Topology Optimization of Engine Exhaust-Washed Structures

Aircraft structure subjected to elevated temperature and acoustic loading present a challenging design environment. Thermal stress in a structural component has typically been alleviated by allowing thermal expansion. However, very little work has been done which directly addresses the situation where such a prescription is not possible. When a structural component has failed due to thermally-induced tensile stresses, the answer to the question of how best to stiffen the structure is far from trivial. In this work, we demonstrate that conventional stiffening techniques, for example, those which add material to the thickness of a failing panel, may actually increase the rate of damage as well as increasing load into sub- and surrounding structure. The typical compliance minimization topology optimization formulation is applied to a thermally-loaded panel resulting in extremely non-optimal configurations. To generate successful thermal stress designs where the objectives are to lower the tensile stresses while simultaneously limiting the amount of additional load into sub- and surrounding structures, a well-known characteristic of topology optimization for a single-load case mechanical loading is exploited which by construction limits additional load into surrounding structure. Acoustic loading is also a major concern as exhaust gases with random frequency content impinge on aircraft structure in the vicinity of the engines. An evolutionary structural optimization algorithm is developed which addresses both the maximum von-Mises stress and minimum natural frequency for a generic thermal protection system. The similarities between the two approaches are demonstrated

Morphing shell structures:A generalised modelling approach

AbstractMorphing shells are nonlinear structures that have the ability to change shape and adopt multiple stable states. By exploiting the concept of morphing, designers may devise adaptable structures, capable of accommodating a wide range of service conditions, minimising design complexity and cost. At present, models predicting shell multistability are often characterised by a compromise between computational efficiency and result accuracy. This paper addresses the main challenges of describing the multistable behaviour of thin composite shells, such as bifurcation points and snap-through loads, through the development of an accurate and computationally efficient energy-based method. The membrane and the bending components of the total strain energy are decoupled by using the semi-inverse formulation of the constitutive equations. Transverse displacements are approximated by using Legendre polynomials and the membrane problem is solved in isolation by combining compatibility conditions and equilibrium equations. This approach provides the strain energy as a function of curvature only, which is of particular interest, as this decoupled representation facilitates efficient solution. The minima of the energy with respect to the curvature components give the multiple stable configurations of the shell. The accurate evaluation of the membrane energy is a key step in order to correctly capture the multiple configurations of the structure. Here, the membrane problem is solved by adopting the Differential Quadrature Method (DQM), which provides accurate results at a relatively small computational cost. The model is benchmarked against three exemplar case studies taken from the literature

Structural sizing of post-buckled thermally stressed stiffened panels

Design of thermoelastic structures can be highly counterintuitive due to design-dependent loading and impact of geometric nonlinearity on the structural response. Thermal loading generates in-plane stresses in a restrained panel, but the presence of geometric nonlinearity creates an extension-bending coupling that results in considerable transverse displacement and variation in stiffness characteristics, and these affects are enhanced in post-bucking regimes. Herein a methodology for structural sizing of thermally stressed post-buckled stiffened panels is proposed and applied for optimization of the blade and hat stiffeners using a gradient-based optimizer. The stiffened panels are subjected to uniform thermal loading and optimized for minimum mass while satisfying stress and stability constraints. The stress constraints are used to avoid yielding of the structure, whereas the stability constraints are used to ensure static stability. Corrugation of the hat stiffeners is also studied through variation of its magnitude and position. A continuation solver has been validated to tackle the highly nonlinear nature of the thermoelastic problem, and formulations for the stability constraints have been derived and imposed to satisfy the static stability of the structure. The study confirms that geometric nonlinearity is an important aspect of sizing optimization and is needed for an accurate modeling of the structural behavior. The results also show that modeling of geometric nonlinearity adds extra complexity to the thermoelastic problem and requires a path-tracking solver. Finally, this work supports that corrugation enhances the stability features of the panel but requires a blending function to reduce stresses at the panel boundaries

Simulations of magnetized multiphase galactic disk regulated by supernovae explosions

What exactly controls star formation in the Galaxy remains controversial. In particular, the role of feedback and magnetic field are still partially understood. We investigate the role played by supernovae feedback and magnetic field onto the star formation and the structure of the Galactic disk. We perform numerical simulations of the turbulent, magnetized, self-gravitating, multi-phase, supernovae regulated ISM within a 1 kpc stratified box. We implemented various schemes for the supernovae. This goes from a random distribution at a fixed rate to distributions for which the supernovae are spatially and temporally correlated to the formation of stars. To study the influence of magnetic field on star formation, we perform both hydrodynamical and magneto-hydrodynamical simulations. We find that supernovae feedback has a drastic influence on the galactic evolution. The supernovae distribution is playing a very significant role. When the supernovae are not correlated with star formation events, they do not modify significantly the very high star formation rate obtained without feedback. When the supernovae follow the accretion, the star formation rate can be reduced by a factor up to 30. Magnetic field is also playing a significant role. It reduces the star formation rate by a factor up to 2-3 and reduces the number of collapse sites by a factor of about 2. The exact correlation between the supernovae and the dense gas appears to have significant consequences on the galactic disk evolution and the star formation. This implies that small scale studies are necessary to understand and quantify the feedback efficiency. Magnetic field does influence the star formation at galactic scales by reducing the star formation rate and the number of star formation sites.Comment: to be published in A&

Thermal buckling analysis for stiffened orthotropic cylindrical shells

Structural analysis of thermal buckling of orthotropic, multilayered, stiffened cylindrical shell using finite differences and determinant plotting or modal iteratio

