Optimization of dynamic response using a monolithic-time formulation

The design of systems for dynamic response may involve constraints that need to be satisfied over an entire time interval or objective functions evaluated over the interval. Efficiently performing the constrained optimization is challenging, since the typical response is implicitly linked to the design variables through a numerical integration of the governing differential equations. Evaluating constraints is costly, as is the determination of sensitivities to variations in the design variables. In this paper, we investigate the application of a temporal spectral element method to the optimization of transient and time-periodic responses of fundamental engineering systems. Through the spectral discretization, the response is computed globally, thereby enabling a more explicit connection between the response and design variables and facilitating the efficient computation of response sensitivities. Furthermore, the response is captured in a higher order manner to increase analysis accuracy. Two applications of the coupling of dynamic response optimization with the temporal spectral element method are demonstrated. The first application, a one-degree-of-freedom, linear, impact absorber, is selected from the auto industry, and tests the ability of the method to treat transient constraints over a large-time interval. The second application, a related mass-spring-damper system, shows how the method can be used to obtain work and amplitude optimal time-periodic control force subject to constraints over a periodic time interval. This research was performed while the first author held a National Research Council Research Associateship Award at the Air Force Research Laboratory. An early version of this paper was presented at the 46th AIAA Aerospace Sciences Meeting and Exhibit, Jan 7–10, 2008, Reno, Nevada.     

Approximate probabilistic optimization using exact-capacity-approximate-response-distribution (ECARD)

Probabilistic structural design deals with uncertainties in response (e.g. stresses) and capacity (e.g. failure stresses). The calculation of the structural response is typically expensive (e.g., finite element simulations), while the capacity is usually available from tests. Furthermore, the random variables that influence response and capacity are often disjoint. In previous work we have shown that this disjoint property can be used to reduce the cost of obtaining the probability of failure via Monte Carlo simulations. In this paper we propose to use this property for an approximate probabilistic optimization based on exact capacity and approximate response distributions (ECARD). In Approximate Probabilistic Optimization Using ECARD, the change in response distribution is approximated as the structure is re-designed while the capacity distribution is kept exact, thus significantly reducing the number of expensive response simulations. ECARD may be viewed as an extension of SORA (Sequential Optimization and Reliability Assessment), which proceeds with deterministic optimization iterations. In contrast, ECARD has probabilistic optimization iterations, but in each iteration, the response distribution is approximated so as not to require additional response calculations. The use of inexpensive probabilistic optimization allows easy incorporation of system reliability constraints and optimal allocation of risk between failure modes. The method is demonstrated using a beam problem and a ten-bar truss problem. The former allocates risk between two different failure modes, while the latter allocates risk between members. It is shown that ECARD provides most of the improvement from risk re-allocation that can be obtained from full probabilistic optimization.     

Honeycomb Wachspress finite elements for structural topology optimization

Traditionally, standard Lagrangian-type finite elements, such as linear quads and triangles, have been the elements of choice in the field of topology optimization. However, finite element meshes with these conventional elements exhibit the well-known “checkerboard” pathology in the iterative solution of topology optimization problems. A feasible alternative to eliminate such long-standing problem consists of using hexagonal (honeycomb) elements with Wachspress-type shape functions. The features of the hexagonal mesh include two-node connections (i.e. two elements are either not connected or connected by two nodes), and three edge-based symmetry lines per element. In contrast, quads can display one-node connections, which can lead to checkerboard; and only have two edge-based symmetry lines. In addition, Wachspress rational shape functions satisfy the partition of unity condition and lead to conforming finite element approximations. We explore the Wachspress-type hexagonal elements and present their implementation using three approaches for topology optimization: element-based, continuous approximation of material distribution, and minimum length-scale through projection functions. Examples are presented that demonstrate the advantages of the proposed element in achieving checkerboard-free solutions and avoiding spurious fine-scale patterns from the design optimization process.     

Uniform strength for large deflections of cantilever beams under end point load

Analysis is conducted for slender beams with a varying cross-section under large non-linear elastic deformation. A thickness variation function is derived to achieve optimal - constant maximum bending stress distribution along the beam for inclined end load of arbitrary direction. Closed form solutions are derived for the large deflections that correspond to the various loading conditions. The analysis is repeated for a beam with optimally varying width (for arbitrary end force) and the width variation function is also determined.     

Topology optimization of structures with integral compliant mechanisms for mid-frequency response

The purpose of this paper is to present a method for developing new truss-like sandwich structures that exhibit desirable mid-frequency vibratory characteristics. Specifically, a genetic algorithm optimization routine is used to determine candidate small scale structural topologies, i.e. unit cells, that may be used in the design of larger scale periodic sandwich structures. This multi-scale procedure is demonstrated starting with several unit cell topology optimization examples. From these examples a specific optimal unit cell is selected for further investigation and integration into a periodic sandwich beam. Computational results indicate that the proposed optimization approach is effective when used to design new structures for reduced mid-frequency vibratory response.     

