Vissarion Papadopoulos

Structural reliability analyis of elastic-plastic structures using neural networks and Monte Carlo simulation

Abstract This paper examines the application of Neural Networks (NN) to the reliability analysis of complex structural systems in connection with Monte Carlo Simulation (MCS). The failure of the system is associated with the plastic collapse. The use of NN was motivated by the approximate concepts inherent in reliability analysis and the time consuming repeated analyses required for MCS. A Back Propagation algorithm is implemented for training the NN utilising available information generated from selected elasto-plastic analyses. The trained NN is then used to compute the critical load factor due to different sets of basic random variables leading to close prediction of the probability of failure. The use of MCS with Importance Sampling further improves the prediction of the probability of failure with Neural Networks.

Robust and efficient methods for stochastic finite element analysis using Monte Carlo simulation

Abstract In the present paper the weighted integral method and the Monte Carlo simulation are used together with innovative solution strategies based on the Preconditioned Conjugate Gradient method (PCG) to produce robust and efficient solutions for the stochastic finite element analysis of space frames. The numerical tests presented demonstrate the superiority of the proposed computational strategies compared to the widely used Neumann expansion method both in terms of accuracy and computational efficiency. The superiority is more pronounced in cases where the analysis needs to be performed for large variations of the stochastic parameters.

A computationally efficient method for the limit elasto plastic analysis of space frames

A computationally efficient method for the first order step-by-step limit analysis of space frames is presented. The incremental non-holonomic analysis is based on the generalized plastic node method. The non-linear yield surface is approximated by a multi-faceted surface, thus avoiding the iterative formulation at each load step. In order to prevent the occurrence of very small load steps a second internal and homothetic to the initial yield surface is implemented which creates a plastic zone for the activation of the plastic modes. This implementation reduces substantially the computational effort of the procedure without affecting the value of the final load. The solution of the linear equilibrium equation at each load step is obtained with the preconditioned conjugate gradient method. Special attention is paid to the fact that the overall stiffness matrix changes gradually with the successive formation of plastic nodes. The application of the conjugate gradient method is based on some recent developments on improved matrix handling techniques and efficient preconditioning strategies. A number of test problems have been performed which show the usefulness of the proposed approach and its superiority in respect to efficient direct methods of solution in both storage requirements and computing time.

Computational Methods in Stochastic Dynamics

Preface.- Random Dynamical Response of a Multibody System with Uncertain Rigid Bodies, by Anas Batou and Christian Soize.- Dynamic Variability Response for Stochastic Systems, by Vissarion Papadopoulos and Odysseas Kokkinos.- A Novel Reduced Spectral Function Approach for Finite Element Analysis of Stochastic Dynamical Systems, by Abhishek Kundu and Sondipon Adhikari.- Computational Stochastic Dynamics based on Orthogonal Expansion of Random Excitations, by X. Frank Xu and George Stefanou.- Numerical solution of the Fokker-Planck equation by finite difference and finite element methods - a comparative study, by L. Pichler, A. Masud and L. A. Bergman.- A Comparative study of Uncertainty Propagation Methods in Structural Problems, by Manuele Corradi, Marco Gherlone, Massimiliano Mattone and Marco Di Sciuva.- Fuzzy and fuzzy stochastic methods for the numerical analysis of reinforced concrete structures under dynamical loading, by Frank Steinigen, Jan-Uwe Sickert, Wolfgang Graf and Michael Kaliske.- Application of interval fields for uncertainty modeling in a geohydrological case, by Wim Verhaeghe, Wim Desmet, Dirk Vandepitte, Ingeborg Joris, Piet Seuntjens and David Moens.- Enhanced Monte Carlo for Reliability-Based Design and Calibration, by Arvid Naess, Marc Maes and Marcus R. Dann.- Optimal Design of Base-Isolated Systems under Stochastic Earthquake Excitation, by Hector A. Jensen, Marcos A. Valdebenito and Juan G. Sepulveda.- Systematic formulation of model uncertainties and robust control in smart structures using Hinfinity and mu-analysis, by Amalia Moutsopoulou, Georgios E. Stavroulakis and Anastasios Pouliezos.- Robust Structural Health Monitoring Using a Polynomial Chaos Based Sequential Data Assimilation Technique, by George A. Saad and Roger G. Ghanem.- Efficient model updating of the GOCE satellite based on experimental modal data, by B. Goller, M. Broggi, A. Calvi and G.I. Schueller.- Identification of properties of stochastic elastoplastic systems, by Bojana V. Rosic and Hermann G. Matthies.- SH surface waves in a half space with random heterogeneities, by Chaoliang Du and Xianyue Su.- Structural seismic fragility analysis of RC frame with a new family of Rayleigh damping models, by Pierre Jehel, Pierre Leger and Adnan Ibrahimbegovic.- Incremental dynamic analysis and pushover analysis of buildings: A probabilistic comparison, by Yeudy F. Vargas, Luis G. Pujades, Alex H. Barbat and Jorge E. Hurtado.- Stochastic analysis of the risk of seismic pounding between adjacent buildings, by Enrico Tubaldi and Michele Barbato.- Intensity Parameters as Damage Potential Descriptors of Earthquakes, by Anaxagoras Elenas.- Classification of Seismic Damages in Buildings Using Fuzzy Logic Procedures, by Anaxagoras Elenas, Eleni Vrochidou, Petros Alvanitopoulos and Ioannis Andreadis.- Damage identification of masonry structures under seismic excitation, by G. De Matteis, F. Campitiello, M.G. Masciotta, and M. Vasta.

