5,413 research outputs found

    Reliability-based design optimization of shells with uncertain geometry using adaptive Kriging metamodels

    Full text link
    Optimal design under uncertainty has gained much attention in the past ten years due to the ever increasing need for manufacturers to build robust systems at the lowest cost. Reliability-based design optimization (RBDO) allows the analyst to minimize some cost function while ensuring some minimal performances cast as admissible failure probabilities for a set of performance functions. In order to address real-world engineering problems in which the performance is assessed through computational models (e.g., finite element models in structural mechanics) metamodeling techniques have been developed in the past decade. This paper introduces adaptive Kriging surrogate models to solve the RBDO problem. The latter is cast in an augmented space that "sums up" the range of the design space and the aleatory uncertainty in the design parameters and the environmental conditions. The surrogate model is used (i) for evaluating robust estimates of the failure probabilities (and for enhancing the computational experimental design by adaptive sampling) in order to achieve the requested accuracy and (ii) for applying a gradient-based optimization algorithm to get optimal values of the design parameters. The approach is applied to the optimal design of ring-stiffened cylindrical shells used in submarine engineering under uncertain geometric imperfections. For this application the performance of the structure is related to buckling which is addressed here by means of a finite element solution based on the asymptotic numerical method

    Likely equilibria of stochastic hyperelastic spherical shells and tubes

    Get PDF
    In large deformations, internally pressurised elastic spherical shells and tubes may undergo a limit-point, or inflation, instability manifested by a rapid transition in which their radii suddenly increase. The possible existence of such an instability depends on the material constitutive model. Here, we revisit this problem in the context of stochastic incompressible hyperelastic materials, and ask the question: what is the probability distribution of stable radially symmetric inflation, such that the internal pressure always increases as the radial stretch increases? For the classic elastic problem, involving isotropic incompressible materials, there is a critical parameter value that strictly separates the cases where inflation instability can occur or not. By contrast, for the stochastic problem, we show that the inherent variability of the probabilistic parameters implies that there is always competition between the two cases. To illustrate this, we draw on published experimental data for rubber, and derive the probability distribution of the corresponding random shear modulus to predict the inflation responses for a spherical shell and a cylindrical tube made of a material characterised by this parameter.Comment: arXiv admin note: text overlap with arXiv:1808.0126

    Optimal design of curved folded plates

    Get PDF
    The plated structures are one of the most frequently used engineering, structures. The object of this research work is the optimal design of curved folded plates. This work is an ongoing investigation. There are various solution methods to analyze this type of structures. Here the finite strip method is used. At first single load condition is considered, but later the multiple load conditions are used for the design. The base formulation is a minimum volume design with displacement constraint what is represented by the compliance. For the multiple loading two equivalent topology optimization algorithms can be elaborated: minimization of the maximum strain energy with respect to a given volume or minimization of the volume of the structure subjected to displacement constraints. The numerical procedures are based on iterative formulas which is formed by the use of the first order optimality condition of the Lagrangian-functions. The application is illustrated by numerical examples

    Tailoring structures using stochastic variations of structural parameters.

