AlLi alloy and aluminum honeycomb panel (AHP) are both excellent materials for aeronautical structures. In this paper, a platetype aeronautical structure (PAS), which is a base mounting structure for 172 kg functional devices, is selected for comparative analysis with different materials. To compare systemlevel performance under multidisciplinary constraints, mathematical models for optimization are established and then structural optimization is carried out using Altair OptiStruct. For AHP, its honeycomb core is regarded as orthotropic material and its mechanical properties are calculated by Allen’s model in order to establish finite element model (FEM). The heights of facing sheet and honeycomb core are selected as design variables for size optimization. For AlLi alloy plate, topology optimization is carried out to obtain its most efficient load path; and then a reconstruction process is executed for practical manufacturing consideration; to obtain its final configuration, accurate size optimization is also used for reconstructed model of AlLi alloy plate. Finally, the optimized mass and performance of two PASs are compared. Results show that AHP is slightly superior to AlLi alloy.
With the development of aerospace technology, the demand of highstrengthlowdensity materials is becoming more and more urgent. Severe mechanical environment and aerodynamic coupling are inevitable because of high launch acceleration and high frequency vibration, so the requirements for strength and stiffness of aeronautical structures are extremely high. Moreover, launch costs have strong restrictions on the overall mass of spacecraft, so the mass of aeronautical structures must be minimized as far as possible. Severe contradiction between strength and mass spurs extensive utilization of advanced alloy material and composite material in aerospace applications, such as aluminum lithium (AlLi) alloys [
Since highstrength alloy material and honeycomb panels are both excellent options for aeronautical structures, it is necessary to conduct a comparative analysis under same boundary conditions and load case. Currently, most researches concentrate on the performance of separate material [
In structural optimization, design variables can be categorized into three groups as topology, shape, and sizing variables. Topological design variables determine an initial structural layout whereas shape and sizing parameters give the shape and dimensions of structures, respectively [
Three levels of structural optimization.
In the current paper, a PAS, which is a base mounting structure for 13 different functional devices, is selected for comparative analysis. Highstrength AlLi alloy and aluminum honeycomb panel are both ideal material for simple PAS, so it is very important for structure designers to determine which material is more superior. The commercial finite element package HyperMesh and OptiStruct 8.0 [
Figure
Performance constraints of the subsystem and its PAS.
Performance  Input loads  Requirement 

Strength and stiffness 

Safety factor is not lower than 1.5 


Resonance frequency  No external input load  Fundamental frequency is not less than 115 Hz 


Harmonic response 

Maximum acceleration of function devices is not more than 22 


Mass  All external input loads  Not more than 30% of total mass of function devices 
Typical PAS and layout of function devices installed on PAS.
Front
Back
Because the frequency range of harmonic response is 0 Hz~100 Hz, mechanical resonance will not happen as the fundamental frequency of subsystem is not less than 115 Hz. Therefore, harmonic response constraints need not be considered in the procedure of structural optimization and performance verifications should be carried out after optimized analysis. Lightweight design is one of the most important tasks of structure design for aerospace applications, so the mass of PAS should be selected as optimization objective and structural stress, deformation, and the first order modal as design constraints.
AHP and AlLi alloy are very different aeronautical materials. AHP is a kind of typical structured material and its configuration is almost determinate, so only size optimization is needed to obtain its optimized structure. Different optimization methods for AHP and AlLi alloy are shown in Figure
Different optimization methods for AHP and AlLi alloy.
Honeycomb panel, which is shown in Figure
Typical structure of hexagonal honeycomb panel and its dimensions.
As shown in Figure
The mechanical properties of 2A12T4 and 2024.
Material grade  Density [kg/m^{−3}]  Young's modulus [MPa]  Shear modulus [MPa]  Poisson’s ratio  Yield strength [MPa] 

2A12T4  2780  70600  28000  0.33  280 
2024  2700  73000  28000  0.44  75.8 
In order to establish finite element model of honeycomb panels, honeycomb core can be equivalent to orthotropic material and its mechanical properties be calculated by Allen’s model [
Equivalent mechanical parameters of 1/820240.003.







11.3  11.3  1.7  370.2  246.6  0.33 
A finite element model of this subsystem is established using Altair OptiStruct. Honeycomb panel is meshed in HyperMesh using fournoded linear quad elements (CQUAD4) and composite properties are applied, where the core is orthotropic material and the sheets are isotropic material. All function devices are simplified by shell element and their mass is equivalent to the thickness of shells. Bolt connections are simplified as multipoint constraints and modeled by the flexible unit (RBE3). Two length of honeycomb panel are fixed in all six degrees of freedom. The finite element model is shown in Figure
Finite element model of subsystem with honeycomb panel.
For structure optimization, performance constraints shown in Table
Lower and upper limit values of design variables.
Design variable  Initial dimension [mm]  Lower limit value [mm]  Upper limit value [mm] 


