1. Introduction

### 1.1. Background

In recent years the commercial aircraft industry is increasing their reliance on composite materials to produce lighter and more durable aircrafts. Figure 1 shows a Boeing 787 aircraft contains 50% by weight of its materials as composites, which is about 32,000 kg of carbonfiber-reinforced polymer (CFRP) [1].

The carbon fiber composites have a higher strength-to-weight ratio than traditional metal materials thus help making the aircraft lighter and to exceed the fuel efficiency target. Due to this important feature, the use of fiber reinforced composite laminates as primary structural components in these important large-scale and weight-critical applications has increased considerably (Table 1). Aircrafts with major composite parts including fuselage, wings, tail sections, doors and interior are presently being developed and gradually brought into service.

For better efficiency in terms of strength and weight-optimization, aerospace structures are frequently appended with stiffener components. Figure 2 shows a 787's disassembled composite fuselage section which is composed of hat-stiffened composite panels that represent the design methodology of meeting the high stiffness while keeping the minimal weight requirements. This laminated composite stiffened panel is a critical component and extensively used structure in aircrafts, and can operate when subjected to harsh environments such as severe dynamic loading.

Many work have been done on design and analysis of hat-stiffener structures. Recent advances in performing global and detailed analyses have made it possible to determine failure modes, strength, durability, and damage tolerance of composite structures with confidence. Bhar et al. [2] performed linearly elastic static and natural vibration analysis using an extended HSDT (higher-order shear deformation theory). Kim et al. [3] manufactured stiffened panels using cocuring, co-bonding and secondary bonding processes and evaluated them using 3D measurement and ultrasonic tester. Lauterbach et al. [4] built analysis tools including an approach for predicting interlaminar damage initiation and degradation models for capturing interlaminar damage growth as well as in plane damage mechanisms. Gangadhara et al. [5] analyzed stiffened panels using formulation based on the concept of equal displacements at the shellstiffener interface. Kumar et al. studied the transient response of laminated stiffened plates using MSC/Patran and LS-DYNA3D [6] and Kristinsdottir et al. [7] presented an optimization formulation for the design of large panels when loads vary over the panel. Junhou et al. and Shenoi et al. [8, 9] examined the key aspects defining the performance characteristics of hatstiffener joints in marine structures. Paul et al. [10] performed an integrated step-by-step design and analysis procedure for the hat-stiffened panels loaded in axial compression using the computer code BUSTCOP. Xiong and coworkers [11] has tested and analyzed the buckling and failure loads of hat-stiffened composite panels. Other research work have been focused on FEA modeling [12–22], manufacturing [23–29], evaluation of microstructures and damage evolution [30–33], and the enhancement of the mechanical properties [34–37] of composites at

Year 1982 1995 2006 2008 Model Boeing 767 Boeing 777 Airbus 380 Boeing 787

Structures Secondary Primary/Secondary Primary/Secondary Primary/Secondary Amount of CFRP/aircraft 1.5 tons Approx. 10 tons Approx. 35 tons Approx. 35 tons Amount of CF/aircraft 1 ton Approx. 7 tons Approx. 23 tons Approx. 23 tons.

Design Optimization and Higher Order FEA of Hat-Stiffened Aerospace Composite Structures

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Figure 2. Disassembled composite fuselage section of the Boeing 787.

Table 1. Increase of carbon fiber composites for aircraft application.

Most commercial CAD/FEA software has included some form of parameterization of design variables. Basic research-level higher order structural elements are also developed. These tools

both materials- and structures-level.

Figure 1. Boeing 787 aircraft contains 50% of composite materials.

Design Optimization and Higher Order FEA of Hat-Stiffened Aerospace Composite Structures http://dx.doi.org/10.5772/intechopen.79488 57


Table 1. Increase of carbon fiber composites for aircraft application.

way to design future complex composites structures, e.g. hat stiffened composites panels,

In recent years the commercial aircraft industry is increasing their reliance on composite materials to produce lighter and more durable aircrafts. Figure 1 shows a Boeing 787 aircraft contains 50% by weight of its materials as composites, which is about 32,000 kg of carbon-

The carbon fiber composites have a higher strength-to-weight ratio than traditional metal materials thus help making the aircraft lighter and to exceed the fuel efficiency target. Due to this important feature, the use of fiber reinforced composite laminates as primary structural components in these important large-scale and weight-critical applications has increased considerably (Table 1). Aircrafts with major composite parts including fuselage, wings, tail sections, doors and interior are presently being developed and gradually brought into service.

For better efficiency in terms of strength and weight-optimization, aerospace structures are frequently appended with stiffener components. Figure 2 shows a 787's disassembled composite fuselage section which is composed of hat-stiffened composite panels that represent the design methodology of meeting the high stiffness while keeping the minimal weight requirements. This laminated composite stiffened panel is a critical component and extensively used structure in aircrafts, and can operate when subjected to harsh environments such as severe

Keywords: design optimization, FEA, hat stiffeners, aerospace composite structures

with reliable and predictable quality and material weight/cost.

