Plastic limit analysis and optimum design of structures for uncertain conditions.

At the application of the plastic analysis and design methods the control of the plastic behaviour of the structures is an important requirement. Since the plastic limit analysis provides no information about the magnitude of the plastic deformations and residual displacements accumulated before the adaptation of the structure, therefore complementary strain energy of the residual forces could be considered an overall measure of the plastic performance of structures and the plastic deformations should be controlled by introducing a bound for magnitude of this energy. If the design uncertainties (manufacturing, strength, geometrical) are expressed by the calculation of the complementary strain energy of the residual forces a reliability based extended plastic limit design problem is formed. In this research, due to the uncertainties the bound for the complementary strain energy of the residual forces is given randomly and a general approach to evaluate the limit load capacity of structures for uncertain conditions is presented. The aim of this study is to evaluate limit load capacity of structures with limited residual strain energy on the probabilistically given conditions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimization of shallow arches against instability using sensitivity derivatives

In this paper, the problem of optimization of shallow frame structures, which involves coupling of axial and bending responses, is discussed. A shallow arch of given shape and given weight is optimized such that its limit point load is maximized. The crosssectional area, A(x), and the moment of inertia, I(x), of the arch obey the relationship I(x) = [A(x)]ⁿ, where N = 1, 2, 3 and is a specified constant. Analysis of the arch for its limit point calculation involves a geometric nonlinear analysis which is performed using a co-rotational formulation.

The optimization is carried out using a second-order projected Langragian algorithm, and the sensitivity derivatives of the critical load parameter with respect to the areas of the finite elements of the arch are calculated using implicit differentiation. Results are presented for an arch of a specified rise to span under two different loadings, and the limitations of the approach for the intermediate rise arches are addressed.     

A bargaining game model for measuring performance of two-stage network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs), where the internal structures of DMUs are treated as a black-box. Recently DEA has been extended to examine the efficiency of DMUs that have two-stage network structures or processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The current paper develops a Nash bargaining game model to measure the performance of DMUs that have a two-stage structure. Under Nash bargaining theory, the two stages are viewed as players and the DEA efficiency model is a cooperative game model. It is shown that when only one intermediate measure exists between the two stages, our newly developed Nash bargaining game approach yields the same results as applying the standard DEA approach to each stage separately. Two real world data sets are used to demonstrate our bargaining game model.     

Modelling of the deformation processes and the localization of plastic deformations in the torsion–tension of solids of revolution

Generalized two-dimensional problems of the torsion of elastoplastic solids of revolution of arbitrary shape for large deformations under non-uniform stress-strain conditions are formulated and a method for their numerical solution is proposed. The use of this method to construct strain diagrams of materials based on experiments on the torsion of axisysmmetric samples of variable thickness until fracture occurs is described. Experimental and numerical investigations of processes of elastoplastic deformation, loss of stability and supercritical behaviour of solid cylindrical steel samples of variable thickness under conditions of monotonic kinematic loading with a torque, a tension and a combined load are presented. The mutual influence of torsion and tension on the deformation process and the limit states is estimated, and the universality (the independence of the form of the stress-strain state) of the “stress intensity – Odqvist parameter” diagram for steel for large deformations is proved.     

Scelernomic analysis of structures considering connection slip

A challenge in structural engineering of space and ground radio and light wave reflectors is to retain surface geometry to a high precision in the context of pinned connections and changing loads. This paper describes a direct approach to assessing worst-case geometric degradation of these structures for hypothesized slots in the members.The paper presents the structural model, an analysis procedure, and illustrative results. The model addresses articulated structures with slots small compared with member lengths. The analysis process implies stepwise linear behavior. The examples encompass determinate and indeterminate two-dimensional trusses.The approach results in an analysis process capable of predicting the extremes of slip accumulation. Like limit analysis, it provides behavior prediction in a finite number of steps with guaranteed success. Data from the sample analyses suggest that fabrication tolerances should be much less than allowable member elongations if long-time high precision is desired.     

On the macroscopic material behaviour of textile reinforced concrete undertensile loading

This paper concerns with the development of the macroscopic material behaviour of textile reinforced concrete (TRC) using an analytical approach. Therefore the heterogeneous structure of TRC is modelled on the mesoscopic level. The overall material behaviour on the macroscopic level is obtained by means of the homogenisation technique. The analytical approach is based on the micro mechanical solution for a single inclusion according to Eshelby . In extension of this solution for multidirectional reinforced concrete an effective field approximation is used. This approach considers the interactions between the different orientated rovings and the micro cracks in an average sense. For the mechanical modelling of the bond behaviour between roving and matrix after initiating of the macro cracking a slip based bond model with a multiple linear shear stress-slip relation is used. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Static and dynamic analysis of cracked or weakened structures

