CN104182598A - Constraint damping structure optimizing and designing method based on level set method - Google Patents

Abstract

The invention relates to a constraint damping structure optimizing and designing method based on a level set method, and belongs to the technical field of structure optimizing and designing. The constraint damping structure optimizing and designing method specifically comprises the steps that a constraint damping structure topological optimizing model and a finite element model are established; the initial configuration of a constraint damping structure is determined, modal analyzing is carried out on the initial configuration, the sensitivity of constraint damping cell units is calculated according to the sensitivity calculation formula, a level set is solved through an upwind method, the design variable is updated, a level set distance function is initialized again, and when the constraint condition is met, iteration is stopped, and a topological configuration is output. According to the method, under the condition that a certain amount of constraint damping material is added, the model loss factor of a constraint damping plate shell structure is maximized, and the best damping vibration reducing effect is acquired on the premise of finite added mass.

Description

Constrained damping structure Optimization Design based on level set method

Technical field

The invention belongs to Optimal Structure Designing field, relate to a kind of constrained damping structure Optimization Design based on level set method.

Background technology

Noise reduction technology is an important topic of engineering design field always.At present, common method is at vibrational structure surface adhesion one deck damping-constraining material.Because passive bound layer damping structure is easy to use, save space, without changing original design, and in very wide temperature and frequency range, there is good vibration damping inhibition.Therefore, be widely used in the fields such as Aeronautics and Astronautics and bullet train.

In traditional engineering application, restriction damping layer is covered in to total surface, in vibration and noise reducing, increased the additional mass of structure.Adopt Level Set Method to be optimized damping-constraining material layout, can effectively improve the utilization factor of damping-constraining material, and topology configuration is regular and interface is clear, utilizes practical engineering application.

Summary of the invention

In view of this, the object of the present invention is to provide a kind of constrained damping structure Optimization Design based on level set method, the method has solved under certain damping-constraining material usage condition, the layout optimization problem of damping-constraining material on plate and shell structure, damping-constraining plate and shell structure mode dissipation factor is maximized, effectively suppress the vibratory response of plate and shell structure, improved damping-constraining stock utilization.

For achieving the above object, the invention provides following technical scheme:

A constrained damping structure Optimization Design based on level set method, comprises the following steps: 1) determine initial configuration, set up its finite element model, initialization symbolic distance function; 2) set up Topological optimization model:

$\left\{\begin{array}{cc}\mathrm{Find}& X={\left\{\begin{array}{cccc}{P}_1& P_2& ...& P_n\end{array}\right\}}^T\\ \mathrm{Min}& f={-\mathrm{\η}}_k\\ s.t.& V=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{P}_i{v}_i\≤V^{*};P_i=0\mathrm{or}{P}_i=1\end{array}\right.$

Wherein: P _ifor design variable, its value is that { 0,1} works as P _i=0 o'clock, represent that damping-constraining born of the same parents unit i is blank cell, damping-constraining material is herein deleted; Work as P _i=1 o'clock, represent that damping-constraining born of the same parents unit i is solid element, be coated with damping-constraining material herein; η _kfor mode dissipation factor, v _ibe the volume of i unit, V ^*it is volume constraint; 3) finite element model is carried out to model analysis, extract the modal strain energy of each unit, adopt Calculation of Sensitivity formula, the sensitivity of calculating each damping-constraining born of the same parents unit; 4) utilize upwind method to solve level set equation, the evolution of implementation structure topology; 5) reinitialize symbolic distance function; 6) determine whether convergence, if the volume of damping-constraining material meets volume constraint, and the interpolation of twice iteration of objective function is less than set-point, be that f (x, k+1)-f (x, k)≤β restrains, if do not restrain, repeating step 3)-6) until convergence.

Further, in step 1) described in establishment damping-constraining born of the same parents unit, comprise the corresponding restraint layer of damping material unit and damping material unit.

The sensitivity formula of each damping-constraining born of the same parents unit of the calculating further, step 3) is:

$\frac{{\∂\mathrm{\η}}_i}{{\∂x}_e}={\mathrm{\η}}_v\frac{E_{\mathrm{sv}}^{\mathrm{ie}}{E}_s^i-(E_{\mathrm{sv}}^{\mathrm{ie}}+E_{\mathrm{sc}}^{\mathrm{ie}})E_{\mathrm{sv}}^i}{{\left(E_s^i\right)}^2}.$

Further, in step 4) in build level set equation and be:

$\frac{\∂\mathrm{\φ}}{\∂t}=n\left(x\right)|\▿\mathrm{\φ}\left(x\right)|$

Level set topological optimization is by solving level set equation, to carry out the evolution of implementation structure topology, and at this, the key that adopts level set method to be optimized is to find suitable normal velocity field n (x), and n (x) value is determined by sensitivity;

In order to meet volume constraint condition, the Lagrangian function of the corresponding optimization problem of Optimized model is:

$L=f+{\mathrm{\λ}}^k[V\left(x\right)-V^{*}]+\frac{1}{{2\mathrm{\Λ}}^k}{[V\left(x\right)-V^{*}]}^2$

In formula: ${\mathrm{\λ}}^{k+1}={\mathrm{\λ}}^k+\frac{1}{{\mathrm{\Λ}}^k}[V\left(x\right)-V^{*}],{\mathrm{\Λ}}^{k+1}={\mathrm{\α\Λ}}^k$

Adopt upwind method to solve level set equation, in solution procedure, time step should meet:

$\mathrm{\Δt}=\frac{h}{\max \left|n\left(x\right)\right|}$

Wherein, the size that h is unit, n (x) is normal velocity field.

