Journal of Aerospace Engineering

The integration of modeling and simulation tools with robust and efficient methods of optimal design offers a rational approach to explore new concepts and designs. However, a widespread adaptation of these tools in the industry design environment will require that they incorporate a systematic analysis of uncertainty in all aspects of the design process. A lack of confidence in designs generated in a simulation-based approach is the result of uncertainties in the predictive capabilities of physics-based models used in the simulations, and poor representation of uncertainties and their propagation in a coupled systems engineering design problem. A data- and knowledge-lean environment, typical of a design process involving novel concepts, further exacerbates the situation; design engineers often make gross assumptions about distributional information of random variables and parameters, thereby adding to the uncertainty associated with the design results. The paper focuses on numerical and analytical tools by which to model uncertainty and risk in a simulation-based design environment, including cases where the uncertainty does not conform to standard probabilistic distributions. A specific focus of the modeling effort is an approach to establish confidence intervals for response predictions available from analytical and numerical models, as well as surrogate approximations used in the design process. Innovative adaptations of formal optimization methods in a nondeterministic design setting are discussed, including design problem formulations that examine the nondeterministic design problem in a multicriteria optimization framework. Simple design problems are used to illustrate the concepts and to underscore the deficiencies in a purely deterministic approach to the design problem.

Although stitched laminates have been shown effective in preventing delamination failure, the presence of stitches results in a degraded in-plane strength and stiffness in such structures. The solution suggested in the paper is based on using stitches only in a part of the structure where they serve as arrestors of delamination cracks, while the part subject to considerable in-plane loading could remain unstitched. This approach, that could be called “functionally graded stitching,” is considered on the example of a double cantilever beam (DCB) with a preexisting delamination crack that has penetrated into the stitched region of the beam. As is shown in the paper, the distribution of stitches in a functionally graded DCB (and in any other laminated structure) should be chosen to prevent three major failure modes. These modes include the failure of the stitches, bending failure of the unstitched delaminated section of the structure, and continuous crack propagation through the stitched region. The results obtained in the paper for the static problem clearly illustrate the feasibility of using functionally graded stitched laminates retaining in-plane strength and stiffness, while providing barriers to delamination cracks in less loaded regions of the structure. Additionally, the approach to the solution of the dynamic problem presented in the paper may be applied to the analysis of fatigue delamination cracks in partially stitched structures.

Many proposed inflatable designs for space applications consist of truss-like or lattice structures due to their simplicity of construction coupled with large stiffness to density ratios. An analytical approach is presented here in order to derive the governing partial differential equations of motion which are decoupled for bending and rotational coordinates of vibrations and applies this formulation to the truss structure model of an innovative space-based radar antenna. Kinetic and potential energy expressions are written in terms of nodal velocities and strain components of bar members within a repeating truss element. Hamilton’s principle is then employed to find the equations of motion for the system. The equations for bending are presented in their decoupled form in order to derive an equivalent Timoshenko beam model for the truss. Finally, the physical characteristics of the continuum model are written in terms of the material and geometrical properties of the original truss, which provide a simple tool for comparing dynamic characteristics of lattices with different properties. The natural frequencies are found for each of the bending coordinates of vibration and are compared to those of a standard finite-element method (FEM) solution, for the purpose of validation. The partial differential equations predictions of the natural frequencies for the truss are very close to the FEM. Finally the errors in the frequency estimations are found in terms of the wavelength of the traveling waves.

This paper is a tutorial exposition of the template approach to the construction of customized mass-stiffness pairs for selected applications in structural dynamics. The exposition focuses on adjusting the mass matrix while a separately provided stiffness matrix is kept fixed. Two well known kinetic-energy discretization methods described in finite-element method (FEM) textbooks since the mid-1960s lead to diagonally lumped and consistent mass matrices, respectively. These two models are sufficient to cover many engineering applications. Occasionally, however, they fall short. The gap can be filled with a more general approach that relies on the use of templates. These are algebraic forms that carry free parameters. This approach is discussed in this paper using one-dimensional structural elements as examples. Templates have the virtue of producing a set of mass matrices that satisfy certain a priori constraint conditions such as symmetry, nonnegativity, invariance, and momentum conservation. In particular, the diagonally lumped and consistent versions can be obtained as instances. Thus those standard models are not excluded. Availability of free parameters, however, allows the mass matrix to be customized to special needs, such as high precision vibration frequencies or minimally dispersive wave propagation. An attractive feature of templates for FEM programming is that only one element implementation as module with free parameters is needed, and need not be recoded when the application problem class changes.

A finite element methodology for analyzing fracture in thin shells in the large strain elastoplastic regime is presented. The postlocalization constitutive model is based on a cohesive surface dissipation mechanism. We employ a Kirchhoff-Love shell model (and the corresponding discretization by finite elements) and make use of the extended finite element technique in the (implicit) form of midsurface displacement and director field discontinuities. Applications showing the possibilities of this technique are shown, and the effect of plastic anisotropy in the crack pattern is numerically inspected.

A cell vertex finite volume algorithm and an artificial compressibility approach are employed to enable simulation of three-dimensional incompressible unsteady turbulent flow using unstructured tetrahedral meshes. Unsteady flow modeling is accomplished through the use of an implicit dual time stepping scheme, and stabilization of the procedure is achieved by the explicit addition of artificial viscosity in the Jameson–Schmidt–Turkel manner. The Spalart–Allmaras detached eddy simulation model is adopted for turbulent flow simulations. The computational performance is enhanced by the incorporation of multigrid acceleration and by parallelization of the solution algorithm. A number of examples are presented to demonstrate the capabilities of the resulting procedure.

The concept of safety factor is nearly universally applied in structural engineering. There are presently several approaches for probabilistic interpretation of the safety factors in the literature. Herein we generalize the above approaches to derive four possible definitions of safety factor that are based on fuzzy sets: (1) the central fuzzy safety factor is defined as the ratio of the centroid abscissas of the membership functions, respectively, of the capacity and the demand of the structure; (2) the characteristic value of fuzzy safety factor as the lower bound of the $\alpha$ cut of the fuzzy safety factor for a specified level of the membership function; (3) the mean value of fuzzy safety factor as the centroid abscissa of the fuzzy capacity-to-demand ratio; and (4) the fuzzy multiplicative safety factor is defined as the abscissa of the centroid of the capacity multiplying to the abscissa of the centroid of the inverse of the demand. Fundamental problem of the strength of materials, namely, tension of an element subjected to an axial load, is analyzed in the context of the above four fuzzy safety factors.

Multiphase and multidomain fluid flows associated with interfacial dynamics, steep jump in fluid properties, and moving boundaries between different phases and materials pose substantial computational challenges. In this paper, recent progresses made in numerical simulation using continuum and lattice–Boltzmann methods are highlighted, with special attention paid to issues related to time varying geometries, adaptive grid refinement, interfacial and geometric tracking, topological changes, and reduced numerical dispersion and dissipation. Illustrative physical applications including: (1) multiple rising bubbles interacting with carrier phase and with each other; (2) wave reflected on an inclined wall; and (3) the Rayleigh–Taylor instability problem, are presented to highlight the various aspects of the techniques developed.