Vissarion Papadopoulos

National Technical University of Athens | NTUA · School of Civil Engineering

This paper introduces a novel approach to infer the material properties of multiscale material systems through a variety of experimental scenarios. We utilize the hierarchical Bayesian paradigm which enables us to integrate multiple experimental data at different length scales and/or different material compositions, in a systematic way. Specificall...

Iso-XFEM is a recently proposed evolutionary topology optimization method, which is based in the extended finite element method (XFEM). Similarly to XFEM, Iso-XFEM utilises the level set approach in order to achieve a high-resolution, smooth, and accurate representation of the design boundary using a fixed finite element mesh. Compared to conventio...

Recent advances in the field of machine learning open a new era in high performance computing for challenging computational science and engineering applications. In this framework, the use of advanced machine learning algorithms for the development of accurate and cost‐efficient surrogate models of complex physical processes has already attracted m...

The potential of quantum computing for scientific and industrial breakthroughs is immense, however, we are still in the Noisy Intermediate-Scale Quantum (NISQ) era, where the currently available quantum devices contain small numbers of qubits, are very sensitive to environmental conditions and prone to quantum decoherence. Even so, existing NISQ co...

The application of multiscale methods that are based on computational homogenization, such as the well established FE^2, remains in most cases a computationally challenging task. In a system that involves more than two length scales, the task of a FE^N (N>2) calculation becomes practically intractable if applied in the frame of conventional computa...

The development of Physics-Informed Neural Networks (PINNs) over the recent years has offered a promising avenue for the solution of partial differential equations, as well as for the identification of unknown equation parameters. This work focuses on the application of PINNs, and in particular, their variation called eXtended PINNs (XPINNs) for th...

Recent advances in the field of machine learning open a new era in high performance computing. Applications of machine learning algorithms for the development of accurate and cost-efficient surrogates of complex problems have already attracted major attention from scientists. Despite their powerful approximation capabilities, however, surrogates ca...

This paper presents a non-intrusive surrogate modeling scheme for transient response analysis of nonlinear structures involving random parameters. The proposed scheme utilizes a two-level neural network architecture as a surrogate model. Specifically, it combines feed-forward neural networks with convolutional autoencoders to deliver a highly accur...

This paper presents a novel non-intrusive surrogate modeling scheme based on deep learning for predictive modeling of complex systems, described by parametrized time-dependent partial differential equations. Specifically, the proposed method utilizes a convolutional autoencoder in conjunction with a feed forward neural network to establish a mappin...

In this work a formulation for non linear multi-scale analysis of thin shells is presented and a modeling scheme is proposed in a FE2 method’s context. The shells may undergo large deformations and exhibit heterogeneous micro-structures consisting of nonlinear materials and cohesive interfaces. Appropriate use of an attached coordinate system, for...

The present paper investigates the thermal properties of carbon nanotube reinforced polyethylene and specifically its potential as highly conductive material. To this end, an integrated approach is proposed combining both numerical and experimental procedures. First, in order to study conductive heat transfer in two-phase materials with imperfect i...

This work proposes a Bayesian framework for determining the mechanical properties of carbon based nanocomposites. In particular, Bayesian parameter inference is applied to learn the parameters that characterize the CNT/polymer interface in the microscale. These parameters are associated with great uncertainties and their characterization is a diffi...

A stochastic data-driven multilevel finite-element (FE2) method is introduced for random nonlinear multiscale calculations. A hybrid neural-network–interpolation (NN–I) scheme is proposed to construct a surrogate model of the macroscopic nonlinear constitutive law from representative-volume-element calculations, whose results are used as input data...

The focus of this paper is on the probabilistic estimation of the buckling capacity of single-bolted members from plain or lipped angle sections with stochastic geometric imperfections. A joint experimental-stochastic mechanics approach is adopted, employing in-house imperfection measurements of angle members in combination with detailed numerical...

This work introduces a surrogate modeling strategy, based on diffusion maps manifold learning and artificial neural networks. On this basis, a numerical procedure is developed for cost-efficient predictions of a complex system’s response modeled by parametrized partial differential equations. The idea is to utilize a collection of solution snapshot...

This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs. For these problems, typical finite element approaches involve the spatiotemporal discretization of the PDE and the solution of the corresponding linear system of...

This work extends isogeometric thin shell formulations to incorporate constitutive laws generated by stochastic multiscale analyses. The integration of the constitutive law is performed through the thickness of the shell, in order to account for material heterogeneity. At each thickness integration point, a corresponding representative volume eleme...

The aim of this work is the investigation of mesoscale/local variability in mechanical properties of clear timber in the radial direction. Clear Norway spruce wood, Picea abies, was used for cutting specimens of different lengths with a small cross-sectional area of 4 × 4 mm², in the radial direction of timber boards, and tested under tensile loadi...