Beneficial effect of the present invention is: the invention solves under certain damping-constraining material usage condition, the layout optimization problem of damping-constraining material on plate and shell structure, damping-constraining plate and shell structure mode dissipation factor is maximized, effectively suppress the vibratory response of plate and shell structure, improved damping-constraining stock utilization.The impact that the sensitivity of considering damping-constraining born of the same parents unit is changed by damping ratios, the Calculation of Sensitivity formula of the damping-constraining born of the same parents unit of having derived.Adopt upwind method to solve level set, obtained the regular and interface of damping-constraining material topology configuration clearly.

Accompanying drawing explanation

In order to make object of the present invention, technical scheme and beneficial effect clearer, the invention provides following accompanying drawing and describe:

Fig. 1 is the schematic flow sheet of the method for the invention.

Embodiment

Below in conjunction with accompanying drawing, the preferred embodiments of the present invention are described in detail.

Fig. 1 is the schematic flow sheet of the method for the invention, in the present embodiment:

The long 0.2m of constrained layer damping structure, wide 0.1m, groundwork thickness is 0.0008m, and viscoelastic layer thickness is 0.00005m, and restraint layer thickness is 0.00013m.Substrate elastic modulus is 700GPa, and Poisson ratio is 0.3, and density is 2800kg/m ³, the elastic modulus of viscoelastic material is 12Mpa, Poisson ratio 0.495, and density is 1200kg/m ³, dissipation factor is 0.5, and restraint layer elastic modulus is 70Gpa, and Poisson ratio is 0.3, and density is 2700kg/m ³.Take damping-constraining materials'use amount as 50% of all standing damping-constraining quality of materials be constraint condition, damping-constraining plate of material is carried out to topological optimization:

1) determine initial configuration, set up its finite element model, initialization symbolic distance function;

2) set up Topological optimization model:

$\left\{\begin{array}{cc}\mathrm{Find}& X={\left\{\begin{array}{cccc}{P}_1& P_2& ...& P_n\end{array}\right\}}^T\\ \mathrm{Min}& f={-\mathrm{\η}}_k\\ s.t.& V=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{P}_i{v}_i\≤V^{*};P_i=0\mathrm{or}{P}_i=1\end{array}\right.$

Wherein, P _ifor design variable, its value is that { 0,1} works as P _i=0 o'clock, represent that damping-constraining born of the same parents unit i is blank cell, damping-constraining material is herein deleted; Work as P _i=1 o'clock, represent that damping-constraining born of the same parents unit i is solid element, be coated with damping-constraining material herein; η _kfor mode dissipation factor, v _ibe the volume of i unit, V ^*be volume constraint, adopt in the present embodiment the damping-constraining material volume of all standing 50%.

3) finite element model is carried out to model analysis, extract the modal strain energy of each unit, adopt Calculation of Sensitivity formula, the sensitivity of calculating each damping-constraining born of the same parents unit;

4) utilize upwind method to solve level set equation, the evolution of implementation structure topology;

5) reinitialize symbolic distance function;

6) determine whether convergence, if the volume of damping-constraining material meets volume constraint, and the interpolation of twice iteration of objective function is less than set-point, and f (x, k+1)-f (x, k)≤β restrains, if do not restrain, repeats 3)-6) step is until convergence;

Described step 1) described in, create damping-constraining born of the same parents unit and comprise damping material unit and the corresponding restraint layer of damping material unit.

Described step 3) sensitivity formula that calculates each damping-constraining born of the same parents unit described in is:

$\frac{{\∂\mathrm{\η}}_i}{{\∂x}_e}={\mathrm{\η}}_v\frac{E_{\mathrm{sv}}^{\mathrm{ie}}{E}_s^i-(E_{\mathrm{sv}}^{\mathrm{ie}}+E_{\mathrm{sc}}^{\mathrm{ie}})E_{\mathrm{sv}}^i}{{\left(E_s^i\right)}^2}$

Described step 4) building level set equation is:

$\frac{\∂\mathrm{\φ}}{\∂t}=n\left(x\right)|\▿\mathrm{\φ}\left(x\right)|$

Level set topological optimization is by solving level set equation, to carry out the evolution of implementation structure topology.Therefore, the key that adopts level set method to be optimized is to find suitable normal velocity field n (x), and n (x) value is determined by sensitivity.