1. Introduction

56 Optimum Composite Structures

1.1. Background

dynamic loading.

fiber-reinforced polymer (CFRP) [1].

Figure 1. Boeing 787 aircraft contains 50% of composite materials.

Figure 2. Disassembled composite fuselage section of the Boeing 787.

Many work have been done on design and analysis of hat-stiffener structures. Recent advances in performing global and detailed analyses have made it possible to determine failure modes, strength, durability, and damage tolerance of composite structures with confidence. Bhar et al. [2] performed linearly elastic static and natural vibration analysis using an extended HSDT (higher-order shear deformation theory). Kim et al. [3] manufactured stiffened panels using cocuring, co-bonding and secondary bonding processes and evaluated them using 3D measurement and ultrasonic tester. Lauterbach et al. [4] built analysis tools including an approach for predicting interlaminar damage initiation and degradation models for capturing interlaminar damage growth as well as in plane damage mechanisms. Gangadhara et al. [5] analyzed stiffened panels using formulation based on the concept of equal displacements at the shellstiffener interface. Kumar et al. studied the transient response of laminated stiffened plates using MSC/Patran and LS-DYNA3D [6] and Kristinsdottir et al. [7] presented an optimization formulation for the design of large panels when loads vary over the panel. Junhou et al. and Shenoi et al. [8, 9] examined the key aspects defining the performance characteristics of hatstiffener joints in marine structures. Paul et al. [10] performed an integrated step-by-step design and analysis procedure for the hat-stiffened panels loaded in axial compression using the computer code BUSTCOP. Xiong and coworkers [11] has tested and analyzed the buckling and failure loads of hat-stiffened composite panels. Other research work have been focused on FEA modeling [12–22], manufacturing [23–29], evaluation of microstructures and damage evolution [30–33], and the enhancement of the mechanical properties [34–37] of composites at both materials- and structures-level.

Most commercial CAD/FEA software has included some form of parameterization of design variables. Basic research-level higher order structural elements are also developed. These tools allow quick, easy and accurate topology and geometry model creation with design constraints, implicit parameterization for easy model variation, integrated Finite Element generator, models and components storage in library for generation of knowledge database and reusability, shape and size optimization in a closed batch loop, on-the-fly definition of design variables and design space, and integration of specific applications like commercial optimization and design tools. In this work, we plan to utilize these aspects to create a Higher Order Abstract Structural Elements, later abbreviated as HOASE.

#### 1.2. Objectives and structure

The goals and key feature of this work include analyzing the geometric parameter sensitivity of the hat stiffener, and developing and demonstrating a proof-of-concept theoretical model which is a parametric analytical solution that is theoretically equivalent to hat-stiffener stiffened panels in mechanical response. The analytical solution contains parametric information incorporating geometric, design allowables, and manufacturing information such as laminate stacking order. The constructions of these equivalent analytical models will be stored in a database from which they can be easily retrieved and parametrically modified.

FEM was utilized to produce sensitivity of structural behavior (deflection, stresses) to basic elements' parameters and for comparing final experimental results with modeling. Laminated plate, hat-stiffener, hat-stiffener bonded to base plate were modeled in MSC NASTRAN for this purpose. Laminated plate modeling in FEM is routine and therefore not discussed for the sake of brevity. The hat stiffener (with and without plate to which it is bonded) are modeled as follows. Height of the stiffener web (h), width of the stiffener cap (W1), bottom width in between stiffener flanges (W2), width of the stiffener flange (due to symmetric, the left and right width are the both L1) are the geometric parameters considered in addition to thickness of a ply, ply orientation and the stacking sequence. The length of the hat stiffener is fixed at

Design Optimization and Higher Order FEA of Hat-Stiffened Aerospace Composite Structures

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Material properties are taken from Cytec information sheet CYCOM 5320 [12–37]. These

QUAD4 MSC Nastran element and PCOMP material properties input was used for analysis. A uniform pressure of 6.89E-2 MPa is applied on each of the two bottom flange surfaces for the hat-stiffener simulation. For the second set of simulations, same magnitude of pressure, 6.89E-2 MPa is applied on the plate to which hat-stiffener is bonded. Longitudinal edges are free to rotate but not translate (Tx = Ty = Tz = 0). The transverse direction edges are free. These longitudinal edge boundary conditions represent fixed edges rather than simply supported, because edge cross sections are constrained from rotation. Same boundary conditions for flat

Longitudinal edges (the two edges of the skin plate only, not including hat stiffener web and top cap) are simply supported as Tx = Ty = Tz = 0 for hat stiffener bonded to the plate. The transverse edges of the plate are subjected to the boundary conditions Tx = Ry = Rz = 0,

508 mm (which is 20 inches).

E1 = 1.59E5 MPa; E2 = 9.3E3 MPa;

Poisson's Ratio v = 0.336;

unidirectional fiber tape tensile properties are:

Figure 3. Hat stiffener basic element with geometric parameters.

Shear modulus G12 = G13 = 5.6E3 MPa.

plates will represent simply supported conditions.

Achieving the above requires specific technical objectives including:

