Reliability-based robust multi-objective optimization applied to engineering system design

ABSTRACT

Probabilistic and non-probabilistic methods have been proposed to deal with design problems under uncertainties. Reliability-based design and robust design are probabilistic strategies traditionally used for this purpose. In the present contribution, reliability-based robust design optimization (RBRDO) is formulated as a multi-objective problem considering the interaction of both approaches. The proposed methodology is based on the differential evolution algorithm associated with two strategies to deal with reliability and robustness, respectively, namely inverse reliability analysis and the effective mean concept. This multi-objective optimization problem considers the maximization of reliability and robustness coefficients as additional objective functions. The effectiveness of the methodology is illustrated by two classical test cases and a rotor-dynamics application. The results demonstrate that the proposed methodology is an alternative method to solve RBRDO problems.     

Time dependent behavior of elements combining ultra-high performance fiber reinforced concretes (UHPFRC) and reinforced concrete

Structural elements combining Ultra-High Performance Fiber Reinforced Concretes (UHPFRC) and concrete offer a high potential in view of rehabilitation and modification of existing structures. The investigation of the time-dependent behavior of composite “UHPFRC-concrete” elements is a fundamental step in the determination of durability and serviceability. For this, an experimental program was conducted on large composite “UHPFRC-concrete” beams and a numerical model was validated with the test results. The experimental results and a parametric study performed with the numerical model showed that UHPFRC and normal strength reinforced concrete are compatible in the long-term and that the critical period of composite “UHPFRC-concrete” elements are the first 90 days after the casting of the UHPFRC layer. Thus, the high potential of such composite elements can be exploited also in the long term.     

Multivariate calibration methods applied to the monitoring of the enzymatic synthesis of amipicilin

An integrated semi-continuous rector, with simultaneous crystallization of the antibiotic, is the most promising alternative for the enzymatic synthesis of semi-synthetic penicillins. Closed-loop optimization of the reactor operation requires the measurement of its state variables. An efficient method for on-line monitoring of these variables, i.e., the species concentrations, which is consistent with the dynamics of the process, is presented here. Multivariate calibration has been used to reduce times of analysis in multicomponent systems, and this is the approach of this work. Three multivariate calibration methods are compared for prediction of the concentrations of the components present in the enzymatic synthesis of ampicillin. UV spectra and their first-order derivatives were used as input data for the models. Results showed that all methods (SPA, PCR and PLS) had similar performances for this system. The use of first-order derivatives of the spectra did not improve substantially the performance of the methods. Bench assays of synthesis of ampicillin using immobilized penicillin G acylase (PGA) as catalyst were carried out to validate the methodology. Its results were compared with HPLC analyses. The technique showed to be very accurate for monitoring the concentrations of ampicillin (desired product) and 6-aminopenicillanic acid (6-APA, most expensive substrate), with precision similar to those obtained by HPLC. Prior information of the initial reactor state may be used to improve the estimation of less sensitive components (phenylglycine methyl ester, PGME and phenylglycine, PG). Modifications on the biocatalyst must be made in order to use the proposed automatic sampler when crystallization of products occurs.     

Dynamic breakdown of elements made of hard alloys

The article deals with the fragmentation of hard-alloy wastes with the aid of shock waves. Experimental investigations with explosive fragmentation of mining and cutting tools were carried out. On the basis of the energy approach of fracture mechanics and numerical gas-dynamic calculations the characteristic dimension of fragments after explosion is evaluated. It was established that under complex dynamic loading the crack resistance of tungsten carbide may be higher than in static tests. Translated from Problemy Prochnosti, No. 5, pp. 115–118, May, 1996. The work was carried out with the financial assistance of the Russian Fund for Basic Research.     

Failure analysis of UHPFRC panels subjected to aircraft engine model impact

Using the finite element approach, this paper evaluates the punching resistance of ultra-high performance fiber reinforced concrete (UHPFRC) panels subjected to the impact of an aircraft engine. The models are analyzed using LS-DYNA, a commercially available software program. The structural components of the UHPFRC panels, aircraft engine model, and their contacts are fully modeled. Included in the analysis is material nonlinearity, which considers damage and failure. The analysis results are then verified with the test results. A parametric study with varying fiber contents is carried out to investigate the punching behavior of the UHPFRC panels under aircraft engine impact. The penetration depth, residual velocity of the aircraft engine, scabbing area, and failure mode of various UHPFRC panels are examined. Punching resistance capacities of reinforced concrete (RC) and steel plated concrete (SC) panels are also investigated in this study.     

Hierarchic finite elements for moderately thick to very thin plates

We consider the numerical solution of Reissner-Mindlin plates. The model is widely used for thin to moderately thick plates. Generally low order finite elements (with degree one or two) are used for the approximation. Unfortunately the solution degenerates very rapidly for small thickness (locking phenomenon). Non standard formulations of the problem are usually combined with low order finite elements to weaken or possibly eliminate the locking of the numerical solution. We introduce a family of hierarchic finite elements and we present a set of numerical results for the plate problem in its plain formulation. We show that reliable solutions are achieved for all thicknesses of practical interest by using high order finite elements. Moreover, the hierarchic structure allows a low cost assessment of the quality of the solution.     

Explicit thickness integration for three-dimensional shell elements applied to non-linear analysis

The problem of multilayered degenerated 3-D shell elements for which the numerical integration is performed for each ply is that of the high generation time in non-linear analysis when the number of plies is important. But these elements give accurate results for thin and moderately thick shells, so in order to reduce the generation time explicit thickness integration is investigated. We first write an expansion of the strain-displacement matrix in power series of the thickness variable in order to obtain explicit expressions of the tangent stiffness matrix and internal force vector, appearing in the non-linear formulation. Explicit expressions of non-linear stiffness matrices are presented, using the explicit integration-first approximation. Simple expressions of several matrices, sub-matrices and vectors appearing in the formulation are given here in order to obtain an important computing-time gain. Next, some numerical validation tests comparing the classical element with numerical thickness integration and this one are discussed to prove validity of this formulation.     

Accurate analysis of smoothly modulated AC waveforms applied to the calibration of fluctuating harmonic analyzers

Calibrated harmonic analyzers are required to underpin international regulations regarding harmonic emissions for electrical appliances. A method to accurately analyze waveforms containing smoothly fluctuating harmonics is described. The response of an analyzer to the characterized waveform is considered and a method to calibrate an analyzer is presented.     

Reliability-based optimization of direct and indirect LCC of RC bridge elements under coupled fatigue-corrosion deterioration processes

An optimal bridge design should minimize the life cycle cost (LCC) of the structure without compromising its safety. Various cost components need to be evaluated when assessing the life cycle cost of a reinforced concrete bridge. When the structure is subjected to performance degradation due to aging, the probabilistic modeling of degradation is required. In this paper, the reliability-based design optimization RBDO is performed on the life cycle cost of the structure subject to deterioration processes of fatigue and corrosion. This paper advances the state of the art by: considering the coupled corrosion fatigue model in the design optimization and by developing a new approach to evaluate the user delay costs on a bridge, based on direct and indirect costs related to degradation and failure. Also, a sensitivity analysis of optimal costs and design variables is performed. The improved life cycle cost analysis presented herein can be applied to select the optimal design of reinforced concrete bridge elements, by minimizing both agency and bridge user costs, while providing the required safety along the structure lifetime, taking into account the most severe degradation processes.     

Graded wavelike two-dimensional photonic crystal made of thin films

A filling-factor-graded wavelike two-dimensional photonic crystal (2DPC) possessing a light-path bending effect that is polarization dependent is theoretically studied by using a qualitative analysis of the isofrequency curves. The numerical simulation results obtained by using the finite-difference time-domain method demonstrate that such a graded 2DPC has potential applications in a polarization splitter and a parallel-plane resonant cavity. A new kind of waveguide structure that combines a filling-factor-graded wavelike 2DPC and one-dimensional multilayer thin films is also discussed.     

On artificial strain of thin curved elements

This paper presents an attempt to clarify further the nature of the overstiffness of thin curved structural elements. It follows the approach presented by Ashwell and co-workers^1,2 who based their study on shape functions of arch elements. Such elements display the same stiff behaviour as complex shell elements but are simpler to study and understand. An examination of several discretizations for a two-dimensional curved beam-column element for linear elastic analysis of arches is performed. This examination and the numerical results obtained from these approximations provide a new interpretation of the artificial strains based on the mapping variables of shape functions. Two new methods to reduce the artificial stiffness of the element are proposed.     

Machine locking of degenerated thin shell elements

The degenerated shell element is one of the most efficient elements for analysing shell structures. However, it is known to result in rather stiff models when used in thin element applications. The phenomena associated with this behaviour are known as locking phenomena. This paper analyses the machine locking mechanism developed in thin to very thin Lagrangian and serendipity elements. The machine related locking phenomenon is distinguished from the shear and membrane locking phenomena. A remedy for the pure machine locking problem is developed for the two elements. The proposed remedy is based on the technique of the modified transverse shear modulus. It is also extended to control shear locking. The proposed technique is shown to completely eliminate machine locking. Also, it is shown to effectively alleviate stiffening effects due to the presence of spurious shear strain.     

Locking of thin plate/shell elements

Often, finite element solutions of thin plate/shell elements become very stiff and the displacement field solutions diverge from those predicted by Kirchhoff's theory. This phenomenon is known as the locking phenomenon. A theoretical fomulation demonstrating its existence is developed, and results of finite element analysis of a single element and mesh are discussed. This leads to a sufficient and necessary criterion which must be satisfied to avoid the locking phenomenon.     

Discontinuous Galerkin method applied to electromagnetic compatibility problems: introduction of thin wire and thin resistive material models

A discontinuous Galerkin (DG) method and some physical models added to this method to treat electromagnetic compatibility problems are presented. This method is very efficient in terms of CPU-time and memory usage because of the use of a high-order spatial approximation on general unstructured meshes. Some comparisons with other schemes are presented to validate the proposed models and to point out the advantages of the DG method. In particular, some improvements of the method like the use of a local timestepping strategy have been studied.     

High‐order finite elements applied to the discrete Boltzmann equation

A discontinuous Galerkin approach for solving the discrete Boltzmann equation is presented, allowing to compute approximate solutions for fluid flow problems. Based on a two‐dimensional high‐order finite element and an explicit Euler time stepping scheme, the D2Q9 model is discretized and the results are compared to the exact solution of the Navier–Stokes equation. Four numerical examples are considered, including stationary and instationary problems with curved boundaries. It is demonstrated that the proposed method allows to obtain the desired, highly efficient exponential convergence. Copyright © 2006 John Wiley & Sons, Ltd.