In order to meet volume constraint condition, the Lagrangian function of the corresponding optimization problem of Optimized model is:

$L=f+{\mathrm{\λ}}^k[V\left(x\right)-V^{*}]+\frac{1}{{2\mathrm{\Λ}}^k}{[V\left(x\right)-V^{*}]}^2$

In formula: ${\mathrm{\λ}}^{k+1}={\mathrm{\λ}}^k+\frac{1}{{\mathrm{\Λ}}^k}[V\left(x\right)-V^{*}],{\mathrm{\Λ}}^{k+1}={\mathrm{\α\Λ}}^k$

Adopt upwind method to solve level set equation, in solution procedure, time step should meet:

$\mathrm{\Δt}=\frac{h}{\max \left|n\left(x\right)\right|}$

Wherein, the size that h is unit, n (x) is normal velocity field.

Finally explanation is, above preferred embodiment is only unrestricted in order to technical scheme of the present invention to be described, although the present invention is described in detail by above preferred embodiment, but those skilled in the art are to be understood that, can to it, make various changes in the form and details, and not depart from the claims in the present invention book limited range.

Claims (4)

1. the constrained damping structure Optimization Design based on level set method, is characterized in that: comprise the following steps:

1) determine initial configuration, set up its finite element model, initialization symbolic distance function;

2) set up Topological optimization model:

$\left\{\begin{array}{cc}\mathrm{Find}& X={\left\{\begin{array}{cccc}{P}_1& P_2& ...& P_n\end{array}\right\}}^T\\ \mathrm{Min}& f=-{\mathrm{\η}}_k\\ s.t.& V=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{P}_i{v}_i\≤V^{*};P_i=0\mathrm{or}{P}_i=1\end{array}\right.$

Wherein: P _ifor design variable, its value is that { 0,1} works as P _i=0 o'clock, represent that damping-constraining born of the same parents unit i is blank cell, damping-constraining material is herein deleted; Work as P _i=1 o'clock, represent that damping-constraining born of the same parents unit i is solid element, be coated with damping-constraining material herein; η _kfor mode dissipation factor, v _ibe the volume of i unit, V ^*it is volume constraint;

3) finite element model is carried out to model analysis, extract the modal strain energy of each unit, adopt Calculation of Sensitivity formula, the sensitivity of calculating each damping-constraining born of the same parents unit;

4) utilize upwind method to solve level set equation, the evolution of implementation structure topology;

5) reinitialize symbolic distance function;

6) determine whether convergence, if the volume of damping-constraining material meets volume constraint, and the interpolation of twice iteration of objective function is less than set-point, be that f (x, k+1)-f (x, k)≤β restrains, if do not restrain, repeating step 3)-6) until convergence.

2. a kind of constrained damping structure Optimization Design based on level set method according to claim 1, is characterized in that: step 1) described in establishment damping-constraining born of the same parents unit, comprise the corresponding restraint layer of damping material unit and damping material unit.

3. a kind of constrained damping structure Optimization Design based on level set method according to claim 1, is characterized in that: step 3) described in the sensitivity formula of each damping-constraining born of the same parents unit of calculating be:

$\frac{{\∂\mathrm{\η}}_i}{{\∂x}_e}={\mathrm{\η}}_v\frac{E_{\mathrm{sv}}^{\mathrm{ie}}{E}_s^i-(E_{\mathrm{sv}}^{\mathrm{ie}}+E_{\mathrm{sc}}^{\mathrm{ie}})E_{\mathrm{sv}}^i}{{\left(E_s^i\right)}^2}.$

4. a kind of constrained damping structure Optimization Design based on level set method according to claim 1, is characterized in that: in step 4) in build level set equation and be:

$\frac{\∂\mathrm{\φ}}{\∂t}=n\left(x\right)|\▿\mathrm{\φ}\left(x\right)|$

Level set topological optimization is by solving level set equation, to carry out the evolution of implementation structure topology, and at this, the key that adopts level set method to be optimized is to find suitable normal velocity field n (x), and n (x) value is determined by sensitivity; In order to meet volume constraint condition, the Lagrangian function of the corresponding optimization problem of Optimized model is:

$L=f+{\mathrm{\λ}}^k\left[V\left(x\right){-V}^{*}\right]+\frac{1}{2{\mathrm{\Λ}}^k}{[V\left(x\right)-V^{*}]}^2$

In formula: ${\mathrm{\λ}}^{k+1}={\mathrm{\λ}}^k+\frac{1}{{\mathrm{\Λ}}^k}[V\left(x\right)-V^{*}],{\mathrm{\Λ}}^{k+1}=\mathrm{\α}{\mathrm{\Λ}}^k$

Adopt upwind method to solve level set equation, in solution procedure, time step should meet:

$\mathrm{\Δt}=\frac{h}{\max \left|n\left(x\right)\right|}$

Wherein, the size that h is unit, n (x) is normal velocity field.