Stiffness modifications in engineering structures, for example due to damage and cracking, will inevitably also lead to changes in deformations, internal forces, natural frequencies and mode shapes of the structures. In this paper, an efficient and simple method for sensitivity analysis of cracked or weakened structures under time-harmonic loading is presented. The method is based on a comparison between the strain energy and the kinetic energy of an uncracked structure and that of a cracked structure in conjunction with the application of exact or approximate Green's functions as described in [3] for the static case. The present analysis enables the prediction of any changes in the displacements and stresses and has a lower computational effort as compared to available classical methods, because only the damaged region has to be re-considered in the method. Green's functions are taken as a basis of the approach, which have the ability to weight the influence of the stiffness modifications in a region of a structure and show how sensitive other regions respond to the stiffness modifications. Based on linear elastic fracture mechanics, cracked or damaged regions are approximated by spring models in the analytical solution of some simple beam problems, while cracked finite elements are used for complicated cases where analytical solutions cannot be obtained. Sensitivity analysis with Green's functions (SAGF) approach is applied to static and dynamic analysis of cracked and weakened structures, which consist of homogeneous materials or fiber reinforced composites like reinforced concretes. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Heavy traffic analysis of M/G/1 type queueing systems with Markov-modulated arrivals

M/G/1 type queueing systems whose arrival rate is a function of an independent continuous time Markov chain are considered. We suggest a simple analytical approach which allows rigorous mathematical analysis of the stationary characteristics under heavy traffic. Their asymptotic behaviour is described in terms of characteristics of the modulating process (defined as a solution of a set of linear algebraic equations). The analysis is based on certain “semi-explicit” formulas for the performance characteristics. This research was supported by INTAS under grant No. 96-0828.     

Thin structures in elasticity: The variational method

The behaviour of two-dimensional and one-dimensional thin elastic structures as membranes, shells, strings, beams, is deduced starting from three-dimensional elastic models and passing to the limit when one or two dimensions go to zero. The variational approach and the Γ-convergence theory are used.     

Diffusion driven instability in an inhomogeneous circular domain

Classical reaction-diffusion systems have been extensively studied and are now well understood. Most of the work to date has been concerned with homogeneous models within one-dimensional or rectangular domains. However, it is recognised that in most applications nonhomogeneity, as well as other geometries, are typically more important. In this paper, we present a two chemical reaction-diffusion process which is operative within a circular region and the model is made nonhomogeneous by supposing that one of the diffusion coefficients varies with the radial variable. Linear analysis leads to the derivation of a dispersion relation for the point of onset of instability and our approach enables both axisymmetric and nonaxisymmetric modes to be described. We apply our workings to the standard Schnackenberg activator-inhibitor model in the case when the variable diffusion coefficient takes on a step-function like profile. Some fully nonlinear simulations show that the linear analysis captures the essential details of the behaviour of the model.     

Shape optimal design of arch dams including dam-water–foundation rock interaction using a grading strategy and approximation concepts

Optimal design of arch dams including dam-water–foundation rock interaction is achieved using the soft computing techniques. For this, linear dynamic behavior of arch dam-water–foundation rock system subjected to earthquake ground motion is simulated using the finite element method at first and then, to reduce the computational cost of optimization process, a wavelet back propagation neural network (WBPNN) is designed to predict the arch dam response instead of directly evaluating it by a time-consuming finite-element analysis (FEA). In order to enhance the performance generality of the neural network, a dam grading technique (DGT) is also introduced. To assess the computational efficiency of the proposed methodology for arch dam optimization, an actual arch dam is considered. The optimization is implemented via the simultaneous perturbation stochastic approximation (SPSA) algorithm for the various conditions of the interaction problem. Numerical results show the merits of the suggested techniques for arch dam optimization. It is also found that considering the dam-water–foundation rock interaction has an important role for safely designing an arch dam.     

Sensitivity analysis of weakened beams on elastic foundation with Green's functions

The approach of Sensitivity Analysis with Green's Functions (SAGF) [1,2] was developed to predict changes in deformations, stresses or eigenfrequencies of structures resulting from stiffness modifications or cracking by considering only the weakened or damaged parts of the structures. This approach results in a local analysis instead of a global analysis by recalculating the whole structure. Consequently, it is computationally less time-consuming than the conventional methods based on a global analysis. The key idea of the SAGF approach is based on the comparison between the elastic strain energies of the original and the weakened structures and the substitution of the virtual displacements by the corresponding Green's functions [1, 2]. Furthermore, an approximate approach for the sensitivity analysis was suggested which is described in [1, 3] in details. This approach enables us to predict the changes in the structural responses due to the stiffness weakening in the beam or in the elastic Winkler foundation by considering only the internal forces or the deflections of the original unweakened system. In addition, an iterative method was developed to enhance the accuracy of the SAGF approach. In this paper, the local SAGF method for sensitivity analysis of elastic beams on Winker foundation with stiffness weakening is presented. The accuracy and the efficiency of the proposed method are verified by using a numerical example. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Product line optimization in the presence of preferences for compromise alternatives

