Analysis and design for the moderately deep postbuckling behavior of composite plates

It is widely acknowledged that tracking the postbuckling response of structures made from thin plates can be problematical. Such difficulty is associated with highly nonlinear effects, including mode jumping, imperfection sensitivity, and their combined interactions. Two widely used techniques that are currently used involve path following and asymptotic expansion. The former is often implemented in commercial finite element codes but can prove unreliable at representing branch switching. The latter is a relatively quick technique due to its recursive linear nature but is only reliable in the vicinity of bifurcations. Due to the overall complex nonlinearity, analytical closed-form solutions do not exist for path following and exist rarely for quadratic asymptotic expansions where simple forms have been adopted. This paper presents an analytical-based approach that enables the efficient optimal design of “moderately deep” nonlinear postbuckling behavior of laminated composite plates under uniaxial or biaxial loading. It provides a closed-form solution that more reliably reflects a deeper postbuckling response than the state of the art. Subsequently, highly efficient postbuckling optimization is attributed to the newly derived closed-form solution and a recent two-level optimization framework

An incremental approach to the solution of global trajectory optimization problems

This paper presents an incremental approach to the solution of multiple gravity assist trajectories (MGA) with deep space maneuvers. The whole problem is decomposed in sub-problems that are solved incrementally. The solution of each sub-problem leads to a progressive reduction of the search space. Unlike other similar methods, the search for solutions of each sub-problem is performed through a stochastic approach. The resulting set of disconnected boxes is transformed into a connected collection of boxes through an affine transformation. For MGA problems, the incremental approach increases both the efficiency and reliability of the optimization process. Two relevant examples will illustrate the effectiveness of the proposed method

On testing global optimization algorithms for space trajectory design

In this paper we discuss the procedures to test a global search algorithm applied to a space trajectory design problem. Then, we present some performance indexes that can be used to evaluate the effectiveness of global optimization algorithms. The performance indexes are then compared highlighting the actual significance of each one of them. A number of global optimization algorithms are tested on four typical space trajectory design problems. From the results of the proposed testing procedure we infer for each pair algorithm-problem the relation between the heuristics implemented in the solution algorithm and the main characteristics of the problem under investigation. From this analysis we derive a novel interpretation of some evolutionary heuristics, based on dynamical system theory and we significantly improve the performance of one of the tested algorithms

Extension of finite perturbative elements for multi-revolution, low-thrust propulsion transfer optimisation

This paper presents an extension of the analytical solution for perturbed Keplerian motion of a spacecraft under the effect of a low-thrust action (Zuiani et al., Acta Astronautica, 2011). The new formulation will include the possibility for treating two different thrusting modes, i.e. with a fixed thrust direction either in a rotating or in an inertial frame. Moreover the contribution of the J2 effect is also included in the analytical formulae. It will be shown that this approach allows for the fast computation of long, many revolution spirals while maintaining adequate accuracy, and it is able to include the combined actions of different perturbations. The proposed approach will also be applied to the case of a spacecraft with a low-thrust engine, which is injected into a Geostationary Transfer Orbit and will subsequently use its on-board propulsion to transfer to a final circular orbit around the Earth. The completion of the whole transfer might require several spirals and this makes the use of a full numerical propagation prohibitive on a sequential machine. In the proposed method, the thrusting pattern, duration and start of each thrusting arc, is defined through a parameterised function. The spiral is then propagated with the above-mentioned analytical approximation. A direct optimisation approach is then used to optimise these control parameters in order to minimise the propellant cost of the transfer, given a fixed transfer time and a set of boundary conditions

On the Preliminary Structural Design Strategy of the Wing of the Next-Generation Civil Tiltrotor Technology Demonstrator

The T-WING project is a Clean Sky 2 research project aimed at designing, manufacturing, qualifying and flight-testing the new wing of the Next-Generation Civil Tiltrotor Technology Demonstrator (NGCTR-TD), as part of the Fast Rotorcraft Innovative Aircraft Demonstrator Platforms (FRC IADP) activities. Requirements, design strategy, methodology and main steps followed to achieve the composite wing preliminary design are presented. The main driving requirements have been expressed in terms of dynamic requirements (e.g., limitations on natural frequencies), aeroelastic requirements, i.e., compliance with European Aviation Safety Agency (EASA) CS-25 and CS-29 Airworthiness Requirements), structural requirements (e.g., target wing structural mass), functional requirements (e.g., fuel tanks, accessibility, assembly and integration, etc.) and wing preliminary loads. Based on the above-mentioned requirements, the first design loop is performed by targeting an optimal wing structure able to withstand preliminary design loads, and simultaneously with stiffness and inertia distributions leading to a configuration free from flutter within the flight envelope. The outcome from the first design loop is then used to refine the model and compute more reliable flight loads and repeat aeroelastic analysis, returning further requirements to be fulfilled in terms of wing stiffness and inertia distributions. The process is iterated till the fulfillment of all the project requirements

