CN103440378B - Wing spar structural topological optimization method based on stress constraint - Google Patents

Abstract

The invention discloses a kind of wing spar structural topological optimization method based on stress constraint, the technical problem big for solving existing method design nail load tangential stress. Technical scheme is to adopt 3D solid unit to set up nail load model. With stress for retraining in the process optimized, the tangential stress at constraint nail carrier unit place is minimum, tries to achieve nail load sensitivity by adjoint method, and with material usage together as the constraint of stiffness optimization, carries out structural Topology Optimization and obtain design result. The method ensure that rigidity of structure performance, simultaneously reasonable distribution structure Path of Force Transfer, it is to avoid stress is concentrated. By embodiment it can be seen that, when restraining structure material bodies proportion by subtraction is all 0.3, not applying stress constraint structure compliance function is 0.0207J, when after applying nail load stress constraint, structure compliance function is constant, bolt maximum shear stress is reduced to 11.3MPa by 17.9MPa, reduce 36.8%, reduce the tangential stress of bolt unit.

Description

Wing spar structural topological optimization method based on stress constraint

Technical field

The present invention relates to a kind of wing spar structural topological optimization method, particularly to a kind of wing spar structural topological optimization method based on stress constraint.

Background technology

Document 1 " Optimal Structure Designing based on the wing spar of ISIGHT/NASTRAN. Wang Xiangsheng etc. airplane design .2008.28 (4): 23-27. " in propose a set of wing spar Optimal Structure Designing optimization method based on ISIGHT/NASTRAN. The method is when meeting wing requirement of strength, and with architecture quality for target in structure optimization, web VONMISES stress, edge strip axial stress and edge strip beam element stress are constraint. Effectively reduced the weight of beam by dimensionally-optimised and Shape optimization, and meet requirement of strength.

Document 2 " high aspect-ratio flying wing structural topology, shape and dimension synthesis optimization design. Wang Wei; Yang Wei; Zhao Meiying. mechanical strength, 2008,30 (4): 596-600. " propose a kind of to can be used for the topology of wing structure location problem two level-three layer, combined shape and sizing optimization method. The first order is topological layer optimization, adopts topological optimization means to obtain substantially spar number and the position of wing structure; The second level, combined shape and sizing optimization, on the basis that the first order optimizes, use Shape optimization means to adjust correction spar position within the specific limits, carry out dimensionally-optimised simultaneously.

Document 1 design variable is beam element cross section parameter, and optimizing type is dimensionally-optimised and Shape optimization. Design variable is subject to the restriction of cross section parameter and type, it is adaptable to node configuration it has been determined that situation. Effect of optimization is limited, it is impossible to reach to optimize the purpose of rivet pin load distribution by change structure Path of Force Transfer.

Method disclosed in document 2 selects overall compliance to be optimization aim at ground floor topological optimization, constraint material volume fraction. But the method does not consider the stress constraint impact on structure at topological optimization layer. Improve structure rigidity, but there will be the situations such as stress concentration.

The factor related in aircraft components design is complicated, including stability, rigidity, intensity, surrender etc. Along with improving constantly of air maneuver performance, the span is also increasing, and this will cause that airfoil root bears bigger load. Due to aerofoil profile, with camber and profile thickness is different everywhere, there is difference in each position rigidity of the span. Bigger displacement difference is there is in the process of spar bending between bolted two parts. Horizontal displacement difference causes that wing wing root place screw produces bigger shearing stress. When this happens, it is necessary to thicken eyelid covering or the stronger securing member of replacing ensures that structure is strong, rigidity redundancy can be produced in design.

Summary of the invention

In order to overcome the deficiency that existing method design nail load tangential stress is big, the present invention provides a kind of wing spar structural topological optimization method based on stress constraint. The method adopts 3D solid unit to set up nail load model. With stress for retraining in the process optimized, the tangential stress at constraint nail carrier unit place is minimum, tries to achieve nail load sensitivity by adjoint method, and with material usage together as the constraint of stiffness optimization, carries out structural Topology Optimization and obtain design result. Topology optimization design introduces the method, it is possible to ensure rigidity of structure performance in the initial design stage of structure, simultaneously reasonable distribution structure Path of Force Transfer, it is to avoid stress is concentrated.

The technical solution adopted for the present invention to solve the technical problems is: a kind of wing spar structural topological optimization method based on stress constraint, is characterized in comprising the following steps:

Step one, building topology Optimized model, definition web be the design domain �� of topological optimization and by discrete for �� for n finite elements, defining optimization object function is that compliance function is minimum, constraints be materials'use volume fraction ratio less thanUnit shearing stress less than

FindX=(x₁, x₂..., x_n)

$\min C\left(X\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{U}_i^T{K}_i{U}_i$

S.t.KU=F(1)

$V\left(X\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{v}_i\≤\stackrel{\‾}{V}$

${\mathrm{\σ}}_s\≤\stackrel{\‾}{\mathrm{\σ}}$

0 < x_i�� 1, i=1 ..., n

In formula, x_iFor the pseudo-density that unit is corresponding, v_iFor unit volume, U_iFor element displacement vector, K_iFor element stiffness matrix, F is node equivalent load vectors, and U is node global displacement vector, and K is structure global stiffness matrix, and C is structure compliance function, ��_sFor unit shearing stress.

Step 2, finite element analysis computation structure dynamic respond U. The shearing stress �� of nail carrier unit is calculated according to U. Introduce adjoint vector ��^T=0,0 ..., 1 ..., 0,0,0}, ��^TEach component be 0, nail carrier unit cross section on shearing stress ��_sCorresponding component is 1. Shearing stress on nail carrier unit cross section:

��_s=��^T�� (2)

Shearing stress in the cell cross-section of constraint nail load

Step 3, calculating shearing stress are for the pseudo-density x of unit in design domain_iSensitivity.