The present paper proposes an XFEM formulation for heat transfer analysis of multi-phase materials with explicit treatment of boundary interactions. The existence of interfacial resistance at the boundaries of the material phases produces discontinuities in the temperature field and a standard finite element treatment would require complex domain d...

In this work an alternative machine learning methodology is proposed, which utilizes nonlinear manifold learning techniques in the frame of surrogate modeling. Under the assumption that the solutions of a parametrized physical system lie on a low‐dimensional manifold embedded in a high‐dimensional Euclidean space, the goal is to unveil the manifold...

In this paper, a data-driven-based computational homogenization method based on neural networks is proposed to describe the nonlinear electric conduction in random graphene-polymer nanocomposites. In the proposed technique, the nonlinear effective electric constitutive law is provided by a neural network surrogate model constructed through a learni...

The present paper proposes a stochastic formulation which enables the effective coupling of spectral stochastic finite elements with geometrically nonlinear analysis of framed structures. This is achieved by projecting the stochastic part of the incremental displacements, formulated in the framework of a Newton–Raphson solution scheme, to a polynom...

In the present paper a Probability Density Evolution formulation is proposed for the limit analysis of stochastic systems, which can accurately and efficiently evaluate the effect the system's random parameters have on its nonlinear and limit response. The proposed formulation of the classic Probability Density Evolution Method reduces the correspo...

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-Loève and spectral representation series expansion methods. Methods for the simulation of non-Gaussian fields are then presented followed by solved numerical examples.

This chapter introduces the fundamentals of the stochastic process theory and its applications. The definition of a stochastic process is given first followed by a description of its characteristic functions and moments. The meaning of ergodicity and stationarity are discussed and a description of the power spectrum is made

This chapter is devoted to reliability analysis methods with emphasis on those developed over the past two decades. The fundamental principles and basic reliability analysis methods are presented, namely the first- and second-order moments and the Monte Carlo simulation. For practical reliability problems, the latter require disproportionate comput...

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 finit...

The book provides a self-contained treatment of stochastic finite element methods. It helps the reader to establish a solid background on stochastic and reliability analysis of structural systems and enables practicing engineers to better manage the concepts of analysis and design in the presence of uncertainty. The book covers the basic topics of...

In intrusive methods for the stochastic analysis of engineering systems, the solution of the stochastic partial differential equations leads to an augmented algebraic system of equations, with respect to the corresponding deterministic problem. The solution of this augmented system can become quite challenging or even impossible due to the increase...

This paper presents a neural network (NN)-based surrogate modeling approach suitable for the geometrically nonlinear analysis of carbon nanotubes (CNTs). In this work we propose an NN-based equivalent beam element (NN-EBE) which is capable of accurately predicting the high-order phenomena caused by size-effects that characterize the behavior of CNT...

The present paper proposes a hierarchical multiscale approach in order to evaluate the nonlinear constitutive behavior of concrete reinforced with carbon nanotubes (CNTs). To this purpose, representative volume elements, consistent to the microstructural topology of the material, are constructed and analyzed using finite elements. As the dimensions...

The present paper proposes a stochastic finite element based methodology in multiple scales for modeling composite materials reinforced with graphene nano-particles. As graphene platelets exhibit a shell-type structural behavior, the problem of finding an equivalent shell element (ESE) that can be used as an effective surrogate to the corresponding...

In this paper, shear wave propagation in soils is examined in a stochastic context considering spatial variability of the shear modulus soil parameter. To this purpose, the recently established concept of dynamic mean and variability response functions (DMRF, DVRF) is reformulated in the framework of stochastic finite element analyses of shear wave...

We propose a hybrid methodology that implements artificial neural networks (ANN) in the framework of Bayesian updating with structural reliability methods (BUS) in order to increase the computational efficiency of BUS in sampling-based Bayesian inference of numerical models. In particular, ANNs are incorporated in BUS with subset simulation (SuS)....

This volume contains the full-length papers presented at the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016) that was held on June 5-10, 2016 on the Crete Island, Greece.

A computational procedure is proposed in this paper for the determination of mesoscale random fields and of the representative volume element (RVE) size of carbon nanotube reinforced composites (CNT-RCs). To this purpose, computer-simulated images of composites with specific weight fraction (%wt) of randomly scattered CNTs are examined. The cases o...

Cold-formed single angle cross-sections are widely used in combination with standard angle cross-sections in lattice towers. Although bracing members are generally axially loaded, bolted connections increase significantly second-order effects, which in most practical cases are neglected. In addition, cold-forming procedures introduce initial geomet...

