growing up gusset, is intelligently tended to the structure with optimal mechanical performance.

Description

Three-dimensional box-structure gusset distribution bionic Optimization Design

Technical field

The present invention relates to a kind of box-structure method for designing, particularly a kind of Bionic Optimum Design method for three-dimensional box-structure gusset distribution.

Background technology

The such as engineering structure such as the lathe bed of large bridge structure, lathe, the crossbeam of crane, being generally all designed to internal placement has the body structure strengthening gusset, to meet the designing requirements such as structural strength, rigidity and stability.The load acting on local can be passed to other parts by gusset in box-structure effectively, thus increases the strength and stiffness of box-structure, makes box-structure have the advantage of high just high-strength light.The distribution of the inner gusset of box-structure is the principal element affecting structural mechanical property, therefore studies the rational deployment of the inner gusset of box-structure, the combination property optimum of structure is very important.

The inner gusset distribution design of box-structure in current engineering is generally the Empirical Design based on beam theory in the mechanics of materials.For the engineering structure under complex load condition, Experience Design cannot obtain preferably design proposal.In order to meet design requirement, usually adopt the method increasing gusset number and gusset thickness, make the architecture quality of design large, materials are many, processed complex.

Summary of the invention

The present invention proposes a kind of three-dimensional box-structure gusset distribution bionic Optimization Design, the method is based on the morphogenetic mechanism of nature branching system, the stiffened panel of three-dimensional box inside configuration is regarded as the branch of growing up from " seed line ", make structure while growth gusset, be tending towards the structure with optimum mechanical property intelligently.

Technical scheme of the present invention is: a kind of three-dimensional box-structure gusset distribution bionic Optimization Design, comprises the steps:

1. first according to the physical dimension of design object, set up the geometric model of design, this geometric model is made up of panel and inner packing material, wherein panel material is identical with design object, inner packing material is a kind of flexible material of hypothesis, and its elastic modulus is 1/1000 of panel material, adopts linear hexahedral element to carry out discrete to packing material region, form the gusset of single order shell unit as box structure by the node connecting hexahedral element, the original depth of gusset is T ₀, T ₀value very little, ignore it to the impact designed a model;

2., according to the load boundary condition of design object, select several elementary boundaries as " seed line ", the gusset be connected with " seed line " is as the movable gusset of growing up; Finite element analysis is carried out to total, and design sensitivity analysis is carried out to movable gusset;

3. gusset is grown up: the mechanism of growing up according to nature branching system, and namely branch is always grown up along the direction and speed that make whole system function optimum, and the thickness of gusset upgrades according to (1) formula:

$T_i^{n+1}=\left\{\begin{array}{cc}{T}_i^U& (T_i^n\&GreaterEqual;T_i^U)\\ \mathrm{\&alpha;}{\left(\frac{G_i}{{\mathrm{\&chi;A}}_i}\right)}^n+(1-\mathrm{\&alpha;})T_i^n& (T_i^L<T_i^n<T_i^U)\\ T_i^L& (T_i^n\&le;T_i^L)\end{array}\right.---\left(1\right)$

T in formula _i(i=1,2,3 ..., I) and be design variable, i.e. the thickness of i-th gusset.T _i ^land T _i ^ut _i. upper and lower bound, A _ibe the area of i-th gusset, α is step factor, G _icalculated by formula (2),

G _i＝－T _iS _i(2)

Wherein S _ibe the design sensitivity of i-th gusset, χ is Lagrange multiplier, calculates according to formula (3),

$\mathrm{\&chi;}=\frac{G_1}{v_1}=\frac{G_2}{v_2}=...\frac{G_n}{v_n}=\frac{\underset{i=1}{\overset{I}{\&Sigma;}}{G}_i}{\underset{i=1}{\overset{I}{\&Sigma;}}{v}_i}=\frac{\underset{i=1}{\overset{I}{\&Sigma;}}{G}_i}{{\mathrm{\&eta;v}}_0}---\left(3\right)$

In formula, η is volume fraction, and namely the gusset of final design accounts for the number percent of material; v ₀it is the volume of initial geometric model;

4. branching process: if the thickness after the renewal of a certain gusset is more than or equal to the difference critical value of setting, two limits of this gusset are considered to have the ability of difference, the all shell units be attached thereto all become newly-increased movable gusset, enter step 3 and carry out next step of growing up; And the thickness of working as a certain gusset reduces to the original depth T of gusset ₀time, this gusset is considered to degenerate, and all shell units be attached thereto can not continue to grow up;

5. repeatedly carry out step 3 and 4, until the gusset cumulative volume of having grown up reaches predetermined cumulative volume upper limit η v ₀.