2  0.15  5 

36  10  100 
The performance of frame structure largely depends on the properties of material. In this paper, AlLi alloy 2090 is selected for comparative analysis with honeycomb panel while all boundary conditions, input loads, and layout of function devices are identical. 2090 is a kind of high performance material and its elastic modulus increased by about 10% while the density decreased by about 10% compared with the conventional aluminum alloy. So its stiffnesstoweight ratio and strengthtoweight ratio are improved remarkably. The mechanical parameters of 2090 versus conventional aluminum alloy 2Al12 are shown in Table
Mechanical parameters of 2090 versus 2Al12.
Material grade  Density 
Young’s modulus 
Yield strength 



2090  2590  78600  530  0.2  30.3 
2Al12  2780  70600  280  0.1  25.4 
For a planeframe structure of pure AlLi alloys, topology optimization is firstly used for a conceptual design proposal and then finetuned for manufacturability. Initial thickness of the planeframe structure is a critical factor for topology optimization and the value of initial thickness directly determined the optimization result. Therefore, four values of initial thickness (40 mm, 50 mm, 60 mm, and 70 mm) are used, respectively, and the best thickness is determined by comparing the optimum results. At last, size optimization is executed to obtain a desired thickness of planeframe structure. Similarly with honeycomb panel, AlLi alloys plate is meshed with fournoded linear quad elements (CQUAD4) and the function devices are meshed in the same way. The finite element model is shown in Figure
Finite element model for AlLi alloys structure of PAS.
Finite element model
Designable and nondesignable portions
In the process of topology optimization of AlLi alloys plate, the initial thickness is defined and the design variable is element density of meshed plate
After topology optimization, size optimization should be carried out to obtain a further optimized thickness of AlLi alloys plate, so the thickness is selected as design variable and its initial value would be the selected result of topology optimization. The mathematical model of size optimization is shown in
After seven times of iteration, the results of structure optimization are obtained and shown in Figure
Maximum von Mises stress and deformation under input loads.
Input loads  Maximum von Mises stress [MPa]  Maximum deformation [mm] 


1.822  0.086 

1.795  0.05237 

1.25  0.1926 
Iterative process curve of honeycomb panel optimization.
Iterations of core’s height
Iterations of facing sheet’s height
Iterations of subsystem’s mass
Modal analysis is carried out after structure optimization, and first two order modes of subsystem are shown in Figure
Natural frequencies of first eight order modes.
Mode order  1  2  3  4  5  6  7  8 

Natural frequency [Hz]  114.8  137  164.7  169.6  186.9  216.5  234.4  238.9 
First and second order mode of subsystem.
First order mode
Second order mode
The topology optimization result using material distribution method is a density distribution of the finite elements in the design domain [
Density contours of AlLi alloy structure with different thickness.
40 mm
50 mm
60 mm
70 mm
The iterative process curves of AlLi alloy structure of different thickness are shown in Figure
Iterative process curve of AlLi alloy plate with different thickness.
The topology optimization modal versus reconstructed model of AlLi alloy plate.
Size optimization of reconstructed model is carried out based on the mathematical model presented in Section
Maximum von Mises stress and deformation under input loads.
Input loads  Maximum von Mises stress [MPa]  Maximum deformation [mm] 


11.3  0.07868 

16.48  0.05293 

17.24  0.1687 
Stress nephogram of subsystem in the
Modal analysis is carried out after size optimization, and first two order modes of subsystem are with AlLi alloy plate shown in Figure
Natural frequencies of first eight order modes.
Mode order  1  2  3  4  5  6  7  8 

Natural frequency [Hz]  115.3  190  215.2  251  186.9  279.6  294.3  317 
First and second order mode of subsystem with AlLi alloy plate.
First order mode
Second order mode
After structural optimization, the optimized performance of two materials is obtained and shown in Table
Comparative analysis of optimization results of two materials.
Performance  Requirements  Optimization results of AHP  Optimization results of AlLi alloy 

Maximum stress  ≤187 MPa  1.82 MPa ( 
17.24 MPa ( 
Maximum deformation  ≤0.3 mm  0.19 mm ( 
0.17 mm ( 
Fundamental frequency  ≥115 Hz  114.8 Hz  115.3 Hz 
Harmonic response  ≤22 
18.5 
19.6 
Mass  Minimized mass  42.72 kg  48.39 kg 
In order to compare the performance of AlLi alloy and honeycomb panel which are both excellent materials for aeronautical structures, the mathematical models of structural optimization are established for these two distinctively different materials. Altair OptiStruct is used to carry out the optimized analysis. Honeycomb panel is seen as an integral structure and only size optimization is used to obtain its optimized heights. Topology and size optimization are applied to obtain the optimized configuration and thickness of the AlLi alloy plate. The mass of optimized AHP including bolt sockets is 42.72 kg and that of AlLi alloy plate is 48.39 kg, so AHP is superior to AlLi alloy for weight reduction consideration. The optimization procedure shows that structural optimization is an excellent method for material selection in the conceptual design phase.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors would like to express their appreciation to National Natural Science Foundation of China (Grants nos. 51175505 and 51305455) for providing the financial support to this work.