    Get PDF
    Imperfections, meaning deviations from an idealized structure, can manifest through unintended variations in a structure’s geometry or material properties. Such imperfections affect the stiffness properties and can change the way structures behave under load. The magnitude of these effects determines how reliable and robust a structure is under loading. Minor changes in geometry and material properties can also be added intentionally, creating a more beneficial load response or making a more robust structure. Examples of this are variable stiffness composites, which have varying fiber paths, or structures with thickened patches. The work presented in this thesis aims to introduce a general approach to creating geodesic random fields in finite elements and exploiting these to improve designs. Random fields can be assigned to a material or geometric parameter. Stochastic analysis can then quantify the effects of variations on a structure for a given type of imperfection. Information extracted from the effects of imperfections can also identify areas critical to a structure’s performance. Post-processing stochastic results by computing the correlation between local changes and the structural performance result in a pattern, describing the effects of local changes. Perturbing the ideal deterministic geometry or material distribution of a structure using the pattern of local influences can increase performance. Examples demonstrate the approach by increasing the deterministic (without imperfections applied) linear buckling load, fatigue life, and post-buckling path of structures. Deterministic improvements can have a detrimental effect on the robustness of a structure. Increasing the amplitude of perturbation applied to the original design can improve the robustness of a structure’s response. Robustness analyses on a curved composite panel show that increasing the amplitude of design changes makes a structure less sensitive to variations. The example studied shows that an increase in robustness comes with a relatively small decrease in the deterministic improvement.Imperfektionen, d. h. die Abweichungen von einer idealisierten Struktur, können sich durch unbeabsichtigte Variationen in der Geometrie oder den Materialeigenschaften einer Struktur ergeben. Solche Imperfektionen wirken sich auf die Steifigkeitseigenschaften aus und können das Verhalten von Strukturen unter Last verändern. Das Ausmaß dieser Auswirkungen bestimmt, wie zuverlässig und robust eine Struktur unter Belastung ist. Kleine Änderungen der Geometrie und der Materialeigenschaften können auch absichtlich eingebaut werden, um ein verbessertes Lastverhalten zu erreichen oder eine stabilere Struktur zu schaffen. Beispiele hierfür sind Verbundwerkstoffe mit variabler Steifigkeit, die unterschiedliche Faserverläufe aufweisen, oder Strukturen mit lokalen Verstärkungen. Die in dieser Dissertation vorgestellte Arbeit zielt darauf ab, einen allgemeinen Ansatz zur Erstellung geodätischer Zufallsfelder in Finiten Elementen zu entwickeln und diese zur Verbesserung von Konstruktionen zu nutzen. Zufallsfelder können Material- oder Geometrieparametern zugeordnet werden. Die stochastische Analyse kann dann die Auswirkungen von Variationen auf eine Struktur für eine bestimmte Art von Imperfektion quantifizieren. Die aus den Auswirkungen von Imperfektionen gewonnenen Informationen können auch Bereiche identifizieren, die für das Tragvermögen einer Struktur kritisch sind. Die Auswertung der stochastischen Ergebnisse durch Berechnung der Korrelation zwischen lokalen Veränderungen und Strukturtragvermögen ergibt ein Muster, das die Auswirkungen lokaler Veränderungen beschreibt. Die Perturbation der idealen deterministischen Geometrie oder der Materialverteilung einer Struktur unter Verwendung des Musters der lokalen Einflüsse kann das Tragvermögen erhöhen. Anhand von Beispielen wird der Ansatz durch die Erhöhung der deterministischen (ohne Imperfektionen) linearen Knicklast, der Lebensdauer und des Nachknickverhaltens von Strukturen aufgezeigt. Deterministische Verbesserungen können sich zum Nachteil der Robustheit einer Struktur auswirken. Eine Vergrößerung der Amplitude der auf den ursprünglichen Designentwurf angewendeten Perturbation kann die Robustheit der Reaktion einer Struktur verbessern. Robustheitsanalysen an einer gekrümmten Verbundplatte zeigen, dass eine Struktur durch eine Vergrößerung der Amplitude der Entwurfsänderungen weniger empfindlich gegenüber Abweichungen wird. Das untersuchte Beispiel zeigt, dass eine Erhöhung der Robustheit mit einem relativ geringen Verlust der deterministischen Verbesserung eingeht

    Nonlinear Morphoelastic Plates I: Genesis of Residual Stress

    Get PDF
    Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate is given. Balance equations are derived via the global constraint principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed and the existence of residually stressed states is established

    The optimisation of brass instruments to include wall vibration effects

    Get PDF
    This thesis focuses on the design optimisation of a brass instrument. The bore profile of such an instrument is known to be the primary influence on the sound of the instrument as it directly controls the shape of the air-column contained within the instruments' walls. It has long been claimed, however, that other factors, such as the wall material and wall vibrations, are also significant, although to a lesser degree. In recent years, it has been proven that wall vibrations do indeed have an audible effect on the sound (Moore et al 2005, Kausel et al 2007, Nachtmann et al 2007, Kausel, Zietlow and Moore 2010). This effect corresponds to a relative increase in the power of upper harmonics of the sound spectrum when vibrations are greatest, and relative increase in the power of the lower harmonics, in particular the fundamental, when vibrations are at their least. The result is a timbral difference where a greater relative power in the upper harmonics results in a 'brighter' sound, and where the opposite results in a 'darker' sound. Studies have also found that the degree of the wall vibration is increased when the resonant frequencies of the air-column and those of the instruments' structure align. It is this principle that this work is based on. The primary objective of this work was to devise a suitable approach for incorporating the wall vibration effect into an optimisation method to investigate the optimum designs for two scenarios: maximum wall vibration and minimum wall vibration. It was also of interest to investigate if there were any design characteristics for each scenario. Two analysis methods were investigated for their suitability, namely free and forced vibration using finite element analysis (FEA). Different approaches to defining the design variables were explored and the suitability of different optimisation algorithms was investigated. The free vibration approach was found to be inadequate for this application due to the inherent omission of valuable magnitude information. The forced vibration approach was found to be more successful, although it was not possible to align a resonance with each frequency of interest