Multistable grid and honeycomb shells

The manufacturing of multistable shells has been dominated by the use of pre-stressed and composite materials. Here we advocate the use of common materials through a simple design that requires no pre-stressing and has an initially developable geometry. A rudimentary demonstrator is constructed and serves as the starting point for further study. An existing homogenisation model for a lattice structure is combined with an analytical strain energy model from the literature to show the mechanical properties needed to construct an initially developable, bistable grid shell. The concept is also tested in a commercial finite element package, where a number of parametric studies are performed. Both the demonstrator and the FE model confirm the validity of the design while a series of parametric studies helps establish the limits of this behaviour with respect to local and global geometry of grid shell and honeycomb structures.EGL was supported by scholarships from the Alexander S. Onassis Public Benefit Foundation and the Cyprus State Scholarship Foundation.This is the accepted manuscript of a paper published in the International Journal of Solids and Structures, Volume 59, 1 May 2015, Pages 46–57, DOI: 10.1016/j.ijsolstr.2015.01.002

Controlling Morphology in Swelling-Induced Wrinkled Surfaces

Wrinkles represent a pathway towards the spontaneous generation of ordered surface microstructure for applications in numerous fields. Examples of highly complex ordered wrinkle structures abound in Nature, but the ability to harness this potential for advanced material applications remains limited. This work focuses on understanding the relationship between the patterns on a wrinkled surface and the experimental conditions under which they form. Because wrinkles form in response to applied stresses, particular attention is given to the nature of the stresses in a wrinkling surface. The fundamental insight gained was then utilized to account for observed wrinkle formation phenomena within more complex geometric and kinetic settings. In order to carefully control and measure the applied stresses on a wrinkling film, a swelling-based system was developed using poly(dimethylsiloxane) (PDMS), surface-oxidized with a UV-ozone treatment. The swelling of the oxidized surface upon exposure to an ethanol vapor atmosphere was characterized using beam-bending experiments, allowing quantitative measurements of the applied stress. The wrinkle morphologies were characterized as a function of the overstress, defined as the ratio of the applied swelling stress to the critical buckling stress of the material. A transition in the dominant morphology of the wrinkled surfaces from dimple patterns to ridge patterns was observed at an overstress value of ~2. The pattern dependence of wrinkles on the ratio of the principal stresses was examined by fabricating samples with a gradient prestress. When swollen, these samples exhibited a smooth morphological transition from non-equibiaxial to equibiaxial patterns, with prestrains as low as 2.5% exhibiting non-equibiaxial characteristics. This transition was seen both in samples with low and high overstresses. To explore the impact of these stress states in more complex geometries, wrinkling hemispherical surfaces with radii of curvature ranging from 50-1000 μm were fabricated using the same material system. Upon wrinkling, the hemispheres formed complex hierarchical assemblies reminiscent of naturally occurring structures. The curvature of a surface exhibited a correlation with its critical buckling stress, independent of other factors. This enables the surface curvature to be used as an independent control over the dimple-to-ridge transition which occurs as a function of overstress. As in the flat buckling surfaces, this transition was shown to occur at an overstress value of ~2. Surface curvature was also shown to improve the observed hexagonal ordering of the dimple arrays, resulting in the formation of regular golf ball structures. Geometric effects in finite flat plates were also examined. Using circular masks during the oxidation process, plates with radii ranging from 0.4-8.6 mm were created. Upon wrinkling, a dimple-to-ridge transition was observed with increasing plate size, with the morphological switch occurring at a radius of ~2 mm. This observed transition was not found to be due to the inherent mechanics of plates of different sizes, but instead to a reduction in the oxide conversion due to shadowing or stagnation caused by the masking process, which lowered the applied overstress. The shape of the finite plate was found to have little impact on the resulting wrinkle morphologies. Kinetic aspects of wrinkling were qualitatively characterized by observing the wrinkling process over the course of swelling. Wrinkling was observed to frontally propagate across the surface, and the ordering of the patterns which developed showed a qualitative correlation with the degree of uniformity in the advancing wrinkle front. Swelling with different solvents was found to lead to the formation of different patterns, based on the swelling kinetics of the UVO-treated PDMS upon exposure to each solvent

Early Thermal Evolution of Planetesimals and its Impact on Processing and Dating of Meteoritic Material

Radioisotopic ages for meteorites and their components provide constraints on the evolution of small bodies: timescales of accretion, thermal and aqueous metamorphism, differentiation, cooling and impact metamorphism. Realising that the decay heat of short-lived nuclides (e.g. 26Al, 60Fe), was the main heat source driving differentiation and metamorphism, thermal modeling of small bodies is of utmost importance to set individual meteorite age data into the general context of the thermal evolution of their parent bodies, and to derive general conclusions about the nature of planetary building blocks in the early solar system. As a general result, modelling easily explains that iron meteorites are older than chondrites, as early formed planetesimals experienced a higher concentration of short-lived nuclides and more severe heating. However, core formation processes may also extend to 10 Ma after formation of Calcium-Aluminum-rich inclusions (CAIs). A general effect of the porous nature of the starting material is that relatively small bodies (< few km) will also differentiate if they form within 2 Ma after CAIs. A particular interesting feature to be explored is the possibility that some chondrites may derive from the outer undifferentiated layers of asteroids that are differentiated in their interiors. This could explain the presence of remnant magnetization in some chondrites due to a planetary magnetic field.Comment: 24 pages, 9 figures, Accepted for publication as a chapter in Protostars and Planets VI, University of Arizona Press (2014), eds. H. Beuther, R. Klessen, C. Dullemond, Th. Hennin