Optimal Shape Design

Simulation-based design optimization methods integrate computer simulations, design modification tools, and optimization algorithms. In hydrodynamic applications, often objective functions are computationally expensive and noisy, their derivatives are not directly provided, and the existence of local minima cannot be excluded a priori,
which motivates the use of deterministic derivative-free global  optimization algorithms. DPSO (Deterministic Particle Swarm Optimization), DIRECT (DIviding RECTangles), two well-known derivative-free global optimization algorithms, and FSA (Fish Shoal Algorithm), a novel metaheuristic introduced herein, are described in the present work. Moreover, the enhancement of DIRECT and DPSO is presented based on global/local hybridization with derivative-free line search methods. DPSO, DIRECT, FSA, and three hybrid algorithms (LS-DF PSO, DIRMIN, and DIRMIN-2) are introduced, and assessed on a benchmark of seventy-three analytical functions, providing an effective and efficient guideline for their use in the simulation-based shape design optimization context. The suggested guidelines are applied on ten hull-form optimization problems, using potential flow and RANS solvers, supported by metamodels. The optimizations pertain the high-speed Delft catamaran and an USS Arleigh Burkeclass destroyer ship, namely the DTMB 5415 model, an early and open-to-public version of the DDG-51. Three shape modification techniques, specifically the free-form deformation and the orthogonal basis functions expansion over 2D and 3D subdomains, are introduced, along with the design-space  dimensionality reduction by generalized Karhunen-Loève expansion. Hybrid algorithms show a faster convergence towards the global minimum than the original global methods and therefore represent a viable option for shape design optimization. Moreover, FSA shows a better effectiveness compared to the other global algorithm (DPSO and DIRECT), allowing for good expectations for its further improvement with a local hybridization, for the future work.

The main idea of this paper is the application of the material derivative (or speed) method (Zolesio [8]) for a shape optimization problem in the electrochemical machining. We develop the material derivative method for the optimal shape design for systems described by a variational inequality. We introduce a penalty method for the problem and discuss a numerical method using the finite element method.

The main idea of this paper is the application of the material derivative (or speed) method (Zolesio [8]) for a shape optimization problem in the electrochemical machining. We develop the material derivative method for the optimal shape design for systems described by a variational inequality. We introduce a penalty method for the problem and discuss a numerical method using the finite element method.

A new optimization problem of controlling the contact pressurep is presented. We seek the minimum of the maximum contact pressurep max under the following conditions: (a) the contact pressure should satisfy the inequalityp ≥ 0 as well as the controlling conditionχ = v(x) p max −p(x) ≥ 0, wherev(x) is the controller function; (b) the gapd between two bodies should be positive or zerod ≥ 0 after deformation; (c) at any possible contact point the conditionpd = 0 should be satisfied and the body that is capable of rigid body motion should be in equilibrium. If the gapd = d(p, Δh) is a linear function of both the pressurep and the contour changeΔh, then the optimization problem is a linear programming problem of restricted basis exchange. Three algorithms are presented for the solution of this problem. Finally, numerical examples will demonstrate the controlling technique for the shape optimization problem of a roller bearing.

A method to simulate the interactions between objects of a mechanism is described. The method can simulate planar kinematic chains of any length. The same method is used with modifications to generate the geometry of one object of a kinematic pair given the required functional relationship and the geometry of the other object. The planar contour shape of each object

Sommario Le vele di una imbarcazione sono sottoposte a grandi spostamenti a causa della loro natura altamente flessibile, per tale motivo, la forma che assumono quando sono sottoposte alla forza del vento è differente da quella di progetto stabilita dal velaio. Nel lavoro gli autori propongono un metodo basato sull'utilizzo della tecnica fotogrammetrica per il rilievo in navigazione di vele in vera grandezza. L'utilizzo di tecniche ottiche di Reverse Engineering consente, infatti, la ricostruzione tridimensionale del modello dell'intera vela. Vengono costruiti i modelli CAD delle vele di un'imbarcazione di classe Meteor in condizioni di navigazione (flying shape) e in condizioni di progetto (design shape) che sono analizzati con metodi CFD. Abstract The sails of a vessel are subjected to large displacements due to their highly flexible nature; therefore, the form they take when they are subjected to the force of the wind project is different from that established by the sailmaker. In the work the authors propose a method based on the use of photogrammetric techniques for the relief of sails in navigation in real size. The use of optical techniques of Reverse Engineering allows, in fact, three-dimensional reconstruction model of the entire wing. CAD models of the sails of a boat in the Meteor-class are built in surfing conditions (flying shape) and in design conditions (design, shape) and are analyzed by CFD methods. Parole chiave: fotogrammetria, vele, flying shape, design shape, CFD. 1. INTRODUZIONE La vela è una superficie di tela o di sottile e robusto materiale sintetico di forma tale che, utilizzando la forza del vento, genera propulsione. Al fine di realizzare geometrie che ottimizzino le performance dell'imbarcazione, esistono particolari software che consentono al velaio di disegnare la vela con una corretta curvatura, originando la sua design shape cioè la sua forma di progetto. Per ottenere una valutazione del comportamento aerodinamico delle vele progettate, queste possono essere sottoposte ad una analisi CFD, la quale, tuttavia, può fornire previsioni di prestazioni inesatte a causa di una differenza non sempre trascurabile tra la forma a riposo delle vele e quella sotto carico o flying shape, poiché le superfici veliche sono sottoposte a grandi spostamenti a causa della loro natura altamente flessibile.

