scholarly journals Optimized lattice-based metamaterials for elastostatic cloaking

2021 ◽  
Vol 477 (2253) ◽  
pp. 20210418
Author(s):  
E. D. Sanders ◽  
M. A. Aguiló ◽  
G. H. Paulino
Keyword(s):  
Objective Function ◽  
Uniaxial Tension ◽  
Weighted Least Squares ◽  
Elliptical Hole ◽  
Adjoint System ◽  
System Optimization ◽  
Small Region ◽  
Shear Loading ◽  
Stiffness Properties ◽  
Stiffness Characteristics

An optimization-based approach is proposed to design elastostatic cloaking devices in two-dimensional (2D) lattices. Given an elastic lattice with a defect, i.e. a circular or elliptical hole, a small region (cloak) around the hole is designed to hide the effect of the hole on the elastostatic response of the lattice. Inspired by the direct lattice transformation approach to elastostatic cloaking in 2D lattices, the lattice nodal positions in the design region are obtained using a coordinate transformation of the reference (undisturbed) lattice nodes. Subsequently, additional connectivity (i.e. a ground structure) is defined in the design region and the stiffness properties of these elements are optimized to mimic the global stiffness characteristics of the reference lattice. A weighted least-squares objective function is proposed, where the weights have a physical interpretation—they are the design-dependent coefficients of the design lattice stiffness matrix. The formulation leads to a convex objective function that does not require a solution to an additional adjoint system. Optimization-based cloaks are designed considering uniaxial tension in multiple directions and are shown to exhibit approximate elastostatic cloaking, not only when subjected to the boundary conditions they were designed for but also for uniaxial tension in directions not used in design and for shear loading.

Wave Energy Converter Array Optimization: A Review of Current Work and Preliminary Results of a Genetic Algorithm Approach Introducing Cost Factors

2015 ◽  
Author(s):  
Chris Sharp ◽  
Bryony DuPont
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Wave Energy ◽  
Reference Model ◽  
A Priori ◽  
System Optimization ◽  
Primary Energy ◽  
Close Relative ◽  
Cost Information ◽  
Multiple Test

Currently, ocean wave energy is a novel means of electricity generation that is projected to potentially serve as a primary energy source in coastal areas. However, for wave energy converters (WECs) to be applicable on a scale that allows for grid implementation, these devices will need to be placed in close relative proximity to each other. From what’s been learned in the wind industry of the U.S., the placement of these devices will require optimization considering both cost and power. However, current research regarding optimized WEC layouts only considers the power produced. This work explores the development of a genetic algorithm (GA) that will create optimized WEC layouts where the objective function considers both the economics involved in the array’s development as well as the power generated. The WEC optimization algorithm enables the user to either constrain the number of WECs to be included in the array, or allow the algorithm to define this number. To calculate the objective function, potential arrays are evaluated using cost information from Sandia National Labs Reference Model Project, and power development is calculated such that WEC interaction affects are considered. Results are presented for multiple test scenarios and are compared to previous literature, and the implications of a priori system optimization for offshore renewables are discussed.

scholarly journals Passive Target Localization Problem Based on Improved Hybrid Adaptive Differential Evolution and Nelder-Mead Algorithm

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Maja B. Rosić ◽  
Mirjana I. Simić ◽  
Predrag V. Pejović
Keyword(s):  
Differential Evolution ◽  
Objective Function ◽  
Weighted Least Squares ◽  
Target Localization ◽  
Localization Problem ◽  
Ml Estimation ◽  
Comparison Results ◽  
Adaptive Differential Evolution ◽  
Highly Nonlinear ◽  
Wide Range

This paper considers a passive target localization problem in Wireless Sensor Networks (WSNs) using the noisy time of arrival (TOA) measurements, obtained from multiple receivers and a single transmitter. The objective function is formulated as a maximum likelihood (ML) estimation problem under the Gaussian noise assumption. Consequently, the objective function of the ML estimator is a highly nonlinear and nonconvex function, where conventional optimization methods are not suitable for this type of problem. Hence, an improved algorithm based on the hybridization of an adaptive differential evolution (ADE) and Nelder-Mead (NM) algorithms, named HADENM, is proposed to find the estimated position of a passive target. In this paper, the control parameters of the ADE algorithm are adaptively updated during the evolution process. In addition, an adaptive adjustment parameter is designed to provide a balance between the global exploration and the local exploitation abilities. Furthermore, the exploitation is strengthened using the NM method by improving the accuracy of the best solution obtained from the ADE algorithm. Statistical analysis has been conducted, to evaluate the benefits of the proposed modifications on the optimization performance of the HADENM algorithm. The comparison results between HADENM algorithm and its versions indicate that the modifications proposed in this paper can improve the overall optimization performance. Furthermore, the simulation shows that the proposed HADENM algorithm can attain the Cramer-Rao lower bound (CRLB) and outperforms the constrained weighted least squares (CWLS) and differential evolution (DE) algorithms. The obtained results demonstrate the high accuracy and robustness of the proposed algorithm for solving the passive target localization problem for a wide range of measurement noise levels.

