Madara Ogot

Stochastic approach to optimal aerodynamic shape design

The purpose of this study was to show that stochastic methods can be applied effectively to optimal aerodynamic shape design problems, and that optimal solutions within relatively complex design spaces can be located in a reasonable amount of computation time. The design methodology presented is based on a modified simulated annealing algorithm and is global in nature, i.e., relative large complex design spaces can be automatically investigated. Current approaches that typically employ gradient-based optimization schemes tend to get caught in the numerous real and false local minima common in the design spaces of practical aerodynamics shape design problems. Within the context of the optimal shape design of a minimum drag axisymmetric forebody problem, a comparison was made between the proposed stochastic methodology and a gradient-based optimization approach. The results obtained clearly demonstrated the ability of this methodology to locate optimal designs in relatively complex design spaces where gradient-based optimization approaches experience difficulties. Further, the computation time required by the stochastic approach compared favorably to that of the gradient-based method. Nomenclature A = cross-sectional area of forebody, m2 Cd = coefficient of drag Fd - force of drag, N m = length of Markov chain n = number of cross sections P = Metropolis criterion R = random number uniformly distributed over the range [0, 1] Rp = baseline parabolic shape r, = radius at the /th cross section, ft T = control parameter Ux - freestream air velocity, m/s z = distance from the nose of the forebody measured along the z axis, ft £max = length of forebody, ft a. = nose angle, deg /3 = control parameter reduction coefficient A£ = change in objective function value p — freestream air density, kg/m3

Jig-Shape Static Aeroelastic Wing Design Problem: A Decoupled Approach

A novel approach to the jig-shape static aeroelastic wing design problem is presented in this paper. Unlike previous design efforts where the aerodynamic and structural analyses were coupled throughout the optimization process, this work presents a truly decoupled approach. The proposed approach performs aerodynamic shape optimization in the first phase to determine an optimal configuration, followed by structural shape optimization in the second phase to find the corresponding jig shape. The latter does not require the performance of any new aerodynamic analyses, resulting in true decoupling of the jig-shape aeroelastic wing design problem. This results in significant reduction in computation time making the design of relatively complex wing structures feasible. For this study high-fidelity codes-ANSYS 5.0 for the structural analyses and a supersonic Euler code for the aerodynamic analyses-were used. A modified simulated annealing algorithm was used as the optimizer. Two examples are presented a forebody problem and the design of a high-speed civil transport wing, to demonstrate the efficacy of the methodology.

Hybrid simulation strategy for multiple planar collisions with changing topologies and local deformation

Abstract The development of a hybrid strategy for the simulation of multiple plastic-elastic collisions is presented. The strategy attempts to bridge the gap between finite element methods (FEM), which typically require excessively long computation times for multiple impact simulations, and lumped parameter approaches that cannot provide accurate local deformation information. The proposed strategy employs a finite element routine solely to simulate the impact phase, thereby obtaining detailed local deformation information. The simulation of the flight phase between impacts, however, proceeds under rigid body dynamics, resulting in significant reduction in computation time. The transfer of control between FEM and rigid body dynamics is automatic and the points of contact need not be known a priori. The progressive object internal plastic strain, determined from FEM, is retained from one impact to the next, thereby ensuring a certain degree of continuity of the physical properties of the body. An example is presented to demonstrate the efficacy of this approach.

Stochastic versus gradient-based optimizers for CFD design

Three modifications to simulated annealing are presented and applied to CPD shape optimization problems. Nearly optimal solutions are found reliably and on the order of hundreds of objective function evaluations.

Discrete Probabilistic Simulated Annealing with Local Search (DPSAwLS)

Early conceptual design within a multi-disciplinary framework often involve large, noisy, multimodal design spaces that tend to be global in nature. This paper presents a stochastic robust design optimization method based on simulated annealing (SA). Discrete Probabilistic Simulated Annealing with Local Search (DPSAwLS), works eectively in these types of design spaces and has proven to be eective for global optimization problems encountered during the early stages of the design process. The nature of the design space makes the use of gradient-based methods unsuitable as they tend to get caught in local minima. Gradient-based methods may be applicable later in the design process once the design space has been reduced and the design needs to be refined. DPSAwLS, (1) results in faster and more reliable convergence to the global minimum than regular simulated annealing, (2) accounts for uncertainty in design and environmental variables, (3) can handle problems with continuous or mixed (continuous and discrete) variables, and (4) is simple to code and can therefore be readily wrapped around any existing analysis routines that are treated as ‘black boxes’. With a drastic reduction in the number of iterations required for convergence, DPSAwLS becomes a practical optimization method for inexpensive (seconds per analysis iteration) and moderately expensive (minutes per analysis iteration) global optimization problems. Two aerodynamic shape optimization problems are presented to demonstrate the ecacy of the approach.

Discretizing Continuous Problems for Faster Global Convergence

Global optimization of mechanical design problems using heuristic methods such as Simulated annealing (SA) and genetic algorithms (GAs) have been able to find global or near-global minima where prior methods have failed. The use of these nongradient based methods allow the broad efficient exploration of multimodal design spaces that could be continuous, discrete or mixed. From a survey of articles in the ASME Journal of Mechanical Design over the last 10 years, we have observed that researchers will typically run these algorithms in continuous mode for problems that contain continuous design variables. What we suggest in this paper is that computational efficiencies can be significantly increased by discretizing all continuous variables, perform a global optimization on the discretized design space, and then conduct a local search in the continuous space from the global minimum discrete state. The level of discretization will depend on the complexity of the problem, and becomes an additional parameter that needs to be tuned. The rational behind this assertion is presented, along with results from four test problems.Copyright

A finite element analysis of the effects of an increasing angle on the Tower of Pisa

The Leaning Tower of Pisa has aroused admiration and curiosity throughout the world for its beauty and unusual lean. This study investigates the effects of increasing lean on the structural integrity of the tower. Employing a three dimensional finite element model, two failure modes are investigated and discussed.

STOCHASTIC OPTIMIZATION FOR AIRCRAFT PRELIMINARY DESIGN

The preliminary design of a blended wing body (BWB) aircraft is performed using a vortex lattice method and a simplified weights analysis. A stochastic optimization method is then used to identify several near optimal designs. Changes in the discretization and iteration tolerance of the aerodynamics code cause large discontinuities and spurious extrema to appear in the objective function. Stochastic optimization techniques provide a robust, systematic means of performing global searches in such design spaces.

An inverse dynamic model of a spherical electrohydraulic actuator for use in a dexterous mechanical hand

The purpose of this article is to develop an inverse dynamic model of a two-degree-of-freedom electrohydraulic actuator. The actuator is to be incorporated at the base of each of three fingers of a nine-degree-of-freedom mechanical hand, currently under development. Motion in the proposed actuator is fa cilitated about intersecting pitch and yaw axes, thus creating spherical actuation. The dynamic model incorporates frictional and hydraulic losses, which are commonly overlooked sources of energy dissipation. The model is to be used in the control scheme of the mechanical hand and in the optimal synthesis procedure of the actuator. The latter application, briefly de scribed here, takes into account specified motion and torque requirements, pressure, peak-input force, and size constraints. Particular attention is paid to traditional performance indices, such as mechanical advantage.