Stochastic finite element-based reliability analysis of space frames

Abstract In the present paper the weighted integral method in conjunction with Monte Carlo simulation is used for the stochastic finite element-based reliability analysis of space frames. The limit state analysis required at each Monte Carlo simulation is performed using a non-holonomic step-by-step elasto-plastic analysis based on the plastic node method in conjunction with efficient solution techniques. This implementation results in cost effective solutions both in terms of computing time and storage requirements. The numerical results presented demonstrate that this approach provides a realistic treatment for the stochastic finite element-based reliability analysis of large scale three-dimensional building frames.

The Method of Separation: A Novel Approach for Accurate Estimation of Evolutionary Power Spectra

One of the most widely used techniques for the simulation of Gaussian evolutionary random fields is the spectral representation method. Its key quantity is the power spectrum, which characterizes the random field in terms of frequency content and spatial evolution in a mean square sense. For the simulation of a random physical phenomenon, the power spectrum can be directly obtained from corresponding measured samples by means of estimation techniques. The present contribution starts with a short review of established power spectrum estimation techniques, which are based on the short-time Fourier, the harmonic wavelet and the Wigner–Ville transforms, and subsequently introduces a method for the estimation of separable random fields, called the method of separation. The characteristic drawbacks of the established methods, i.e. the limitation of simultaneous space–frequency localization or the appearance of negative spectral density, lead to poor estimation results, if the Fourier transform of the input samples consists of a narrow band of frequencies. The proposed method of separation, combining accurate spectrum resolution in space with an optimum localization in frequency, considerably improves the estimation accuracy in the presence of strong narrow-bandedness, which is illustrated by a practical example from stochastic imperfection modeling in structures.

Stochastic Finite Element Method

Chapter 3 presents the fundamentals of the Stochastic Finite Element Method in the framework of the stochastic formulation of the virtual work principle. The resulting stochastic partial differential equations are solved with either non-intrusive Monte Carlo simulation methods, or intrusive approaches such as the versatile spectral stochastic finite element method. Additional approximate methodologies such as the Neumann and Taylor series expansion methods are also presented together with some exact analytic solutions that are available for statically determinate stochastic structures. The concept of the variability response function is then developed and generalized for general stochastic finite element systems.

Buckling load variability of cylindrical shells with stochastic imperfections

In this paper, the effect of random initial geometric, material and thickness imperfections on the buckling load of isotropic cylindrical shells is investigated. To this purpose, a stochastic spatial variability of the elastic modulus as well as of the thickness of the shell is introduced in addition to the random initial geometric deviations of the shell structure from its perfect geometry. The modulus of elasticity and the shell thickness are described by two-dimensional univariate (2D-1V) homogeneous non-Gaussian translation stochastic fields. The initial geometric imperfections are described as a 2D-1V homogeneous Gaussian stochastic field. A numerical example is presented examining the influence of the non-Gaussian assumption on the variability of the buckling load. In addition, useful conclusions are derived concerning the effect of the various marginal probability density functions as well as of the spectral densities of the involved stochastic fields on the buckling behaviour of shells, as a result of a detailed sensitivity analysis.

Dynamic Variability Response for Stochastic Systems

In this study we implement the concept of Variability Response Functions (VRFs) in dynamic systems. The variance of the system response can be readily estimated by an integral involving the Dynamic VRF (DVRF) and the uncertain system parameter power spectrum. With the proposed methodology spectral and probability distribution-free upper bounds can be easily derived. Also an insight is provided with respect to the mechanisms controlling the system’s response. The necessarily asserted conjecture of independence of the DVRF to the spectral density and the marginal probability density is validated numerically through brute-force Monte Carlo simulations.

Representation of a Stochastic Process

Chapter 2 describes various methods used for the simulation of a stochastic process such as point discretization methods as well as the most popular Karhunen-Loeve and spectral representation series expansion methods. Methods for the simulation of non-Gaussian fields are then presented followed by solved numerical examples.