The present paper proposes a Galerkin finite element projection scheme for the solution of the partial differential equations (pde’s) involved in the probability density evolution method, for the linear and nonlinear static analysis of stochastic systems. According to the principle of preservation of probability, the probability density evolution o...

Incremental dynamic analysis (IDA) is a powerful method for the seismic performance assessment of structures. IDA is also very efficient for handling uncertainty due to the mechanical properties of the structure. In the latter case, IDA should be performed within a Monte Carlo framework requiring the execution of a vast number of nonlinear response...

Different factors such as age, location of timber within the tree, structural imperfections, load history such as wind and snow etc. can affect the material properties of timber. Consequently, there is a high variability in the mechanical properties which is sometimes referred to as ‘random spatial variability’. In this work, the spatial variabilit...

Different factors such as age, location of timber within the tree, structural imperfections, load history such as wind and snow etc. can affect the material properties of timber. Consequently, there is a high variability in the mechanical properties which is sometimes referred to as ‘random spatial variability’. In this work, the spatial variabilit...

Interfacial shear strength (ISS) is known to significantly affect the mechanical performance of carbon-nanotube (CNT) reinforced composites. To illustrate the combined effect of ISS and CNT weight fraction on the behavior of CNT/polymer, a CNT/polymer cantilever beam was analyzed using a three-level multiscale technique. (1) At the atomic level, a...

This volume contains the full-length papers presented in the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2015) that was held on May 25-27, 2015 on the Crete Island, Greece. COMPDYN 2015, one of the thematic Conferences of the European Community on Computational Methods in Applied...

SUMMARYA methodology is proposed in this paper to construct an adaptive sparse polynomial chaos (PC) expansion of the response of stochastic systems whose input parameters are independent random variables modeled as random fields. The proposed methodology utilizes the concept of variability response function (VRF) in order to compute an a priori lo...

In this study a methodology is presented for effective analysis of dynamic systems with stochastic material properties. The concept of dynamic mean and variability response functions, recently established for linear stochastic single degree of freedom oscillators, is extended to general finite element systems such as statically indeterminate beam/f...

This work revisits the computational performance of non-intrusive Monte Carlo versus intrusive Galerkin methods of large-scale stochastic systems in the framework of high performance computing environments. The purpose of this work is to perform an assessment of the range of the relative superiority of these approaches with regard to a variety of s...

In this paper a general formulation is proposed for the dynamic analysis of stochastic structures with uncertain material properties. A straightforward generalization of the mean and variability response function concept is introduced leading to closed form integral expressions for the dynamic mean and variability response of statically indetermina...

The present work sets up a methodology that allows the estimation of the spatial distribution of the second-order error of the response, as a function of the number of terms used in the truncated Karhunen-Loève (KL) series representation of the random field involved in the problem. For this purpose, the concept of the variability response function...

A nonlinear hierarchical multiscale approach is proposed in this work, for the characterization of the mechanical and damping properties of carbon nanotube reinforced composites (CNT-RCs) considering slippage at CNT/polymer interface. The proposed numerical strategy encompasses various length scales, from nano to micro to macro. Individual CNTs are...

In this paper, the effect of initial geometric imperfections on the buckling load of steel tubes (relatively thick cylindrical shells) under axial load and lateral pressure is investigated. The geometric imperfections are modeled as a 2D-1V non-homogeneous Gaussian stochastic field simulated using the spectral representation method. The evolutionar...

Subset Simulation (SS) is a powerful tool, simple to implement and capable of solving a broad range of reliability analysis problems. In many cases however, SS leads to reliability predictions that exhibit a large variability due to the fact that the robustness of the SS prediction depends on the selection of an adequate width of the proposal distr...

The stability analysis of steel tubes (relatively thick cylindrical shells) is important, e.g. for the design and construction of offshore pipeline members. In this work, the effect of initial geometric imperfections on the buckling load of steel tubes under axial load and external lateral pressure is investigated. The geometric imperfections are m...

A hierarchical multiscale approach is proposed in this work for the characterization of the mechanical and damping properties of carbon nanotube reinforced composites (CNT-RCs). The proposed numerical strategy encompasses various length scales, from nano to micro to macro. Individual straight CNTs are modeled at the nanoscale as space frame structu...

Carbon nanotube reinforced composites (CNT-RCs) are heterogenous materials which can exhibit enhanced mechanical and damping properties. Prior to their exploitation in engineering practice, insight knowledge of their microstructural behavior is required. Specifically the interatomic CNT-polymer interfacial interaction and thus the developed interfa...

This work examines the effect of random geometric imperfections in the buckling response of I-profile steel beam–column members as well as portal frame structures. Geometric imperfections are assumed to be non-homogeneous Gaussian random fields. Samples of these fields are generated using the spectral representation method with evolutionary power s...

