Stochastic free vibration analyses of composite shallow doubly curved shells – A Kriging model approach

This paper presents the Kriging model approach for stochastic free vibration analysis of composite shallow doubly curved shells. The finite element formulation is carried out considering rotary inertia and transverse shear deformation based on Mindlin’s theory. The stochastic natural frequencies are expressed in terms of Kriging surrogate models. The influence of random variation of different input parameters on the output natural frequencies is addressed. The sampling size and computational cost is reduced by employing the present method compared to direct Monte Carlo simulation. The convergence studies and error analysis are carried out to ensure the accuracy of present approach. The stochastic mode shapes and frequency response function are also depicted for a typical laminate configuration. Statistical analysis is presented to illustrate the results using Kriging model and its performance.     

Material design and development: From classical thermodynamics to CALPHAD and ICME approaches

This paper presents an overview and examples of material design and development using (1) classical thermodynamics; (2) CALPHAD (calculation of phase diagrams) modeling; and (3) Integrated Computational Materials Engineering (ICME) approaches. Although the examples are given in lightweight aluminum and magnesium alloys for structural applications, the fundamental methodology and modeling principles are applicable to all materials and engineering applications. The examples in this paper have demonstrated the effectiveness and limitations of classical thermodynamics in solving specific problems (such as nucleation during solidification and solid-state precipitation in aluminum alloys). Computational thermodynamics and CALPHAD modeling, when combined with critical experimental validation, have been used to guide the selection and design of new magnesium alloys for elevated-temperature applications. The future of material design and development will be based on a holistic ICME approach. However, key challenges exist in many aspects of ICME framework, such as the lack of diffusion/mobility databases for many materials systems, limitation of current microstructural modeling capability and integration tools for simulation codes of different length scales.     

Optimal shift partitioning of pharmacies

The pharmacy service requires that some pharmacies are always available and shifts have to be organized: a shift corresponds to a subset of pharmacies that must be open 24 hours a day on a particular week. Under the requirement that each pharmacy belongs to exactly one shift and the assumption that users minimize the distance to the closest open pharmacy during each shift, we want to determine a partition of the pharmacies into a given number of shifts, such that the total distance covered by users is minimized. It may be also required that shift cardinalities are balanced. We discuss different versions and the related computational complexity, showing that the problem is NP-hard in general. A set packing formulation is presented and solved by branch-and-price, together with a fast solution technique based on a tabu search. They have been applied to real and random instances showing that (i) the set packing formulation is very tight and often exhibits no integrality gap; (ii) the branch-and-price solves problems of practical relevance to optimality in a reasonable amount of time (order of minutes); (iii) the tabu search finds optimal or near-optimal solutions in order of seconds.     

Ready, Set, Go! The Voronoi diagram of moving points that start from a line

It is an outstanding open problem of computational geometry to prove a near-quadratic upper bound on the number of combinatorial changes in the Voronoi diagram of points moving at a common constant speed along linear trajectories in the plane. In this note we observe that this quantity is Θ(n²) if the points start their movement from a common line.     

Numerical solution for shape optimization of an impactor penetrating into a semi-infinite target

The shape of the impactor with the maximum depth of penetration (DOP) for a given impact velocity is found using a numerical procedure for solving a corresponding non-classical variational problem. It is shown that the optimum shape in a general case is close to a blunt cone. The variation of the optimal shape of the impactor and the dependence of the DOP vs. the initial (impact) velocity and friction coefficient is studied. The analysis is performed also for optimal conical impactors.     

The complexity of economic equilibria for house allocation markets

We prove NP-completeness of deciding the existence of an economic equilibrium in so-called house allocation markets. House allocation markets are markets with indivisible goods in which every agent holds exactly one copy of some good.     

Optimal Solutions for the Temporal Precedence Problem

Abstract. In this paper we refer to the Temporal Precedence Problem on Pure Pointer Machines . This problem asks for the design of a data structure, maintaining a set of stored elements and supporting the following two operations: insert and precedes . The operation insert (a) introduces a new element a in the structure, while the operation precedes (a,b) returns true iff element a was inserted before element b temporally. In [11] a solution was provided to the problem with worst-case time complexity O (log log n ) per operation and O(n log log n) space, where n is the number of elements inserted. It was also demonstrated that the precedes operation has a lower bound of Ω (log log n ) for the Pure Pointer Machine model of computation. In this paper we present two simple solutions with linear space and worst-case constant insertion time. In addition, we describe two algorithms that can handle the precedes (a,b) operation in O (log log d ) time, where d is the temporal distance between the elements a and b .     

Rectilinear steiner tree heuristics and minimum spanning tree algorithms using geographic nearest neighbors

We study the application of the geographic nearest neighbor approach to two problems. The first problem is the construction of an approximately minimum length rectilinear Steiner tree for a set ofn points in the plane. For this problem, we introduce a variation of a subgraph of sizeO(n) used by YaO [31] for constructing minimum spanning trees. Using this subgraph, we improve the running times of the heuristics discussed by Bern [6] fromO(n ² log n) toO(n log² n). The second problem is the construction of a rectilinear minimum spanning tree for a set ofn noncrossing line segments in the plane. We present an optimalO(n logn) algorithm for this problem. The rectilinear minimum spanning tree for a set of points can thus be computed optimally without using the Voronoi diagram. This algorithm can also be extended to obtain a rectilinear minimum spanning tree for a set of nonintersecting simple polygons.The results in this paper are a part of Y. C. Yee's Ph.D. thesis done at SUNY at Albany. He was supported in part by NSF Grants IRI-8703430 and CCR-8805782. S. S. Ravi was supported in part by NSF Grants DCI-86-03318 and CCR-89-05296.     

The rank one mixed μ problem and ‘kharitonov-type’ analysis

The general mixed μ problem has been shown to be NP hard, so that the exact solution of the general problem is computationally intractable, except for small problems. In this paper we consider not the general problem, but a particular special case of this problem, the rank one mixed μ problem. We show that for this case the mixed μ problem is equivalent to its upper bound (which is convex), and it can in fact be computed easily (and exactly). This special case is shown to be equivalent to the so-called ‘affine parameter variation’ problem (for a polynomial with perturbed coefficients) which has been examined in detail in the literature, and for which several celebrated ‘Kharitonov-type’ results have been proven.     

Computational complexity of queries based on itemsets

We investigate determining the exact bounds of the frequencies of conjunctions based on frequent sets. Our scenario is an important special case of some general probabilistic logic problems that are known to be intractable. We show that despite the limitations our problems are also intractable, namely, we show that checking whether the maximal consistent frequency of a query is larger than a given threshold is NP-complete and that evaluating the Maximum Entropy estimate of a query is PP-hard. We also prove that checking consistency is NP-complete.