Optimal hole shape for minimum stress concentration using parameterized geometry models

The goal of this work is to obtain optimal hole shape for minimum stress concentration in two-dimensional finite plates using parameterized geometry models. The boundary shape for a hole is described by two families of smooth curves: one is a “generalized circular” function with powers as two parameters; the other one is a “generalized elliptic” function a and b are ellipse axes) with powers as two parameters and one of the ellipse axes as the third parameter. Special attention is devoted to the practicability of parameterized equations and the corresponding optimal results under the condition with and without the curvature radius constraint. A number of cases were examined to test the effectiveness of the parameterized equations. The numerical examples show that extremely good results can be obtained under the conditions with and without curvature radius constraint, as compared to the known solutions in the literature. The geometries of the optimized holes are presented in a form of compact parametric functions, which are suitable for use and test by designers. It is anticipated that the implementation of the suggested parameterized equations would lead to considerable improvements in optimizing hole shape with high quality.     

Extraction of genomic DNA and detection of single nucleotide polymorphism genotyping utilizing an integrated magnetic bead-based microfluidic platform

This study presents a new magnetic bead-based microfluidic platform, which integrates three major modules for rapid leukocytes purification, genomic DNA (gDNA) extraction and fast analysis of genetic gene. By utilizing microfluidic technologies and magnetic beads conjugated with CD_15/45 antibodies, leukocytes in a human whole blood sample can be first purified and concentrated, followed by extraction of gDNA utilizing surface-charge switchable, DNA-specific, magnetic beads in the lysis solution. Then, specific genes associated with genetic diseases can be amplified by an on-chip polymerase chain reaction (PCR) process automatically. The whole pretreatment process including the leukocytes purification and gDNA extraction can be performed in an automatic fashion with the incorporation of the built bio-separators consisting of microcoils array within less than 20 min. The detection of single nucleotide polymorphism (SNP) genotyping of methylenetetra-hydrofolate reductase (MTHFR) C677T region associated with an increased risk of genetic diseases was further performed to demonstrate the capability of the proposed system. The extracted gDNA can be transported into a micro PCR chamber for on-chip fast nucleic acid amplification of detection genes with minimum human intervention. Hence, the developed system may provide a powerful automated platform for pretreatment of human leukocytes, gDNA extraction and fast analysis of genetic gene.     

Adaptive sorting: an information theoretic perspective

We present two algorithms that are near optimal with respect to the number of inversions present in the input. One of the algorithms is a variation of insertion sort, and the other is a variation of merge sort. The number of comparisons performed by our algorithms, on an input sequence of length n that has I inversions, is at most . Moreover, both algorithms have implementations that run in time . All previously published algorithms require at least comparisons for some c > 1. M. L. Fredman was supported in part by NSF grant CCR-9732689.     

Relational structures model of concurrency

The paper deals with the foundations of concurrency theory. We show how structurally complex concurrent behaviours can be modelled by relational structures (X, ¨, \sqsubset){(X, \diamondsuit, \sqsubset)} , where X is a set (of event occurrences), and ¨{\diamondsuit} (interpreted as commutativity) and \sqsubset{\sqsubset} (interpreted as weak causality) are binary relations on X. The paper is a continuation of the approach initiated in Gaifman and Pratt (Proceedings of LICS’87, pp 72–85, 1987), Lamport (J ACM 33:313–326, 1986), Abraham et al. (Semantics for concurrency, workshops in computing. Springer, Heidelberg, pp 311–323, 1990) and Janicki and Koutny (Lect Notes Comput Sci 506:59–74, 1991), substantially developed in Janicki and Koutny (Theoretical Computer Science 112:5–52, 1993) and Janicki and Koutny (Acta Informatica 34:367–388, 1997), and recently generalized in Guo and Janicki (Lect Notes Comput Sci 2422:178–191, 2002) and Janicki (Lect Notes Comput Sci 3407:84–98, 2005). For the first time the full model for the most general case is given.     

Variations for the <Emphasis Type="Italic">Q</Emphasis>- and <Emphasis Type="Italic">H</Emphasis>-factors in the polar decomposition

In this paper, the variations of both subunitary polar factors and Hermitian positive semidefinite polar factors in the polar decomposition are studied. New perturbation bounds of both polar factors are given without the restriction that A and its perturbed matrix à have the same rank. These improve recent results.