Armando Miguel Awruch

Comparison of response surface and neural network with other methods for structural reliability analysis

The evaluation of the failure probability and safety levels of structural systems is of extreme importance in structural design, mainly when the variables are eminently random. Some examples of random variables on real structures are material properties, loads and member dimensions. It is necessary to quantify and compare the importance of each one of these variables in the structural safety. Many researchers studied structural reliability problems and nowadays there are several approaches for these problems. Two recent approaches, the Response Surface (RS) and the Artificial Neural Network (ANN) techniques, have emerged attempting to solve complex and more elaborated problems. In this work, these two techniques are presented, and comparison are carried out using the well known First Order Reliability Method (FORM), Direct Monte Carlo Simulation and Monte Carlo Simulation with Adaptive Importance Sampling technique with approximated and exact limit state functions. Problems with simple limit state functions (LSF) and closed form solutions of the failure probability are solved in order to highlight the advantages and shortcomings using these techniques. Some remarks are outlined regarding the fact that RS and ANN techniques have presented equivalent precision levels. It is observed that in problems where the computational cost of structural evaluations (looking for the failure probability and safety levels) is high, these two techniques may turn feasible the evaluation of the structural reliability through simulation techniques.

On stochastic finite elements for structural analysis

Abstract This paper considers the stochastic finite element analysis of structures resulting from random spatial variability of material properties, when they are subjected to loads of deterministic nature. Direct Monte Carlo simulation, Monte Carlo with Neumann expansion of the stiffness matrix and Taylor series expansion combined with the classical finite element approach are applied and compared with respect to accuracy and computational efficiency. Dynamic and non-linear problems are also included.

Probabilistic finite element analysis of concrete gravity dams

Abstract A methodology for the probabilistic analysis of concrete gravity dams is presented, Concrete properties and seismic excitation are considered as random variables. The seismic excitation is considered as a non-stationary stochastic process which is artificially generated. Concrete properties have random variations over the spatial domain. Structural response is obtained employing the finite element method to solve the equations of motion of the coupled system dam-reservoir-foundation. Structural safety is evaluated with respect to the main failure modes (cracking, concrete crushing and sliding at the dam-foundation interface) using the Monte Carlo method.

Some aspects on three-dimensional numerical modelling of reinforced concrete structures using the finite element method

Abstract This paper deals with some aspects related to three-dimensional numerical modelling of reinforced concrete structures using the Finite Element Method (FEM). Some subjects such as the solution technique of the non-linear equilibrium equations and the constitutive model for concrete and reinforcement steel are emphasised and commented. A robust method for the evaluation of the intersecting points of the embedded reinforcement bars into the three-dimensional finite element mesh is also presented. The main advantages of the Generalised Displacement Control Method with the Generalised Displacement Parameter to improve the response of the concrete and reinforced concrete analyses are highlighted. Finally, a series of numerical examples related to the above-mentioned aspects are presented.

Numerical simulation of the wind action on a long-span bridge deck

A numerical model to study the aerodynamic and aeroelastic bridge deck behavior is presented in this paper. The flow around a rigid fixed bridge cross-section, as well as the flow around the same cross-section with torsional motion, are investigated to obtain the aerodynamic coefficients, the Strouhal number and to determine the critical wind speed originating dynamic instability due to flutter. The two-dimensional flow is analyzed employing the pseudo-compressibility approach, with an Arbitrary Lagrangean-Eulerian (ALE) formulation and an explicit two-step Taylor-Galerkin method. The finite element method (FEM) is used for spatial discretization. The structure is considered as a rigid body with elastic restrains for the cross-section rotation and displacement components. The fluid-structure interaction is accomplished applying the compatibility and equilibrium conditions at the fluid-solid interface. The structural dynamic analysis is performed using the classical Newmarks method.