Recent advances in customer choice analysis demonstrated the strong impact of compromise alternatives on the behaviour of decision-makers in a wide range of decision situations. Compromise alternatives are characterized by an intermediate performance on some of the relevant attributes. For instance, price compromises are well known in the sense that customers tend to buy neither the cheapest, nor the most expensive alternative, but the mid-priced one. However, thus far, the literature on product line optimization has not considered such context effects.In this paper, we propose a model-based approach for optimal product line selection which incorporates customers’ preferences for compromise alternatives. We consider customer choice in a realistic, sophisticated fashion by applying an established utility model that integrates compromise variables into a multinomial logit model. We formulate the resulting optimization problem as a mixed-integer linear program. The challenging feature for modelling – making the formulation substantially more complicated than existing ones without compromises – are the endogenous effects of selected products on other alternatives’ utilities that need to be adequately captured via compromise variables. Based on data we collected by a stated choice experiment in a retail setting, we perform a computational study and demonstrate the superiority of our product line selection approach compared to a reference model that does not take compromises into account. Even under uncertainty of the estimated utility parameters, profit gains of, on average, 23% can be achieved in our experimental setting.     

Constraint augmentation in pseudo-singularly perturbed linear programs

In this paper we study a linear programming problem with a linear perturbation introduced through a parameter ε > 0. We identify and analyze an unusual asymptotic phenomenon in such a linear program. Namely, discontinuous limiting behavior of the optimal objective function value of such a linear program may occur even when the rank of the coefficient matrix of the constraints is unchanged by the perturbation. We show that, under mild conditions, this phenomenon is a result of the classical Slater constraint qualification being violated at the limit and propose an iterative, constraint augmentation approach for resolving this problem.     

The effect of surface topography on weakly nonlinear roll waves

The propagation of short waves in turbulent single layer flows forming on inclined surfaces has received considerable interest in the past. It is well known that such flows on flat surfaces are unstable if the Froude number of the unperturbed uniform state exceeds a critical value. In the initial linear stage disturbances grow exponentially with propagation distance but it has been shown that weakly nonlinear effects may limit the maximum wave amplitude under strictly periodic conditions leading in turn to a train of permanent roll waves. The present study investigates how the flow behaviour is affected if the slope of the bounding surface is no longer constant but changing slowly in the streamwise direction. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Poisson Distribution for Linear Statistics of Random Permutations

We examine the asymptotic distribution laws of integer-valued linear statistics defined via the multiplicities of lengths of cycles comprising a random permutation taken with equal probability. We establish necessary and sufficient conditions for the weak convergence to the Poisson limit law. The approach can be applied to investigate other logarithmic structures. __________ Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 537–552, October–December, 2005.     

Additive efficiency decomposition in two-stage DEA

Kao and Hwang (2008) [Kao, C., Hwang, S.-N., 2008. Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan. European Journal of Operational Research 185 (1), 418–429] develop a data envelopment analysis (DEA) approach for measuring efficiency of decision processes which can be divided into two stages. The first stage uses inputs to generate outputs which become the inputs to the second stage. The first stage outputs are referred to as intermediate measures. The second stage then uses these intermediate measures to produce outputs. Kao and Huang represent the efficiency of the overall process as the product of the efficiencies of the two stages. A major limitation of this model is its applicability to only constant returns to scale (CRS) situations. The current paper develops an additive efficiency decomposition approach wherein the overall efficiency is expressed as a (weighted) sum of the efficiencies of the individual stages. This approach can be applied under both CRS and variable returns to scale (VRS) assumptions. The case of Taiwanese non-life insurance companies is revisited using this newly developed approach.     

Capturing coalescence and break-up processes in vertical gas–liquid flows: Assessment of population balance methods

Gas–liquid flows are commonly encountered in industrial flow systems. Numerical studies have been performed to assess the performances of different population balance approaches – direct quadrature method of moments (DQMOMs), average bubble number density (ABND) model and homogeneous MUlti-SIze-Group (MUSIG) model – in tracking the changes of gas void fraction and bubble size distribution under complex flow conditions and to validate the model predictions against experimental measurements from medium- and large-sized vertical pipes. Subject to different gas injection method and flow conditions, bubble size evolution exhibited a coalescence dominant trend in the medium-sized pipe; while bubble break-up was found to be dominant in large-sized pipe. The two experiments were therefore strategically selected for carrying out a thorough examination of existing population balance models in capturing the complicated behaviour of bubble coalescence and break-up. In general, predictions of all the different population balance approaches were in reasonable agreement with experimental data. More importantly, encouraging results have been obtained in adequately capturing the dynamical changes of bubbles size due to bubble interactions and transition from wall peak to core peak gas void fraction profiles. As a compromise between numerical accuracy and computational time, DQMOM has performed rather well in capturing the essential two-phase flow structures within the medium- and large-sized vertical pipes when compared to those of ABND and homogeneous MUSIG models. From a practical perspective, the ABND model may still be considered as a more viable approach for industrial applications of gas–liquid flow systems.