299 research outputs found
Application of the Hughes-LIU algorithm to the 2-dimensional heat equation
An implicit explicit algorithm for the solution of transient problems in structural dynamics is described. The method involved dividing the finite elements into implicit and explicit groups while automatically satisfying the conditions. This algorithm is applied to the solution of the linear, transient, two dimensional heat equation subject to an initial condition derived from the soluton of a steady state problem over an L-shaped region made up of a good conductor and an insulating material. Using the IIT/PRIME computer with virtual memory, a FORTRAN computer program code was developed to make accuracy, stability, and cost comparisons among the fully explicit Euler, the Hughes-Liu, and the fully implicit Crank-Nicholson algorithms. The Hughes-Liu claim that the explicit group governs the stability of the entire region while maintaining the unconditional stability of the implicit group is illustrated
Improvement of normalization methods for eigenvector derivatives
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76868/1/AIAA-11108-459.pd
SQG-Differential Evolution for difficult optimization problems under a tight function evaluation budget
In the context of industrial engineering, it is important to integrate
efficient computational optimization methods in the product development
process. Some of the most challenging simulation-based engineering design
optimization problems are characterized by: a large number of design variables,
the absence of analytical gradients, highly non-linear objectives and a limited
function evaluation budget. Although a huge variety of different optimization
algorithms is available, the development and selection of efficient algorithms
for problems with these industrial relevant characteristics, remains a
challenge. In this communication, a hybrid variant of Differential Evolution
(DE) is introduced which combines aspects of Stochastic Quasi-Gradient (SQG)
methods within the framework of DE, in order to improve optimization efficiency
on problems with the previously mentioned characteristics. The performance of
the resulting derivative-free algorithm is compared with other state-of-the-art
DE variants on 25 commonly used benchmark functions, under tight function
evaluation budget constraints of 1000 evaluations. The experimental results
indicate that the new algorithm performs excellent on the 'difficult' (high
dimensional, multi-modal, inseparable) test functions. The operations used in
the proposed mutation scheme, are computationally inexpensive, and can be
easily implemented in existing differential evolution variants or other
population-based optimization algorithms by a few lines of program code as an
non-invasive optional setting. Besides the applicability of the presented
algorithm by itself, the described concepts can serve as a useful and
interesting addition to the algorithmic operators in the frameworks of
heuristics and evolutionary optimization and computing
Design of Laminated Plates for Maximum Buckling Load
The buckling load of laminated plates having midplane symmetry is maximized for a given total thickness. The thicknesses of the layers are taken as the design variables. Buckling analysis is carried out using the finite element method. The optimality equations are solved by a homotopy method which permits tracing optima as a function of total thickness. It is shown that for any design with a given stacking sequence of ply orientations, there exists a design associated with any other stacking sequence which possesses the same bending stiffness matrix and same total thickness. Hence, from the optimum design for a given stacking sequence, one can directly determine the optimum design for any rearrangement of the ply orientations, and the optimum buckling load is independent of the stacking sequence
Bi-objective optimization of pylon-engine-nacelle assembly: weight vs. tip clearance criterion
Tracking Structural Optima as a Function of Available Resources by a Homotopy Method
Optimization problems are typically solved by starting with an initial estimate and proceeding iteratively to improve it until the optimum is found. The design points along the path from the initial estimate to the optimum are usually of no value. The present work proposes a strategy for tracing a path of optimum solutions parameterized by the amount of available resources. The paper specifically treats the optimum design of a structure to maximize its buckling load. Equations for the optimum path are obtained using Lagrange multipliers, and solved by a homotopy method. The solution path has several branches due to changes in the active constraint set and transitions from unimodal to bimodal solutions. The Lagrange multipliers and second-order optimality conditions are used to detect branching points and to switch to the optimum solution path. The procedure is applied to the design of a foundation which supports a column for maximum buckling load. Using the total available foundation stiffness as a homotopy parameter, a set of optimum foundation designs is obtained
Multiple-Surrogate Approach to Helicopter Rotor Blade Vibration Reduction
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77383/1/AIAA-40291-933.pd
A new LC-MS method for the detection and quantification of hexabromocyclododecane diasteroisomers and tetrabromobisphenol - a flame retardants in environmental samples
A micro-accelerometer MDO benchmark problem
Many optimization and coordination methods for multidisciplinary design optimization (MDO) have been proposed in the last three decades. Suitable MDO benchmark problems for testing and comparing these methods are few however. This article presents a new MDO benchmark problem based on the design optimization of an ADXL150 type lateral capacitive micro-accelerometer. The behavioral models describe structural and dynamic effects, as well as electrostatic and amplification circuit contributions. Models for important performance indicators such as sensitivity, range, noise, and footprint area are presented. Geometric and functional constraints are included in these models to enforce proper functioning of the device. The developed models are analytical, and therefore highly suitable for benchmark and educational purposes. Four different problem decompositions are suggested for four design cases, each of which can be used for testing MDO coordination algorithms. As a reference, results for an all-in-one implementation, and a number of augmented Lagrangian coordination algorithms are given. © 2009 The Author(s)
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