    Summary of Research Report

    Get PDF
    Ten papers, published in various publications, on buckling, and the effects of imperfections on various structures are presented. These papers are: (1) Buckling mode localization in elastic plates due to misplacement in the stiffner location; (2) On vibrational imperfection sensitivity on Augusti's model structure in the vicinity of a non-linear static state; (3) Imperfection sensitivity due to elastic moduli in the Roorda Koiter frame; (4) Buckling mode localization in a multi-span periodic structure with a disorder in a single span; (5) Prediction of natural frequency and buckling load variability due to uncertainty in material properties by convex modeling; (6) Derivation of multi-dimensional ellipsoidal convex model for experimental data; (7) Passive control of buckling deformation via Anderson localization phenomenon; (8)Effect of the thickness and initial im perfection on buckling on composite cylindrical shells: asymptotic analysis and numerical results by BOSOR4 and PANDA2; (9) Worst case estimation of homology design by convex analysis; (10) Buckling of structures with uncertain imperfections - Personal perspective

    Effect of cutout on stochastic natural frequency of composite curved panels

    Get PDF
    The present computational study investigates on stochastic natural frequency analyses of laminated composite curved panels with cutout based on support vector regression (SVR) model. The SVR based uncertainty quantification (UQ) algorithm in conjunction with Latin hypercube sampling is developed to achieve computational efficiency. The convergence of the present algorithm for laminated composite curved panels with cutout is validated with original finite element (FE) analysis along with traditional Monte Carlo simulation (MCS). The variations of input parameters (both individual and combined cases) are studied to portray their relative effect on the output quantity of interest. The performance of the SVR based uncertainty quantification is found to be satisfactory in the domain of input variables in dealing low and high dimensional spaces. The layer-wise variability of geometric and material properties are included considering the effect of twist angle, cutout sizes and geometries (such as cylindrical, spherical, hyperbolic paraboloid and plate). The sensitivities of input parameters in terms of coefficient of variation are enumerated to project the relative importance of different random inputs on natural frequencies. Subsequently, the noise induced effects on SVR based computational algorithm are presented to map the inevitable variability in practical field of applications

    Large Wind Energy Converter: Growian 3 MW

    Get PDF
    The final report on the projected application of larger-scale wind turbine on the northern German coast is summarized. The designs of the tower, machinery housing, rotor, and rotor blades are described accompanied various construction materials are examined. Rotor blade adjustment devices auxiliary and accessory equipment are examined

    Dealing with Imperfection Sensitivity of Composite Structures Prone to Buckling

    Get PDF
    The Space industry demands for lighter and cheaper launcher transport systems. Structural weight reduction by exploitation of structural reserves in composite launcher structures contributes to this aim, however, it requires accurate, fast and experimentally validated stability analysis of real structures under realistic loading conditions. Structures in space applications can be imperfection sensitive because their maximum load is often equal or close to the first buckling load. The current design guidelines were developed only for metallic structures and are from 1968. For composites structures no appropriate guidelines exist. To fill this gap DLR developed a promising “Single Perturbation Load Approach” which exploits the worst imperfections idea efficiently. In the running EU project DESICOS (New Robust DESIgn Guideline for Imperfection Sensitive COmposite Launcher Structures) this approach will be further investigated and combined with a stochastic approach resulting in a future design approach. This chapter deals with the state-of-the-art in buckling of imperfection sensitive composite structures, recent investigations on the new design approach, and the DESICOS project. It describes the line of actions of the new design approach, and specifies the theoretical and experimental work to be carried out
    corecore