Search results for "upper bound"
showing 10 items of 12 documents
Long-range interactions in 1D heterogeneous solids with uncertainty
2013
Abstract In this paper, the authors aim to analyze the response of a one-dimensional non-local elastic solid with uncertain Young's modulus. The non-local effects are represented as long-range central body forces between non-adjacent volume elements. Following a non-probabilistic approach, the fluctuating elastic modulus of the material is modeled as an interval field. The analysis is conducted resorting to a novel formulation that confines the overestimation effect involved in interval models. Approximate closed-form expressions are derived for the bounds of the interval displacement field.
One-dimensional heterogeneous solids with uncertain elastic modulus in presence of long-range interactions: Interval versus stochastic analysis
2013
The analysis of one-dimensional non-local elastic solids with uncertain Young's modulus is addressed. Non-local effects are represented as long-range central body forces between non-adjacent volume elements. For comparison purpose, the fluctuating elastic modulus of the material is modeled following both a probabilistic and a non-probabilistic approach. To this aim, a novel definition of the interval field concept, able to limit the overestimation affecting ordinary interval analysis, is introduced. Approximate closed-form expressions are derived for the bounds of the interval displacement field as well as for the mean-value and variance of the stochastic response.
Time-dependent asymmetric traveling salesman problem with time windows: Properties and an exact algorithm
2019
Abstract In this paper, we deal with the Time-Dependent Asymmetric Traveling Salesman Problem with Time Windows. First, we prove that under special conditions the problem can be solved as an Asymmetric Traveling Salesman Problem with Time Windows, with suitable-defined time windows and (constant) travel times. Second, we show that, if the special conditions do not hold, the time-independent optimal solution provides both a lower bound and (eventually) an upper bound with a worst-case guarantee for the Time-Dependent Asymmetric Traveling Salesman Problem with Time Windows. Finally, a branch-and-bound algorithm is presented and tested on a set of 4800 instances. The results have been compared…
Lower and Upper Probability Bounds for Some Conjunctions of Two Conditional Events
2018
In this paper we consider, in the framework of coherence, four different definitions of conjunction among conditional events. In each of these definitions the conjunction is still a conditional event. We first recall the different definitions of conjunction; then, given a coherent probability assessment (x, y) on a family of two conditional events \(\{A|H,B|K\}\), for each conjunction \((A|H) \wedge (B|K)\) we determine the (best) lower and upper bounds for the extension \(z=P[(A|H) \wedge (B|K)]\). We show that, in general, these lower and upper bounds differ from the classical Frechet-Hoeffding bounds. Moreover, we recall a notion of conjunction studied in recent papers, such that the res…
An upper bound for nonlinear eigenvalues on convex domains by means of the isoperimetric deficit
2010
We prove an upper bound for the first Dirichlet eigenvalue of the p-Laplacian operator on convex domains. The result implies a sharp inequality where, for any convex set, the Faber-Krahn deficit is dominated by the isoperimetric deficit.
The DMT of Real and Quaternionic Lattice Codes and DMT Classification of Division Algebra Codes
2021
In this paper we consider the diversity-multiplexing gain tradeoff (DMT) of so-called minimum delay asymmetric space-time codes. Such codes are less than full dimensional lattices in their natural ambient space. Apart from the multiple input single output (MISO) channel there exist very few methods to analyze the DMT of such codes. Further, apart from the MISO case, no DMT optimal asymmetric codes are known. We first discuss previous criteria used to analyze the DMT of space-time codes and comment on why these methods fail when applied to asymmetric codes. We then consider two special classes of asymmetric codes where the code-words are restricted to either real or quaternion matrices. We p…
Optimality conditions for shakedown design of trusses
1995
This paper deals with optimal shakedown design of truss structures constituted by elastic perfectly plastic material. The design problem is formulated by means of a statical approach on the grounds of the shakedown lower bound theorem, and by means of a kinematical approach on the grounds of the shakedown upper bound theorem. In both cases two different types of design problem are formulated: one searches for the minimum volume design whose shakedown limit load is assigned; the other searches for the maximum shakedown limit load design whose volume is assigned. The Kuhn-Tucker equations of the four problems here above mentioned are found by utilizing a variational approach; these equations …
Limit analysis of arch-beam structures by dynamic programming
1974
We study one-dimensional structures like arch-beams in the limit state of plastic collapse, on the ground of a two-dimensional yielding surface (bending moment and normal generalized stress). The proposed method, which is able to give a numerical solution of the problem of finding the limit load, rests on the upper bound theorem of limit analysis and uses dynamic programming. We examine also some questions linked with numerical procedures. A future work devoted to applications will complete the treatment.
Optimal shakedown design of beam structures
1994
The optimal design of plane beam structures made of elastic perfectly plastic material is studied according to the shakedown criterion. The design problem is formulated by means of a statical approach on the grounds of the shakedown lower bound theorem, and by means of a kinematical approach on the grounds of the shakedown upper bound theorem. In both cases two different types of design problems are formulated: one searches for the minimum volume design whose shakedown limit load is assigned; the other searches for the design of the assigned volume whose shakedown limit load is maximum. The optimality conditions of the four problems above are found by the use of a variational approach; such…
Shakedown optimal design of reinforced concrete structures by evolution strategies
2000
Approaches the shakedown optimal design of reinforced concrete (RC) structures, subjected to variable and repeated external quasi‐static actions which may generate the well‐known shakedown or adaptation phenomenon, when constraints are imposed on deflection and/or deformation parameters, in order to simulate the limited flexural ductility of the material, in the presence of combined axial stress and bending. Within this context, the classical shakedown optimal design problem is revisited, using a weak upper bound theorem on the effective plastic deformations. For this problem a new computational algorithm, termed evolution strategy, is herein presented. This algorithm, derived from analogy …