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

Abstract

The invention discloses a stress-constrained topological optimization method for wing spar structure, which is used to solve the technical problem of large nail-loaded tangential stress in the prior design method. The technical solution is to use three-dimensional solid elements to establish a nail-loaded model. In the optimization process, the stress is used as a constraint, and the tangential stress at the nail-loaded unit is constrained to be the minimum. The nail-loaded sensitivity is obtained by the adjoint method, and the material consumption is used as a constraint for stiffness optimization. The structural topology optimization is carried out to obtain the design results. This method can ensure the structural stiffness performance, and at the same time reasonably allocate the structural force transmission path to avoid stress concentration. It can be seen from the examples that when the constrained structural material volume ratio is 0.3, the structural compliance function without stress constraint is 0.0207J. When the structural compliance function remains unchanged after the nail-loaded stress constraint is applied, the maximum shear stress of the bolt From 17.9MPa to 11.3MPa, a reduction of 36.8%, reducing the tangential stress of the bolt unit.

Description

Topology optimization method of wing spar structure based on stress constraints

technical field

The invention relates to a topology optimization method for wing spar structure, in particular to a stress constraint-based topology optimization method for wing spar structure.

Background technique

Document 1 "Structure optimization design of wing spar based on ISIGHT/NASTRAN. Wang Xiangsheng et al. Aircraft Design. 2008.28(4): 23-27." proposed a set of ISIGHT/NASTRAN-based optimization design of wing spar structure method. In the case of meeting the strength requirements of the wing, the method takes the structural quality as the target in the structural optimization, and the web VONMISES stress, the axial stress of the flange and the stress of the flange beam element are constrained. The weight of the beam is effectively reduced through size optimization and shape optimization, and the strength requirements are met.

Document 2 "Comprehensive Optimal Design of Topology, Shape and Size of Large Aspect Ratio Flying Wing. Wang Wei, Yang Wei, Zhao Meiying. Mechanical Strength, 2008, 30(4):596-600." Two-level and three-level topology, shape and size optimization methods for structural layout problems. The first level is topology layer optimization, which uses topology optimization to obtain the approximate number and position of wing spars; the second level, shape and size optimization, based on the first level of optimization, uses shape optimization within a certain range Adjust the corrected spar position and optimize the size at the same time.

The design variable in Document 1 is the section parameters of beam elements, and the optimization types are size optimization and shape optimization. Design variables are limited by section parameters and types, and are applicable to situations where the structural configuration has been determined. The optimization effect is limited, and the purpose of optimizing the load distribution of rivets cannot be achieved by changing the structural force transmission path.

In the method disclosed in Document 2, the overall compliance is selected as the optimization goal in the first layer of topology optimization, and the material volume fraction is constrained. However, this method does not consider the influence of stress constraints on the structure in the topology optimization layer. The rigidity of the structure is improved, but stress concentration and the like will occur.

The factors involved in the design of aircraft components are complex, including stability, stiffness, strength, yield, etc. As aircraft maneuverability continues to improve, so does the wingspan, which causes greater loads on the wing roots. Due to the curvature of the airfoil and the different thicknesses of the airfoil, there are differences in the stiffness of each part of the wingspan. There is a large displacement difference between the two parts of the bolted connection during the bending of the spar. The lateral displacement difference causes a large shear stress on the screws at the wing root. When this happens, it is necessary to thicken the skin or replace stronger fasteners to ensure a strong structure, which will result in rigidity redundancy in the design.

Contents of the invention

In order to overcome the disadvantage of the existing design method that the nail-loaded tangential stress is large, the present invention provides a stress-constrained topology optimization method for wing spar structures. In this method, three-dimensional solid elements are used to establish the nail-loaded model. In the optimization process, the stress is used as a constraint, and the tangential stress at the nail-loaded unit is constrained to be the minimum. The nail-loaded sensitivity is obtained by the adjoint method, and the material consumption is used as a constraint for stiffness optimization. The structural topology optimization is carried out to obtain the design results. Introducing this method in the topology optimization design can ensure the structural stiffness performance in the initial design stage of the structure, and at the same time reasonably allocate the structural force transmission path to avoid stress concentration.

The technical scheme that the present invention solves its technical problem is: a kind of topological optimization method of wing spar structure based on stress constraint, it is characterized in comprising the following steps:

Step 1. Establish a topology optimization model, define the beam web as the design domain Ω of topology optimization and discretize Ω into n finite elements, define the optimization objective function as the minimum compliance function, and the constraint condition is that the volume ratio of the material used is less than The unit shear stress is less than

findX=(x ₁ , x ₂ , . . . , x _n )

$\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$

s.t.KU=F(1)

$\mathrm{<span\; class="notranslate">\; V</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}$

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; \&le;</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}$

0<x _i ≤1, i=1,...,n

where x _i is the pseudo-density corresponding to the element, v _i is the unit volume, U _i is the element displacement vector, K _i is the element stiffness matrix, F is the equivalent load vector of the node, U is the overall displacement vector of the node, and K is the structure The total stiffness matrix, C is the structural compliance function, and σ _s is the element shear stress.