The invention has the beneficial effects as follows: the method is based on the morphogenetic mechanism of nature branching system, the stiffened panel of three-dimensional box inside configuration is regarded as the branch of growing up from " seed line ", make structure while growth gusset, be tending towards the structure with optimum mechanical property intelligently.The structure rib plate layout that the box-structure gusset distribution bionic optimal design that the present invention proposes obtains is more clear, and thickness is roughly known, decreases last handling process.

Accompanying drawing explanation

Fig. 1 is design geometric model, and wherein (a) is the geometric model of inner packing material, and (b) is the linear hexahedral element in geometric model;

Fig. 2 is that the clamped box-structure in corner bears designing a model of Centralconcentrated load effect;

Fig. 3 is the initial geometric model forming design object;

Fig. 4 is gusset unit optimization result stereographic map of the present invention;

Fig. 5 is gusset unit optimization result vertical view of the present invention;

Fig. 6 is that in optimizing process, optimization aim structural strain can than the iteration course figure with optimization confined volume ratio;

Fig. 7 is that OptiStruct Optimization Software is optimized result.

Embodiment

A kind of three-dimensional box-structure gusset distribution bionic Optimization Design, comprises the steps:

1., first according to the physical dimension of design object, set up the geometric model of design.This geometric model is made up of panel and inner packing material, and wherein panel material is identical with design object, and inner packing material is a kind of flexible material of hypothesis, and its elastic modulus is 1/1000 of panel material.Adopt linear hexahedral element to carry out discrete to packing material region, form the gusset of single order shell unit as box structure by the node connecting hexahedral element, the thickness of initial gusset is very little, the negligible T of numerical value ₀.Design with geometric model as shown in Figure 1.

2. according to the load boundary condition of design object, select several elementary boundaries as " seed line ", the gusset be connected with " seed line " is the movable gusset that can grow up; Finite element analysis is carried out to total, and design sensitivity analysis is carried out to movable gusset.

3. gusset is grown up: the mechanism of growing up according to nature branching system, and namely branch is always grown up along the direction and speed that make whole system function optimum, and the thickness of gusset upgrades according to (1) formula.

$T_i^{n+1}=\left\{\begin{array}{cc}{T}_i^U& (T_i^n\&GreaterEqual;T_i^U)\\ \mathrm{\&alpha;}{\left(\frac{G_i}{{\mathrm{\&chi;A}}_i}\right)}^n+(1-\mathrm{\&alpha;})T_i^n& (T_i^L<T_i^n<T_i^U)\\ T_i^L& (T_i^n\&le;T_i^L)\end{array}\right.---\left(1\right)$

T in formula _i(i=1,2,3 ..., I) and be design variable, i.e. the thickness of i-th gusset.T _i ^land T _i ^ut _i. upper and lower bound, A _ibe the area of i-th gusset, α is step factor, G _icalculated by formula (2), wherein S _iit is the design sensitivity of i-th gusset.χ is Lagrange multiplier, can calculate according to formula (3).

G _i＝－T _iS _i(2)

$\mathrm{\&chi;}=\frac{G_1}{v_1}=\frac{G_2}{v_2}=...\frac{G_n}{v_n}=\frac{\underset{i=1}{\overset{I}{\&Sigma;}}{G}_i}{\underset{i=1}{\overset{I}{\&Sigma;}}{v}_i}=\frac{\underset{i=1}{\overset{I}{\&Sigma;}}{G}_i}{{\mathrm{\&eta;v}}_0}---\left(3\right)$

In formula, η is volume fraction, and namely the gusset of final design accounts for the number percent of material; v ₀it is the volume of initial geometric model.

4. branching process: if the thickness after the renewal of a certain gusset is more than or equal to the difference critical value of setting, two limits of this gusset are considered to have the ability of difference, the all shell units be attached thereto all become newly-increased movable gusset, enter step (3) and carry out next step of growing up; And the thickness of working as a certain gusset reduces to the original depth T of gusset ₀time, this gusset is considered to degenerate, and all shell units be attached thereto can not continue to grow up;

5. step 3 and 4 is carried out repeatedly, until the gusset cumulative volume of having grown up reaches predetermined cumulative volume upper limit η v ₀.

For the clamped box-structure in corner, applicability of the present invention is described.

As shown in Figure 2, model length is respectively L, W, H, and the ratio of model length, width and height is L:W:H=4:4:1.

The Bionic Optimum Design method of application box-structure gusset distribution, by discrete for model be 8 × 8 × 2 grids, connect solid element node and generate gusset unit, finally form the initial geometric model of design object as shown in Figure 3.

