THEORETICAL AND NUMERICAL ANALYSIS OF AN ALUMINUM FOAM SANDWICH STRUCTURE

: The aim of the research was to develop a new lightweight sandwich structure, which can be used for elements of air containers. The structure consists of aluminum foam core with fiber reinforced composite face-sheets. Nine different laminated glass or/and carbon fiber reinforced plastic face-sheet combinations were investigated. Finite element analysis of the sandwich structures was introduced. Single-objective optimization of the new sandwich structure was achieved for minimal weight. Five design constraints were considered: stiffness of the structure, face-sheet failure, core shear, face-sheet wrinkling, size constraints for design variables. The elaborated composite structure results significant weight savings due to low density.


Introduction
The purpose of the study is the design of a lightweight structure consists of fiber reinforced plastic face-sheets (nine different laminated glass fiber or/and carbon fiber reinforced plastic face-sheet combinations) and aluminum foam core. The fiber reinforced plastic face-sheets and the core has a small density and high specific stiffness, which can meet the stiffness requirements and reduce the weight of the sandwich structure. The elaborated structural model can be used for manufacturing of walls, floor and roof of containers to fulfill the requirements of shipping and airlines

A new sandwich structural model
The newly constructed sandwich structure consists of aluminum (Al) foam core with laminated glass fiber and/or carbon fiber reinforced plastic face-sheets, see Fig. 1. The dimensions and weights of the core and face-sheets used in this structure are given in Table I. The technical notes of the flexure model program for symmetrical sandwich structures were clarified. The norm of the model is MIL-STD-401B [14].  is the density of the E-glass fiber/epoxy resin laminate; is the density of the carbon fiber/epoxy resin laminate; is the density of the foam core; is the thickness of the face-sheet; is the thickness of the foam core and ℎ is the total thickness of the sandwich structure.
is the weight of the foam core; is the weight of the face-sheet; is the total weight of the sandwich structure.

Aluminum foam core
The foam core is closed cell formed from Al alloy. The mechanical properties of the core make it ideal for several applications. These properties include high strength and stiffness to weight ratio and high energy absorption as shown in Table II, [15].

Laminated fiber reinforced plastic face-sheets
Nine different sandwich constructions were studied, which consist of Al foam core with upper and lower skin face-sheets. The laminated glass fiber and/or carbon fiber reinforced plastic face-sheets were symmetrical concerning to the mid-plane of the sandwich structure. Every skin face-sheet composed of 4-layers. The fiber orientation in the face-sheets is having cross ply (0°, 90°) and angle ply ±45°. Table III includes the mechanical properties of the different composite layers.

Finite element analysis of the investigated sandwich structures
In this study, the deflection, skin stress and core shear stress were calculated numerically by using finite element analysis (Digimat-HC) program for 4-point flexural model, where is the applied load; is the deflection of sandwich structure; is the skin stress and is the core shear stress. Numerical results of the finite element analysis can be seen in (Table IV -Table VI); and in ( Fig. 2 -Fig. 4) of print screens of the finite element analysis results for all of nine constructions is not possible in this study due to space constraints.

Minimum weight optimization of the investigated sandwich structure
The optimization method for the newly constructed sandwich structure (Fig. 1) was elaborated. The fibers orientation in the face-sheets is having angles of cross ply 0°, 90° and angle ply ±45°. The optimal design variables were face-sheet thickness and core thickness to minimize the weight of the sandwich structures, Eqs. properties of the laminated face-sheet [18]. The constraints of the optimization problem are stiffness, face-sheet failure, core shear, face-sheet wrinkling.  The sandwich structure stiffness, the maximum load of face-sheet failure, core shear and skin wrinkling for every core thickness and face-sheet thickness were calculated.

Pollack Periodica 15, 2020, 3
With all these data, for every step, the minimum face-sheet thickness was calculated that accomplishes the load defined and the stiffness required, Eq. (4). The software calculates the minimum weight condition for the sandwich structure, which corresponds to the face-sheet thickness and the core thickness. This software is a modified version of the software in the composite sandwich optimizer 2017, GitHub, Inc [19]. The program was developed to fit with the flexure model. The results of numerical (Digimat-HC) program were used as inputs to achieve the desired results (maximum deformation "#$ and maximum load "#$ ).

Total weight objective functions
Weight of E-glass fiber/epoxy resin face-sheets with aluminum foam core: Weight of carbon fiber/epoxy resin face-sheets with aluminum foam core: Weight of hybrid face-sheets with aluminum foam core:

Design constraint
Constraint for the stiffness of the sandwich structure: The minimum stiffness of sandwich structure * +, " was calculated by using given data from and numerical results (Digimat-HC) ( and ).

Results of the optimization
The final results are optimum core thickness ( ! ), optimum face thickness ( ! ) and minimum weight ( " ) as shown in (Table IV -Table VI) and (Fig. 5 -Fig. 7). The optimization results of all 9 constructions are not possible in this study due to space constraints.

Numerical results in case of different types of laminated composite face-sheets
According to the numerical results of sandwich structures with aluminum foam core and different types of composite face-sheets, as shown in (Table IV -Table VI) and (Fig. 2 -Fig. 4), the deflection and core shear stress of the sandwich structures with carbon fiber/epoxy resin face-sheet are less than the deflection and core shear stress of the sandwich structures with hybrid and E-glass fiber/epoxy resin face-sheet respectively, because of the carbon fiber having higher stiffness-to-weight ratio compared to E-glass fiber. The skin stress of the sandwich structures with E-glass fiber/epoxy resin face-sheet is less than the skin stress of the sandwich structures with carbon fiber/epoxy resin and hybrid face-sheet respectively, because of the E-glass fiber having high strength-to-weight ratio and more flexible compared to carbon fiber.

Theoretical results in case of different types of laminated composite face-sheets
According to the theoretical results, as shown in (Table IV -Table VI) and (Fig. 5 -Fig. 7), the weight of the sandwich structures with carbon fiber/epoxy resin face-sheet is smaller than the weight of the sandwich structures with E-glass fiber/epoxy resin and hybrid of face-sheets.

Conclusions
The aim of the study was to develop a new sandwich structure, which can be used for manufacturing of walls, floor and roof of lightweight containers. The aim of the application of lightweight containers is to provide significant weight savings compared to conventional steel containers, which results in lower fuel consumption of transport vehicles and less environmental damage.
The new sandwich structure consists of aluminum foam core with upper and lower composite face-sheets. Nine different laminated glass fiber or/and carbon fiber reinforced plastic face-sheet combinations were investigated. In the study the finite element analysis of the investigated sandwich structures was introduced.
The optimization method was also elaborated for the new sandwich structure. The objective function was the total weight of the structure and five design constraints were taken into consideration, which were the following: total stiffness of the structure; facesheet failure; core shear; face-sheet wrinkling and size constraint for design variables.
Single-objective optimization of the new sandwich structural model was achieved for minimal weight. In the case study the optimal structure, which ensures the minimal weight of the sandwich structure is a carbon fiber/epoxy laminated face-sheet with 4 layers, with fiber orientation (+45°, -45°, +45°, -45°) and Al foam core, which thickness is 19.183 mm. This optimal Al foam sandwich structure provides 28.54% weight saving compared to the original structure.
It can be concluded based on the results of the research, that the application of the elaborated sandwich structure can be suggested in those applications where weight saving is the most important design aim.