: An overview of the virtual crack closure technique is presented. The approach used is discussed, the history summarized, and insight into its applications provided. Equations for two-dimensional quadrilateral elements with linear and quadratic shape functions are given. Formula for applying the technique in conjuction with three-dimensional solid elements as well as plate/shell elements are also provided. Necessary modifications for the use of the method with geometrically nonlinear finite element analysis and corrections required for elements at the crack tip with different lengths and widths are discussed. The problems associated with cracks or delaminations propagating between different materials are mentioned briefly, as well as a strategy to minimize these problems. Due to an increased interest in using a fracture mechanics based approach to assess the damage tolerance of composite structures in the design phase and during certification, the engineering problems selected as examples and given as references focus on the application of the technique to components made of composite materials.

/pdf/virtual-crack-closure-technique-history-approach-and-53akn4ewzt.pdf

Virtual crack closure technique: History, approach, and applications

Topology optimization has become an effective tool for least-weight and performance design, especially in aeronautics and aerospace engineering. The purpose of this paper is to survey recent advances of topology optimization techniques applied in aircraft and aerospace structures design. This paper firstly reviews several existing applications: (1) standard material layout design for airframe structures, (2) layout design of stiffener ribs for aircraft panels, (3) multi-component layout design for aerospace structural systems, (4) multi-fasteners design for assembled aircraft structures. Secondly, potential applications of topology optimization in dynamic responses design, shape preserving design, smart structures design, structural features design and additive manufacturing are introduced to provide a forward-looking perspective.

Topology Optimization in Aircraft and Aerospace Structures Design

Simulations are often computationally expensive and the need for multiple realizations, as in uncertainty quantification or optimization, makes surrogate models an attractive option. For expensive high-fidelity models (HFMs), however, even performing the number of simulations needed for fitting a surrogate may be too expensive. Inexpensive but less accurate low-fidelity models (LFMs) are often also available. Multi-fidelity models (MFMs) combine HFMs and LFMs in order to achieve accuracy at a reasonable cost. With the increasing popularity of MFMs in mind, the aim of this paper is to summarize the state-of-the-art of MFM trends. For this purpose, publications in this field are classified based on application, surrogate selection if any, the difference between fidelities, the method used to combine these fidelities, the field of application and the year published. 
Available methods of combining fidelities are also reviewed, focusing our attention especially on multi-fidelity surrogate models in which fidelities are combined inside a surrogate model. Computation time savings are usually the reason for using MFMs, hence it is important to properly report the achieved savings. Unfortunately, we find that many papers do not present sufficient information to determine these savings. Therefore, the paper also includes guidelines for authors to present their MFM savings in a way that is useful to future MFM users. Based on papers that provided enough information, we find that time savings are highly problem dependent and that MFM methods we surveyed provided time savings up to 90%. 
Keywords: Multi-fidelity, Variable-complexity, Variable-fidelity, Surrogate models, Optimization, Uncertainty quantification, Review, Survey

Review of multi-fidelity models

Post-buckling optimisation of composite stiffened panels using neural networks

Multifidelity surrogates are essential in cases where it is not affordable to have more than a few high-fidelity samples, but it is affordable to have as many low-fidelity samples as needed. In the...

Issues in Deciding Whether to Use Multifidelity Surrogates

A design study for structural optimization of a hat-stiffened laminated composite panel concept for an upper cover panel of a typical passenger bay of a blended wing-body transport airplane configuration is described. The feasibility of a hat-stiffened composite panel concept for an upper cover panel is investigated and is compared on the basis of weight to a thick sandwich panel concept that has been selected by designers as the baseline concept for the upper cover panel. The upper cover panel is designed for two load cases: internal pressure only and combined internal pressure and spanwise compression due to wing bending. The structural optimization problem is formulated using the panel weight as the objective function, with constraints on stress and buckling. The spacing of the hat stiffeners, the thickness of the skin, and the thickness of the components of the hat stiffener are used as design variables. The initial geometry of the hat-stiffened panel design is determined using the PANDA2 program by restricting the design to have uniform cross section in the spanwise direction. Because of the pressure loading, a more efficient design has variable cross section. Such designs are obtained by combining the STAGS finite element program with the optimization program in the Microsoft EXCEL spreadsheet program using response surfaces. Buckling and stress response surfaces are constructed from multiple STAGS analyses and are used as constraints in the optimization. The optimization conducted with the response surfaces results in considerable weight savings compared to the uniform cross section design, albeit a more complex design. Initial optimization cycles identify a design space where simple approximate analyses, such as Euler-Bernoulli beam theory and Kirchhoff plate theory applied to laminated composites, can be used to predict the behavior of the structure.

Structural Optimization of a Hat-Stiffened Panel Using Response Surfaces

A combined analytical and experimental study of a blade-stiffened composite panel subjected to axial compression was conducted. The study e rst examined the effects of the differences between a simple model used to design the panel and the actual experimental conditions. It was found that the large imperfection used in the design process compensated for the simplifying assumptions of the design model, and the experimental failure load was only 10% higher than the design load. Next, e nite element analyses wereperformed in order to correlateanalytical and experimental results. The buckling loads from e nite element analyses agreed well with the experimental failure loads. However, substantial differences were found in the out-of-plane displacements of the panel. Finite element simulations of nonuniform load introduction with general contact dee nitions improved correlation between the measured and predicted out-of-plane deformations.

/pdf/analytical-experimental-correlation-for-a-stiffened-26b555gken.pdf

Analytical-Experimental Correlation for a Stiffened Composite Panel Loaded in Axial Compression

http://www2.mae.ufl.edu/sankar/Publications/PDFArticles/2002/Park.pdf

Crack-tip force method for computing energy release rate in delaminated plates

This paper describes a design study for the structural optimization of a typical bay of a blended wing body transport. A hat stiffened laminated composite shell concept is used in the design. The geometry of the design is determined with the PANDA2 program, but due to the presence of varying axial loads, a more accurate analysis procedure is needed. This is obtained by combining the STAGS finite element analysis program with response surface approximations for the stresses and the buckling loads. This design procedure results in weight savings of more than 30 percent, albeit at the expense of a more complex design. The response surface approximations allow easy coupling of the structural analysis program with the optimization program in the easily accessible Microsoft EXCEL spreadsheet program. The response surface procedure also allows the optimization to be carried out with a reasonable number of analyses. In particular, it allows combining a large number of inexpensive beamanalysis stress calculations with a small number of the more accurate STAGS analyses.

Structural optimization of a hat stiffened panel by response surface techniques

Analytical and experimental study of a blade stiffened composite panel subject to axial compression was conducted. The study first examines the effect of differences between the conditions used to design the panel and experimental conditions. Next, the analytical model is compared to experimental results. Several structural analysis programs including PANDA2, STAGS, and ABAQUS have been used to achieve high fidelity in the analysis. Comparisons between analytical and experimental results show that buckling load from STAGS agree well with failure load from test. However, substantial differences are found in the out-of-plane displacements of the panel. These differences may be due to some loading eccentricity, rotation of the load introduction edge, as well as imperfections in the panel.

Oung Park

Papers

Structural Optimization of a Hat-Stiffened Panel Using Response Surfaces

Analytical-Experimental Correlation for a Stiffened Composite Panel Loaded in Axial Compression

Crack-tip force method for computing energy release rate in delaminated plates

Structural optimization of a hat stiffened panel by response surface techniques

Analytical and experimental study of a blade stiffened panel in axial compression