Wing structure of the next-generation civil tiltrotor: From concept to preliminary design

The main objective of this paper is to describe a methodology to be applied in the preliminary design of a tiltrotor wing based on previously developed conceptual design methods. The reference vehicle is the Next-Generation Civil Tiltrotor Technology Demonstrator (NGCTR-TD) developed by Leonardo Helicopters within the Clean Sky research program framework. In a previous work by the authors, based on the specific requirements (i.e., dynamics, strength, buckling, functional), the first iteration of design was aimed at finding a wing structure with a minimized structural weight but at the same time strong and stiff enough to comply with sizing loads and aeroelastic stability in the flight envelope. Now, the outcome from the first design loop is used to build a global Finite Element Model (FEM), to be used for a multi-objective optimization performed by using a commercial software environment. In other words, the design strategy, aimed at finding a first optimal solution in terms of the thickness of composite components, is based on a two-level optimization. The first-level optimization is performed with engineering models (non-FEA-based), and the second-level optimization, discussed in this paper, within an FEA environment. The latter is shown to provide satisfactory results in terms of overall wing weight, and a zonal optimization of the composite parts, which is the starting point of an engineered model and a detailed FEM (beyond the scope of the present work), which will also take into account manufacturing, assembly, installation, accessibility and maintenance constraints

A density-matching approach for optimization under uncertainty

Modern computers enable methods for design optimization that account for uncertainty in the system - so-called optimization under uncertainty (OUU). We propose a metric for OUU that measures the distance between a designer-specified probability density function of the system response (the target) and the system response's density function at a given design. We study an OUU formulation that minimizes this distance metric over all designs. We discretize the objective function with numerical quadrature, and we approximate the response density function with a Gaussian kernel density estimate. We offer heuristics for addressing issues that arise in this formulation, and we apply the approach to a CFD-based airfoil shape optimization problem. We qualitatively compare the density-matching approach to a multi-objective robust design optimization to gain insight into the method.This research was funded through a Dorothy Hodgkin Postgraduate Award, which is jointly sponsored by the Engineering and Physical Sciences Research Council (EPSRC) (UK) and Rolls-Royce plc. The first author would like to acknowledge the financial assistance provided by the Center for Turbulence Research at Stanford University and St. Edmund's College, Cambridge. The authors would like to thank Shahrokh Shahpar of Rolls-Royce plc for his advice on various aspects of this work. The authors also thank the reviewers for their suggestions and comments, which improved the overall quality of this manuscript. The second author's work is supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-SC-0011077.This is the final version of the article. It first appeared from Elsevier via https://doi.org/10.1016/j.cma.2016.03.00

Automated multigravity assist trajectory planning with a modified ant colony algorithm

The paper presents an approach to transcribe a multigravity assist trajectory design problem into an integrated planning and scheduling problem. A modified Ant Colony Optimization (ACO) algorithm is then used to generate optimal plans corresponding to optimal sequences of gravity assists and deep space manoeuvers to reach a given destination. The modified Ant Colony Algorithm is based on a hybridization between standard ACO paradigms and a tabu-based heuristic. The scheduling algorithm is integrated into the trajectory model to provide a fast time-allocation of the events along the trajectory. The approach demonstrated to be very effective on a number of real trajectory design problems

Protograph-Based LDPC Code Design for Probabilistic Shaping with On-Off Keying

This work investigates protograph-based LDPC codes for the AWGN channel with OOK modulation. A non-uniform distribution of the OOK modulation symbols is considered to improve the power efficiency especially for low SNRs. To this end, a specific transmitter architecture based on time sharing is proposed that allows probabilistic shaping of (some) OOK modulation symbols. Tailored protograph-based LDPC code designs outperform standard schemes with uniform signaling and off-the-shelf codes by 1.1 dB for a transmission rate of 0.25 bits/channel use.Comment: Invited Paper for CISS 201