A finite element approach for multiphase fluid flow in porous media

The main scope of this work is to carry out a mathematical framework and its corresponding finite element (FE) discretization for the partially saturated soil consolidation modelling in presence of an immiscible pollutant. A multiphase system with the interstitial voids in the grain matrix filled with water (liquid phase), water vapour and dry air (gas phase) and with pollutant substances, is assumed. The mathematical model addressed in this work was developed in the framework of mixture theory considering the pollutant saturation-suction coupling effects. The ensuing mathematical model involves equations of momentum balance, energy balance and mass balance of the whole multiphase system. Encouraging outcomes were achieved in several different examples.

Reliability of reinforced concrete structures using stochastic finite elements

In this paper, special emphasis is given to uncertainties in the evaluation of the structural behavior, looking for a better representation of the system characteristics and quantification of the significance of these uncertainties in structural design. The reliability analysis of reinforced concrete structures is performed taking into account the spatial variability of material properties. The finite element method is used to analyze reinforced concrete structures. A multidimensional non‐Gaussian stochastic field generation model (independent of the finite element mesh) is developed and used. The reliability analysis is carried out employing the first order reliability method. Numerical examples are presented to study how to generate correlated non‐Gaussian stochastic fields and determine the reliability of a reinforced concrete structure with respect to a limit state function.

Influence of the saturation-suction relationship in the formulation of non-saturated soil consolidation models

The main scope of this paper is to present a fully coupled numerical model for isothermal soil consolidation analysis based on a combination of different stress states. Being originally a non-symmetric problem, it may be straightforward reduced to a symmetric one, and general guidelines for the conditions in which this reduction may be carried out, are addressed. Non-linear saturation-suction and permeability-suction functions were incorporated into a Galerkin approach of the non-saturated soil consolidation problem, which was solved using the finite element method. In order to validate the model, various examples, for which previous solutions are known, were solved. The use of either a strongly non-linear and non-symmetric formulation or a simple symmetric formulation with accurate prediction in deformation and pore-pressures is extremely dependent on the soil characteristic curves and their derivatives and this aspect is taken into account in the present mathematical approach. The emergent coupling effects may be easily uncoupled in the computer model by merely recasting some coefficients of the discrete equation system.

Three-dimensional simulation of high compressible flows using a multi-time-step integration technique with subcycles

Abstract An algorithm to simulate three-dimensional high compressible flows using the finite element method and a multi-time-step integration technique with subcycles is presented in this work. An explicit two-step Taylor–Galerkin scheme is adopted to integrate in time the continuum equations. When explicit schemes are used, the time-steps must satisfy the CFL stability conditions. If the smallest critical time-step is adopted uniformly for the whole domain, the integration scheme may consume a large amount of CPU time. Multi-time-step integration techniques are very suitable in these cases because elements and nodes are separated into several groups and a different time-step is assigned to each group. In this way, each group of elements is integrated with a time interval which is much closer to the critical time-steps of the elements in the group. This results in great computational savings, mainly when element sizes and properties are very different, leading to significant differences in the local critical time-step values. Multi-time-steps integration techniques are also very useful in transient problems, taking into account that at the end of each subcycle, values of the unknowns at the same time level are obtained. The multi-time-step algorithm is applied to analyze the supersonic flow (Mach=8.5) past a sphere immersed in a non-viscous flow, and the results and computational performance are compared with those obtained when a uniform time-step is used over the whole domain.

Large eddy simulation of three-dimensional turbulent flows by the finite element method

The main objectives of this work are the formulation, implementation and applications of a numerical algorithm to simulate turbulent, incompressible, isothermal flows. The transient three-dimensional flow is analyzed using an explicit Taylor-Galerkin scheme and the finite element method with hexahedrical eight-node element. Turbulence is simulated using Large Eddy Simulation. For sub-grid scales two models were implemented, the classical Smagorinskys model and the dynamic eddy viscosity model. For the second filtration, which is necessary in the dynamic model, a new method was developed based on independent finite elements that involve each node in the original mesh. The implemented scheme is efficient and good results with low additional computational cost were obtained. Results for two classical problems, the driven cavity and the backward facing step are presented. Comments about the model applicability for flows with high Reynolds numbers are also presented.