Authors: Chang Hong Liu, X.C. Qing, F.Z. Xuan, S.T. Tu

Abstract: According to the non-probabilistic finite element algorithms, the random finite element equations are translated into the interval finite element equations. Firstly, with the concept of confidence interval in the probability, a interval number can be taken as the random variable with the uniform distribution. Secondly, the uniform random Monte Carlo (MC) finite element method and optimization finite element method are presented. Finally, the example shown, when the numbers of random parameters are small, the two algorithms are all effective. But when numbers of random parameters are large, only the uniform random finite element method has the stabilized solving ability.

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Authors: Animesh Agrawal, Chandra Jeet, Siddharth Jaiswal

Abstract: *:* *Optimization* *is* *the* *art* *of* *obtaining* *the* *best* *results* *under* *given* *circumstances.* *In* *design,* *construction* *and* *maintenance* *of* *any* *engineering* *system,* *the* *ultimate* *goal* *is* *either* *to* *minimize* *the* *effort* *required* *or* *to* *maximize* *the* *desired* *benefits.* *The* *various* *processes* *of* *optimization* *come* *under* *the* *subject* *Operation* *Research* *(O.R.).* *O.R.* *one* *of* *the* *branch* *of* *mathematics* *which* *is* *concerned* *which* *the* *application* *of* *scientific* *methods* *and* *techniques* *to* *design* *making* *problems* *and* *establishing* *optimal* *situations.* *In* *this* *project* *we* *aim* *to* *find* *the* *optimum* *design* *of* *a* *hydrodynamics* *bearing* *through* *operations* *research* *techniques.* *The* *two* *methods* *used* *are* *stochastic* *programming* *and* *geometric* *programming.* *The* *existing* *design* *procedure* *treats* *design* *variables* *as* *deterministic* *ones.* *In* *actual* *practice* *due* *to* *manufacturing* *tolerances* *etc.* *design* *variables* *do* *not* *remain* *deterministic* *but* *become* *probabilistic.* *The* *probabilistic* *nature* *of* *these* *should* *be* *given* *proper* *consideration* *while* *designing.* *This* *project* *deals* *with* *an* *approach* *which* *takes* *into* *account* *the* *probabilistic* *nature* *of* *designs* *variables,* *as* *well* *as* *probability* *of* *satisfying* *constraint* *equations.* *Stochastic* *signomial* *geometric* *programming* *has* *been* *used* *for* *optimization.*

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Authors: Jakub Venclovský, Petr Štěpánek, Ivana Laníková

Abstract: It is possible to see various applications of mathematical optimization in civil engineering (structural design, reconstruction of transportation networks etc.) Initially, deterministic approaches have been introduced to solve these problems. But despite their complexity, these approaches are insufficient to comprehend the probabilistic nature of said problems and thus provide only suboptimal solutions. Hence the effort comes to reconsider these deterministic approaches and deal with uncertainties involved in said problems in less straightforward way. The goal of the paper is to present the algorithm for stochastic optimization of design of steel-reinforced concrete cross-section. This algorithm is based on internal cycle of deterministic optimization using reduced gradient method and external cycle of stochastic optimization using regression analysis. Firstly, the deterministic problem is introduced and described. It is followed by the description of uncertainties, which are involved in the process, and stochastic reformulation of the problem. Then the algorithm itself is introduced and the paper ends with presentation of the results of performed calculations.

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