Optimisation of Periodic Structure Subject to Parametric Alteration

2007 ◽  
Author(s):  
Yu-Ming Chen ◽  
Teng-Yuan Wu ◽  
Lai-Sheng Chen
Keyword(s):  
Computational Model ◽  
Objective Function ◽  
Periodic Structure ◽  
Ritz Method ◽  
Dynamic Responses ◽  
Cantilever Beams ◽  
Antenna Structure ◽  
Stiffness Properties ◽  
Structure Vibration ◽  
Lumped Masses

The dynamic responses of repetitive system are relatively sensitive to modification where slight changes in the geometric parameters can destroy the structure symmetry. This paper treats antenna structure as a study example and investigates its vibration behaviors subject to parametric changes. An analytically derived computational model based on the Rayleigh-Ritz method for modeling the periodic structure is produced. This is particularly useful in treating continuous structure with non-uniform mass and/or stiffness properties. The antenna structure is represented by a number of cantilever beams elevated at an angle and built-in into a hub and coupled by springs. This work performs two optimizations separately: (a) by optimizing the location of equally weighted lumped masses along each cantilever beams and, (b) optimizing the location of springs. Effects of altering these parameters with the objective function of minimizing the structure vibration is addressed in this work.

scholarly journals Derivation of the Adjoint Drift Flux Equations for Multiphase Flow

Fluids ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 31 ◽  
Author(s):  
Shenan Grossberg ◽  
Daniel S. Jarman ◽  
Gavin R. Tabor
Keyword(s):  
Multiphase Flow ◽  
Objective Function ◽  
Settling Velocity ◽  
Flow Problem ◽  
Adjoint System ◽  
Drift Flux ◽  
Adjoint Approach ◽  
Continuous Adjoint ◽  
First Time ◽  
Mathematical Derivation

The continuous adjoint approach is a technique for calculating the sensitivity of a flow to changes in input parameters, most commonly changes of geometry. Here we present for the first time the mathematical derivation of the adjoint system for multiphase flow modeled by the commonly used drift flux equations, together with the adjoint boundary conditions necessary to solve a generic multiphase flow problem. The objective function is defined for such a system, and specific examples derived for commonly used settling velocity formulations such as the Takacs and Dahl models. We also discuss the use of these equations for a complete optimisation process.

scholarly journals Stiffness analysis of glued connection of the timber-concrete structure

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Jana Daňková ◽  
Pavel Mec ◽  
Tereza Majstríková
Keyword(s):  
Mathematical Analysis ◽  
Composite Structure ◽  
Concrete Structure ◽  
3D Model ◽  
Deformation Behaviour ◽  
Element Model ◽  
Shear Loading ◽  
Design Parameters ◽  
Building Structures ◽  
Stiffness Characteristics

Abstract This paper presents results of experimental and mathematical analysis of stiffness characteristics of a composite timber-concrete structure. The composite timberconcrete structure presented herein is non-typical compared to similar types of building structures. The interaction between the timber and concrete part of the composite cross-section is not based on metal connecting elements, but it is ensured by a glued-in perforated mesh made of plywood. The paper presents results of experimental and mathematical analysis for material alternatives of the solution of the glued joint. The slip modulus values were determined experimentally. Data obtained from the experiment evaluated by means of regression analysis. Test results were also used as input data for the compilation of a 3D model of a composite structure by means of the 3D finite element model. On the basis of result evaluation, it can be stated that the stress-deformation behaviour at shear loading of this specific timber-concrete composite structure can be affected by the type of glue used. Parameters of the 3D model of both alternative of the structure represent well the behaviour of the composite structure and the model can be used for predicting design parameters of a building structure.

The Anti-Plane Shear Problem of Two Symmetric Cracks Originating from an Elliptical Hole in 1D Hexagonal Piezoelectric QCs

2014 ◽  
Vol 936 ◽  
pp. 127-135 ◽  
Author(s):  
Juan Yang ◽  
Xing Li
Keyword(s):  
Electric Displacement ◽  
Elliptical Hole ◽  
Shear Loading ◽  
Intensity Factors ◽  
Plane Shear ◽  
Complex Variable Function ◽  
Phonon Field ◽  
Variable Function ◽  
Complex Variable Function Method ◽  
Shear Problem

Using the complex variable function method and the technique of conformal mapping, the fracture mechanics of two symmetric collinear cracks originating from an elliptical hole in a one-dimensional (1D) hexagonal piezoelectric quasicrystals (QCs) are investigated under anti-plane shear loading and electric loading. The crack is assumed to be either electrical impermeable or permeable. The exact solutions in closed-form of the stress intensity factors (SIFs) of the phonon field and the phason field, and the electric displacement intensity factors (EDIFs) are obtained. In the limiting cases, the new results such as Griffith crack, a circular hole with equal two edge cracks and cross crack can be obtained from the present solutions. In the absence of the phason field, the obtainable results in this paper match with the classical results.