The sensitivity that step 4, basis are tried to achieve is optimized, and Optimized Iterative obtains result.

The invention has the beneficial effects as follows: the method adopts 3D solid unit to set up nail load model. With stress for retraining in the process optimized, the tangential stress at constraint nail carrier unit place is minimum, tries to achieve nail load sensitivity by adjoint method, and with material usage together as the constraint of stiffness optimization, carries out structural Topology Optimization and obtain design result. Topology optimization design introduces the method, it is possible to ensure rigidity of structure performance in the initial design stage of structure, simultaneously reasonable distribution structure Path of Force Transfer, it is to avoid stress is concentrated. By embodiment it will be seen that when restraining structure material bodies proportion by subtraction is all 0.3, not applying stress constraint structure compliance function is 0.0207J.When after applying nail load stress constraint, structure compliance function is constant, bolt maximum shear stress is reduced to 11.3MPa by 17.9MPa, reduces 36.8%, significantly reduces the tangential stress of bolt unit.

Below in conjunction with detailed description of the invention, the present invention is elaborated.

Detailed description of the invention

The present invention specifically includes following steps based on the wing spar structural topological optimization method of stress constraint.

To consider that with the cantilever beam of eyelid covering the topology optimization design of nail load illustrates the present invention. Cantilever beam thickness is 40mm, length 1000mm, height 250mm. Cantilever beam is connected with non-design domain beam by 7 bolts. Non-design domain cantilever thickness 40mm, length 1000mm, height 37.5mm. Bolt length 10, cross section is the square of 20 �� 20. Young's modulus E=2.63GP, Poisson's ratio ��=0.1. Cantilever beam one end applies concentrfated load P=60N, upwardly directed.

(a) building topology Optimized model, definition cantilever beam be the design domain �� of topological optimization, and by discrete for �� be 9600 3 dimension element entities, x_iFor the pseudo-density that unit is corresponding, v_iFor unit volume, U_iFor element displacement vector, K_iFor element stiffness matrix, F is node equivalent load vectors, and U is node global displacement vector, and K is structure global stiffness matrix, and C is structure compliance function. Definition stiffness optimization problem: optimization aim is that compliance function is minimum, and constraints is that materials'use volume fraction ratio is little by 0.3, and unit shearing stress is less than 12Mpa:

FindX=(x₁, x₂... x_n)

$\min C\left(X\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{U}_i^T{K}_i{U}_i$

S.t.KU=F

$V\left(X\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{v}_i\&le;0.3$

��_s��12Mpa

0 < x_i�� 1, i=1 ..., 9600 (1)

The dynamic respond U of (b) finite element analysis computation structure. The shearing stress �� of bolt unit is calculated according to U. Introduce adjoint vector ��^T=0,0 ..., 1 ..., 0,0,0}, ��^TEach component be 0, the shearing stress �� in cell cross-section_sCorresponding component is 1. Shearing stress in cell cross-section:

��_s=��^T�� (2)

Shearing stress �� in the cell cross-section of constraint bolt_s��12MPa��

C () calculates shearing stress for the pseudo-density x of unit in design domain_iSensitivity.

D () introduces the stress constraint of bolt unit in optimization process, be optimized according to the above-mentioned sensitivity tried to achieve, and Optimized Iterative obtains result.

The wing spar structural topological optimization method adopting stress constraint nail load can effectively reduce nail load. With rigidity for target, confined volume mark be the topological optimization of 0.3 through 47 step iteration convergences, the maximum shear stress of optimum results is 17.9Mpa. After constraining the shearing stress of bolt unit, iteration restrains through 64 steps, and maximum shear stress converges on 11.3Mpa. Optimum results parameter comparison is in Table 1.

Table 1

Contrast optimum results is it can be seen that the cantilever beam truss structure not retraining shearing stress is many, and rigidity is stronger. Poor with non-design rigidity bigger, it is easy to produce bigger tangential stress; The cantilever beam truss structure of constraint shearing stress is uniformly distributed, and can simultaneously work as good supporting role, and ensure coordination structure deformation while the rigidity of structure, it is to avoid stress concentration.

Claims (1)

1. the wing spar structural topological optimization method based on stress constraint, it is characterised in that comprise the following steps:

Step one, building topology Optimized model, definition web be the design domain �� of topological optimization and by discrete for �� for n finite elements, defining optimization object function is that compliance function is minimum, constraints be materials'use volume fraction ratio less than, unit shearing stress less than:

In formula, x_iFor the pseudo-density that unit is corresponding, the vector that X is made up of unit puppet density, v_iFor unit volume, U_iFor element displacement vector, K_iFor element stiffness matrix, F is node equivalent load vectors, and U is node global displacement vector, and K is structure global stiffness matrix, and C is structure compliance function, ��_sFor unit shearing stress;

Step 2, finite element analysis computation structure node global displacement vector U; The shearing stress �� of bolt unit is calculated according to U; Introduce adjoint vector ��^T=0,0 ..., 1 ..., 0,0,0}, ��^TEach component be 0, nail carrier unit cross section on unit shearing stress ��_sCorresponding component is 1; Unit shearing stress on nail carrier unit cross section:

��_s=��^T��(2)

Unit shearing stress in the cell cross-section of constraint nail load

Step 3, calculating shearing stress are for the pseudo-density x of unit in design domain_iSensitivity;

The sensitivity that step 4, basis are tried to achieve is optimized, and Optimized Iterative obtains result.