Coastal erosion is and will be an increasing major environmental issue. We apply shape optimization techniques to the design of coastal structures such as breakwaters, groins and other innovative shapes. Ac-tually, we compute the solution of a boundary value problem describing the water waves scattered by the structure and modify accordingly its shape, in order to minimize a pre-defined cost function taking into account the strength (energy) of the waterwaves. The optimization procedure relies on a new global semi-deterministic algorithm, able to pursue beyond local minima.

1. Introduction Noise generated by turbulent boundary layers near the trailing edge of lifting surfaces continues to pose a challenge for many applications. Much of the previous work on this topic has focused on development of accurate computational methods for the prediction of ...

The state of the art presented here has been established by the participants of this European “Smart systems” network. It reflects their major examination of the three fundamental areas of modeling, optimization and control, and numerical simulation. The investigation of the modeling consists in studing the appropriate models for linear and nonlinear coupling effects, for new composite structures (with their nonlinearities induced by hysteresis, phase transitions, contact or presence of cracks) and the associated time-dependent equations. The exploration in Optimization and Control concern theoretical questions on exact controllability, stabilization, active, passive, hybrid vibration control, optimal shape design (such as the best location of a pattern of sensors, actuators, techniques for nondestructive damage detection, etc.) and practical questions about the robustness and accuracy of the design control systems. Regarding the numerical simulation, two kinds of research have to b...

Fillets are usually the most critical regions in mechanical parts especially under fatigue loading, considering that an increase in the maximum stress level considerably shortens the fatigue life of a part. The aim of this study is to find the best shape for a fillet in a shouldered shaft or plate so that the maximum equivalent stress has the lowest possible value. Optimization is achieved using a stochastic global search algorithm called the direct search simulated annealing. The boundary is defined using spline curves passing through a number of key points. The method is also applicable to shape optimization problems in which geometric constraints are imposed and, for this reason, tangential stress is not uniform along the optimal fillet boundary. Optimal shapes are obtained for flat and round bars subject to axial, bending, torsional, or combined loads. The results show that stress concentration factors close to one can be achieved even for bars with significant variations in cro...

Optimal shape design of interior permanent-magnet (IPM) synchronous motor has large effect in reducing the torque pulsation of the motor. However, the shape design variations should be feasible and manufacturable. In this research, optimal shape is obtained by drilling small circular holes in rotor. Optimal position and radius of these holes are found to effectively suppress the torque pulsation of IPM motor-drive on different steady-state and load conditions. A coupled magnetic field, electrical circuit, and mechanical system program is developed for the optimization purpose. Time stepping finite element method is used for the magnetic field analysis. The optimal design has been evaluated at different operating conditions, which shows good improvement in all load conditions. The optimal design also shows improvement in the field weakening region for high speed operation

Coastal erosion is and will be an increasing major environmental issue. We apply shape optimization techniques to the design of coastal structures such as breakwaters, groins and other innovative shapes. Actually, we compute the solution of a boundary value problem describing the water waves scattered by the structure and modify accordingly its shape, in order to minimize a pre-defined cost function taking into account the strength (energy) of the waterwaves. The optimization procedure relies on a new global semi-deterministic algorithm, able to pursue beyond local minima.

The current study is related to the issue of computer-aided reverse engineering. Although the proposed technique has been suggested and adopted for the image-based planar objects, it is extendable to the objects in three dimensions (3D) with some modifications. The objective of the present study is to provide a robust and automated solution and methodology for the applications of reverse