A methodology is proposed for the Performance-Based optimum seismic Design (PBD) of structures implementing vulnerability objectives. Vulnerability objectives are introduced through target limit-state probabilities of exceedance. This is achieved by performing additional probabilistic design checks. The PBD framework implementing vulnerability obje...

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...

The effect of interfacial shear strength (ISS) on the mechanical and damping properties of carbon nanotube reinforced composites (CNT-RCs) is investigated in the present study using a multiscale simulation. The atomic lattice of CNTs is modeled with the modified molecular structural mechanics (MMSM) approach and reduced to an equivalent beam elemen...

A characteristic example of structures with complex stochastic response is that of shell structures. The analysis and design of shells are challenging since their behavior can be unpredictable with regard to geometry or boundary conditions. In this paper, a stochastic finite element (SFE) analysis is performed using the TRIC shear-deformable facet...

The concept of variability response functions (VRFs) is extended in this work to linear stochastic systems under dynamic excitations. An integral form for the variance of the dynamic response of stochastic systems is considered, involving a Dynamic VRF (DVRF) and the spectral density function of the stochastic field modeling the uncertain system pr...

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 th...

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...

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 an...

Buckling loads of thin-walled I-section beam-columns exhibit a wide stochastic scattering due to the uncertainty of imperfections. The present paper proposes a finite element based methodology for the stochastic buckling simulation of I-sections, which uses random fields to accurately describe the fluctuating size and spatial correlation of imperfe...

One of the most widely used techniques for the simulation of non-homogeneous 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. The paper at hand proposes a method for the estimation of separable...

A stochastic vulnerability-based robust design procedure of isotropic shell structures possessing uncertain initial geometric as well as material and thickness properties that are modeled as random fields is assessed against conventional and reliability-based robust design procedures. The main idea of the vulnerability-based design philosophy is to...

In this work, an enhanced hybrid method proposed by the authors for the simulation of homogeneous non-Gaussian stochastic fields, is extended to the non-homogeneous case i.e. the simulation of non-homogeneous non-Gaussian stochastic processes and fields with prescribed marginal distribution and temporally or spatially varying spectral density funct...

In this paper, the effect of material and thickness spatial variation on the buckling load of isotropic shells with random initial geometric imperfections is investigated. To this purpose, a random 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...

This study focusses on the estimation of seismic fragility curves for all common bridge types found in modern greek motorways. At first a classification scheme is developed in order to classify the existing bridges into a sufficient number of classes. A total of 11 representative bridge classes resulted, based on the type of piers, deck, and pier-t...

A computationally efficient method is presented for the buckling analysis of shells with random imperfections, based on a linearized buckling approximation of the limit load of the shell. A Stochastic Finite Element Method approach is used for the analysis of the “imperfect” shell structure involving random geometric deviations from its perfect geo...

This paper investigates the effect of material and thickness spatial variation on the buckling load of isotropic shells with random initial geometric imperfections. To this purpose, a random 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...

Probabilistic analysis is an emerging field of structural engineering which is very significant in structures of great importance like dams, nuclear reactors etc. In this work a Neural Networks (NN) based Monte Carlo Simulation (MCS) procedure is proposed for the vulnerability analysis of large concrete dams, in conjunction with a non-linear finite...

In the present paper, the effect of random non-uniform axial loading on the buckling behaviour of isotropic thin-walled imperfect cylindrical shells is investigated. Random initial (out-of-plane) geometric imperfections, thickness and material property variability, together with a non-uniform stochastic axial loading are incorporated into a cost-ef...

In the present paper, the effect of material and thickness imperfections on the buckling load of thin isotropic cylindrical shells is investigated. To this purpose, a 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. The ma...

The optimum design of isotropic shell structures with random initial geometric, material and thickness imperfections is investigated in this paper and a robust and efficient methodology is presented for treating such problems. For this purpose, the concept of an initial “imperfect” structure is introduced involving not only geometric deviations of...

A general finite element-based formulation is presented for the analysis of the mean and mean square response of stochastic structural systems whose material properties are described by random fields. A flexibility-based formulation is followed that does not involve any approximations. Closed-formed integral expressions for the mean and mean square...

The integral form for the variance of the response of stochastic statically indeterminate structural systems involving the so-called variability response function (VRF) and the spectral density function of the stochastic field modelling the uncertain system properties is established for the first time in this paper using evolutionary spectra theory...

The effect of material and thickness imperfections on the buckling load of isotropic shells is investigated in this paper. For this purpose, the concept of an initial ‘imperfect’ structure is introduced involving not only geometric deviations of the shell structure from its perfect geometry but also a spatial variability of the modulus of elasticit...