Optimization of thin-walled structures like an aircraft wing, aircraft fuselage or submarine hull often involves dividing the shell surface into numerous localized panels, each characterized by its own set of design variables. The process of extracting information about a localized panel (nodal coordinates, mesh connectivity) from a finite element model, input file is usually a problem-specific task. In this work, a generalized process to extract localized panels from the two-dimensional (2D) mesh is discussed. The process employs set operations on elemental connectivity information and is independent of nodal coordinates. Thus, it is capable of extracting panel of any shape given the boundary and thus can be used during optimization of a wide range of structures. A method to create stiffeners on the resulting local panels is also presented, and the effect of stiffener element size on buckling is studied. The local panel extraction process is demonstrated by integrating it into a distributed MDO framework for optimization of an aircraft wing having curvilinear spars and ribs (SpaRibs). A range of examples is included wherein the process is used to create panels on the wing-skin, bounded by adjacent SpaRibs.
One of the most important concerns while designing vehicles is to reduce structural weight, which can directly lead to a reduction in fuel consumption. During the era when computers were expensive and not so powerful, structural design was mostly done by hand calculation on simplified mathematical models. However, since the seventies, due to the rapid increase in computational power numerical solution techniques like Finite Element Analysis (FEA) have gained immense popularity. Not only the details and the complexity of the system can be included in the analysis, but multiple disciplines can now be considered while setting up a structural optimization problem. This avenue of research where several disciplines are incorporated into the optimization problem is known as Multidisciplinary Design Optimization (MDO). The major advantage of solving such a problem arises when relevant disciplines are not independent of each other; in other words, the disciplines interact with each other.
Application of MDO for structural design can be traced back to the work of Schmit [1,2,3]. In these work, finite element methods and algorithms for numerical optimization were used. In subsequent years, Starnes, J. and Haftka [4], Haftka et al. [5] and Fulton et al. [6] designed aircraft wings considering constraints on strength, stability and flutter velocity. With the help of commercial softwares like ANSYS, MDO can be applied to complex 3D spacial structures as well (For example as done by Aru et al. [7]). With the advance in computational power, MDO rapidly gained popularity power in aerospace (Li et al. [8]) and automobile engineering and soon, problems were solved involving a complete three dimensional structures (Devarajan et al. [9]; Singh et al. [10]; Fulton et al. [11]; Kroo et al. [12], Manning [13]; Shihan [14]; Antoine and Kroo [15]; Henderson et al. [16]; Alonso and Colonno [17]). The processes followed in MDO have either monolithic or distributed architectures (Martins and Lambe [18]). In any MDO, the first step is almost always to describe the system using a set of design variables which are often selected by Design of Experiment (DOE) techniques (An example of DOE can be found in the article by Kumar et al. [19]). The goal is to find the best values for the design variables that minimizes (or maximizes) the objective function while satisfying constraints in several disciplines. For example, in problems involving structural design, the size, shape or topology of the structure are described by a set of design variables. By applying appropriate numerical optimization algorithms, the problem is solved for a set of design variables that gives minimum weight or maximum compliance while satisfying constraint like maximum von Mises stress, minimum buckling factor, maximum displacement etc. In a monolithic architecture, all the design variables and constraints are considered in a single optimization process. This process, commonly known as All-at-Once optimization (Sobieszczanski-Sobieski and Haftka [20]), although simple to implement, is computationally expensive when the number of design variables is large. Such problems involving a large number of design variables are often solved using the other process of MDO i.e. distributed architecture. The distributed MDO architectures involves the decomposition of complex systems into multiple smaller components which are then described by a lower number of design variables and optimized independently. The process is usually implemented using parallel computation which can reduce wall clock time by several times. This process of decomposition of a system into a simple sub-system is often known as global/local design optimization.
The aircraft wing is a complex structure consisting of the outer aerofoil shell known as the wing-skin, and internal stiffening elements: the ribs and spars. The global/local optimization of wing design has been used by several research groups including Cimpa et al. [21], Yang et al. [22] and Barkanov et al. [23]. Even though the availability of computational power makes the exploration of large design space feasible, there has always been a concern in the industry about manufacturing limitations. It is often very expensive to produce unconventional designs using conventional manufacturing processed. However, with the invention of 3D printing techniques, the manufacturing industry is likely to be revolutionized over the next few decades. A new additive manufacturing technique known as Electron Beam Free Form Fabrication or EBF3, in short, has recently been developed by Taminger and Hafley [24] at NASA Langley Research Center to fabricate metallic structures of complex shapes, which now can be printed with significant precision. This technology inspired Kapania et al. at Virginia Tech (Locatelli et al. [25]; Locatelli et al. [26]; Jrad et al. [27]; Devarajan et al. [28]; Miglani et al. [29]) to propose the use of curvilinear stiffening elements to reduce
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