Step 2, calculating the displacement response U of the structure by finite element analysis. Calculate the shear stress σ of the nail-loaded unit according to U. The adjoint vector λ ^T ={0,0,…,1,…,0,0,0} is introduced, each component of λ ^T is 0, and the component corresponding to the shear stress σ _s on the cross-section of the nail-loaded unit is 1. Shear stress on the cross-section of the nail-loaded unit:

σ _s = λ ^T σ (2)

Shear stress on the cross-section of a constrained nail-loaded element

Step 3: Calculate the sensitivity of the shear stress to the pseudo-density _xi of the elements in the design domain.

Step 4: Perform optimization according to the obtained sensitivity, and obtain the result through optimization iterations.

The beneficial effect of the invention is: the method adopts three-dimensional solid elements to establish a nail-loaded model. In the optimization process, the stress is used as a constraint, and the tangential stress at the nail-loaded unit is constrained to be the minimum. The nail-loaded sensitivity is obtained by the adjoint method, and the material consumption is used as a constraint for stiffness optimization. The structural topology optimization is carried out to obtain the design results. Introducing this method in the topology optimization design can ensure the structural stiffness performance in the initial design stage of the structure, and at the same time reasonably allocate the structural force transmission path to avoid stress concentration. It can be seen from the examples that when the volume ratio of the constrained structure material is also 0.3, the compliance function of the constrained structure without stress is 0.0207J. When the structural compliance function remains unchanged after the nail-loaded stress constraint is applied, the maximum shear stress of the bolt is reduced from 17.9MPa to 11.3MPa, which is a decrease of 36.8%, which greatly reduces the tangential stress of the bolt element.

The present invention will be described in detail below in combination with specific embodiments.

detailed description

The stress constraint-based topology optimization method of the wing spar structure of the present invention specifically includes the following steps.

The present invention is illustrated by taking the topological optimization design of a cantilever beam with a skin considering nail loading as an example. The thickness of the cantilever beam is 40mm, the length is 1000mm, and the height is 250mm. The cantilever beam is connected to the non-design domain beam by 7 bolts. The thickness of the non-design domain beam is 40mm, the length is 1000mm, and the height is 37.5mm. The length of the bolt is 10, and the section is a square of 20×20. Young's modulus E=2.63GP, Poisson's ratio μ=0.1. A concentrated load P=60N is applied to one end of the cantilever beam, and the direction is upward.

(a) Establish a topology optimization model, define the cantilever beam as the design domain Ω of topology optimization, and discretize Ω into 9600 3D unit entities, x _i is the pseudo-density corresponding to the unit, v _i is the unit volume, and U _i is the unit Displacement vector, K _i is the element stiffness matrix, F is the equivalent load vector of the node, U is the overall displacement vector of the node, K is the total stiffness matrix of the structure, and C is the structural compliance function. Define the stiffness optimization problem: the optimization goal is the minimum compliance function, the constraints are that the volume ratio of the material used is less than 0.3, and the unit shear stress is less than 12Mpa:

findX=(x ₁ , x ₂ , . . . x _n )

$\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$

s.t.KU=F

$\mathrm{<span\; class="notranslate">\; V</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 0.3</span>}$

σ _s ≤12Mpa

0<x _i ≤1, i=1,...,9600(1)

(b) The displacement response U of the structure is calculated by finite element analysis. Calculate the shear stress σ of the bolt element according to U. The adjoint vector λ ^T ={0,0,…,1,…,0,0,0} is introduced, each component of λ ^T is 0, and the component corresponding to the shear stress σ _s on the element cross section is 1. Shear stress on element cross-section:

σ _s = λ ^T σ (2)

The shear stress σ _s on the unit cross-section of the constraining bolts is ≤12MPa.

(c) Calculate the sensitivity of the shear stress to the pseudo-density _xi of the elements in the design domain.

(d) Introduce the stress constraint of the bolt element in the optimization process, optimize according to the sensitivity obtained above, and optimize iteratively to obtain the result.

The topology optimization method of wing spar structure using stress-constrained nail load can effectively reduce the nail load. With the stiffness as the target, the topology optimization with a constrained volume fraction of 0.3 converges after 47 iterations, and the maximum shear stress of the optimization result is 17.9Mpa. After constraining the shear stress of the bolt element, the iteration converges after 64 steps, and the maximum shear stress converges to 11.3Mpa. The parameter comparison of the optimization results is shown in Table 1.

Table 1

Comparing the optimization results, it can be seen that there are many cantilever beam truss structures that do not restrain the shear stress, and the stiffness is stronger. The difference between the rigidity and non-design stiffness is large, and it is easy to generate large tangential stress; the cantilever beam truss structure that constrains the shear stress is evenly distributed, which can play a good supporting role at the same time, and coordinate structural deformation while ensuring structural rigidity, avoiding 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.