In order to obtain the body structure with maximum stiffness, structure optimization mathematical model is,

findT＝[T ₁,T ₂,...,T _n] ^T

minU(T)(4)

s.t.g(T)＝v－ηv ₀≤0

0<T ^L<T _i<T ^Ui＝1,2,...,n

In formula, U is structural strain energy.

According to support and the carrying situation of box-structure, select 5 " seed lines " as shown in Figure 3 on geometric model.Finite element analysis is carried out to structure, the design sensitivity of computational activity gusset.The state of judgement activity gusset unit, if meet degeneration requirement, then this gusset unit exits movable gusset group; If meet difference condition, then the gusset be connected with this gusset unit is placed in movable gusset array, participates in next round and grows up.When the gusset cumulative volume of having grown up reaches predetermined cumulative volume upper limit η v ₀, then exit circulation, otherwise continue to grow up.In this example, η gets 1.25.

Optimum results as Fig. 4, shown in 5.Fig. 6 is that in optimizing process, optimization aim structural strain can than the iteration course figure with optimization confined volume ratio, and the volume of structure is restrained along with the growth of iteration step, through 100 iteration, until reach volume upper limit and stop.Strain energy reduces gradually along with the growth of iteration step and tends to be steady, final strain energy U/U ₀=1.11 × 10 ^-2.

If Fig. 7 is that OptiStruct Optimization Software is optimized result, visible both to obtain rib plate layout consistent, be all the distribution form of cross bar, effectively can transfer loads to the strong point, and be the most effective Path of Force Transfer.But the structure rib plate layout that the box-structure gusset distribution bionic optimal design that the present invention proposes obtains is more clear, and thickness is roughly known, decreases last handling process, understand advantage of the present invention furtherly.

Claims (1)

1. a three-dimensional box-structure gusset distribution bionic Optimization Design, is characterized in that, comprise the steps:

(1) first according to the physical dimension of design object, set up the geometric model of design, this geometric model is made up of panel and inner packing material, wherein panel material is identical with design object, inner packing material is a kind of flexible material of hypothesis, and its elastic modulus is 1/1000 of panel material, adopts linear hexahedral element to carry out discrete to packing material region, form the gusset of single order shell unit as box structure by the node connecting hexahedral element, the original depth of gusset is T ₀, T ₀value very little, ignore it to the impact designed a model;

(2) according to the load boundary condition of design object, select several elementary boundaries as " seed line ", the gusset be connected with " seed line " is as the movable gusset of growing up; Finite element analysis is carried out to total, and design sensitivity analysis is carried out to movable gusset;

(3) gusset is grown up: the mechanism of growing up according to nature branching system, and namely branch is always grown up along the direction and speed that make whole system function optimum, and the thickness of gusset upgrades according to (1) formula:

$T_i^{n+1}=\left\{\begin{array}{cc}{T}_i^U& (T_i^n\&GreaterEqual;T_i^U)\\ \mathrm{\&alpha;}{\left(\frac{G_i}{{\mathrm{\&chi;A}}_i}\right)}^n+(1-\mathrm{\&alpha;})T_i^n& (T_i^L<T_i^n<T_i^U)\\ T_i^L& (T_i^n\&le;T_i^L)\end{array}\right.---\left(1\right)$

T in formula _i(i=1,2,3 ..., I) and be design variable, i.e. the thickness of i-th gusset. with t _i. upper and lower bound, A _ibe the area of i-th gusset, α is step factor, G _icalculated by formula (2),

G _i＝－T _iS _i(2)

Wherein S _ibe the design sensitivity of i-th gusset, χ is Lagrange multiplier, calculates according to formula (3),

$\mathrm{\&chi;}=\frac{G_1}{v_1}=\frac{G_2}{v_2}=...\frac{G_n}{v_n}=\frac{\underset{i=1}{\overset{I}{\&Sigma;}}{G}_i}{\underset{i=1}{\overset{I}{\&Sigma;}}{v}_i}=\frac{\underset{i=1}{\overset{I}{\&Sigma;}}{G}_i}{{\mathrm{\&eta;v}}_0}---\left(3\right)$

In formula, η is volume fraction, and namely the gusset of final design accounts for the number percent of material; v ₀it is the volume of initial geometric model;

(4) branching process: if the thickness after the renewal of a certain gusset is more than or equal to the difference critical value of setting, two limits of this gusset are considered to have the ability of difference, the all shell units be attached thereto all become newly-increased movable gusset, enter step (3) and carry out next step of growing up; And the thickness of working as a certain gusset reduces to the original depth T of gusset ₀time, this gusset is considered to degenerate, and all shell units be attached thereto can not continue to grow up;

(5) step (3) and (4) are repeatedly carried out, until the gusset cumulative volume of having grown up reaches predetermined cumulative volume upper limit η v ₀.