The Influence of Internal Friction on the Stability of High Speed Rotors With Anisotropic Supports

1969 ◽  
Vol 91 (4) ◽  
pp. 1105-1113 ◽  
Author(s):  
E. J. Gunter ◽  
P. R. Trumpler
Keyword(s):  
Internal Friction ◽  
High Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Analog Computer ◽  
Three Dimensional Model ◽  
Stiffness Properties ◽  
Stiffness Characteristics ◽  
The Stability ◽  
Internal Rotor

This paper evaluates the stability of the single mass rotor with internal friction on damped, anisotropic supports. The paper shows under what conditions the rotor stability may be improved by an undamped support with anisotropic stiffness properties. A three dimensional model is presented to show the influence of rotor and support stiffness characteristics on stability. Curves are also presented on how support damping may also improve or even reduce rotor stability. An analog computer solution of the governing equations of motion is presented showing the shaft transient motion for various speed ranges, and also plots of the rotor steady state motion are given for various speeds up to and including the stability threshold. The analysis is used to explain many of the experimental observations of B. L. Newkirk concerning stability due to internal rotor friction.

Multi-Objective System Optimization of Engine Crankshafts Using an Integration Approach

2008 ◽  
Author(s):  
Albert Albers ◽  
Noel Leon ◽  
Humberto Aguayo ◽  
Thomas Maier
Keyword(s):  
Genetic Algorithms ◽  
Objective Function ◽  
Computer Aided Design ◽  
Fitness Function ◽  
Computing Time ◽  
System Optimization ◽  
General Strategy ◽  
3D Cad ◽  
Aided Design

The ever increasing computer capabilities allow faster analysis in the field of Computer Aided Design and Engineering (CAD & CAE). CAD and CAE systems are currently used in Parametric and Structural Optimization to find optimal topologies and shapes of given parts under certain conditions. This paper describes a general strategy to optimize the balance of a crankshaft, using CAD and CAE software integrated with Genetic Algorithms (GAs) via programming in Java. An introduction to the groundings of this strategy is made among different tools used for its implementation. The analyzed crankshaft is modeled in commercial parametric 3D CAD software. CAD is used for evaluating the fitness function (the balance) and to make geometric modifications. CAE is used for evaluating dynamic restrictions (the eigen-frequencies). A Java interface is programmed to link the CAD model to the CAE software and to the genetic algorithms. In order to make geometry modifications to our case study, it was decided to substitute the profile of the counterweights with splines from its original “arc-shaped” design. The variation of the splined profile via control points results in an imbalance response. The imbalance of the crankshaft was defined as an independent objective function during a first approach, followed by a Pareto optimization of the imbalance from both correction planes, plus the curvature of the profile of the counterweights as restrictions for material flow during forging. The natural frequency was considered as an additional objective function during a second approach. The optimization process runs fully automated and the CAD program is on hold waiting for new set of parameters to receive and process, saving computing time, which is otherwise lost during the repeated startup of the cad application.

Automobile Active Suspension System Optimization Design Based on Modified Multi-Objective Genetic Algorithm

2012 ◽  
Vol 157-158 ◽  
pp. 1515-1518 ◽  
Author(s):  
Yi Zhang ◽  
Chao Lu ◽  
Hu Zhang
Keyword(s):  
Objective Function ◽  
High Dimension ◽  
Optimization Design ◽  
Single Point ◽  
Active Suspension ◽  
System Optimization ◽  
Suspension System ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Set Up

A dynamic model of automobile active suspension system is established, based on which a high dimension objective model for active suspension system is set up. And through linear combinations, high dimension multi-objective function is translated into a low dimension objective function. The modified NSGAII with single point compound crossover has been adopted to realize the optimization. In the paper, the performance active suspension system can realize integrated optimization. The results show that this way can effectively enhance effect of the automobile active suspension system.

scholarly journals An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip

2015 ◽  
Author(s):  
Marijn Nijenhuis ◽  
J. P. Meijaard ◽  
Just L. Herder ◽  
Shorya Awtar ◽  
Dannis M. Brouwer
Keyword(s):  
Three Dimensional ◽  
Beam Element ◽  
Element Analysis ◽  
Cross Sectional ◽  
Flexure Mechanism ◽  
Stiffness Properties ◽  
Spatial Beam ◽  
Discrete Nature ◽  
Stiffness Characteristics

A flexure strip has constraint characteristics, such as stiffness properties and error motions, that limit its performance as a basic constituent of flexure mechanisms. This paper presents a framework for modeling the deformation and stiffness characteristics of general three-dimensional flexure strips that exhibit bending, shear and torsion deformation. The formulation is based on a finite strain discrete spatial beam element with refinements to account for plate-like behavior due to constrained cross-sectional warping. This framework is suited for analytical calculations thanks to the accuracy of the beam element, while its discrete nature allows for easy implementation in numeric software to serve as calculation aid. As case study, a closed-form parametric analytical expression is derived for the lateral support stiffness of a parallel flexure mechanism. This captures the deteriorating support stiffness when the mechanism moves in the intended degree of freedom. By incorporating relevant geometric nonlinearities and a warping constraint stiffening factor, an accurate load-displacement and stiffness expression for the lateral support direction is obtained. This result is verified by nonlinear finite element analysis.

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