Lavinia Borges

An iterative algorithm for limit analysis with nonlinear yield functions

Abstract A mathematical programming algorithm is proposed for the general limit analysis problem. Plastic behavior is described by a set of linear or nonlinear yield functions. Abstract formulations of limit analysis are first considered and a Quasi-Newton strategy for solving the optimality conditions is then sketched. The structure of the problem arising from a finite element discretization is taken into account in order that the algorithm should be able to solve large scale problems.

An algorithm for shakedown analysis with nonlinear yield functions

Abstract This paper is devoted to propose an algorithm to solve the discrete form of the shakedown analysis problem with a nonlinear yield function. Firstly, variational formulations for shakedown analysis of structures under variable loads are considered. Secondly, the corresponding discrete forms are briefly recalled. Then, the algorithm is derived by combining a Newton formula based on the discrete equality conditions with a return mapping procedure focusing plastic admissibility. The proposed numerical procedure can be applied to finite element models with large number of degrees of freedom because the algorithm is specially designed to take advantage of the structure of such models. The numerical procedure is applied to a square plate with a circular hole under variable traction in two directions, and the obtained approximations are compared with available results. Finally, a rectangular plate with two small holes is considered in both plane strain and plane stress conditions. All application use the Mises condition without linearization.

A GENETIC ALGORITHM APPLIED TO COMPOSITE ELASTIC PARAMETERS IDENTIFICATION

The aim of this work is to present a technique to identify elastic parameters of composite materials. The identification is based on model updating involving an optimization process in which the objective function is defined as the difference between analytical natural frequencies and their experimental counterparts. Such analytical natural frequencies are obtained by means of the finite element method while the experimental ones are obtained by standard modal tests. The optimization problem is solved by a genetic algorithm (GA), which does not require the cost function gradient avoiding the expensive eigenvectors computation presents in gradient methods. The proposed technique is assessed by a number of different tests.

Numerical and Experimental Approach for Identifying Elastic Parameters in Sandwich Plates

This article deals with the identification of elastic parameters (engineering constants) in sandwich honeycomb orthotropic rectangular plates. A non-destructive method is introduced to identify the elastic parameters through the experimental measurements of natural frequencies of a plate undergoing free vibrations. Four elastic constant are identified. The estimation of the elastic parameter problem is solved by minimizing the differences between the measured and the calculated natural frequencies. The numerical method to calculate the natural frequencies involves the formulation of Rayleigh-Ritz using a series of characteristic orthogonal polynomials to properly model the free edge boundary conditions. The analysis of the results indicates the efficiency of the method.

Elasto‐plastic stress analysis of thick‐walled FGM pipes

The paper is concerned with quasi‐static deformation processes of elastic‐plastic FGM structures. It is assumed that the structures undergo small strain and the material properties of the graded layer are modeled by the modified rule of mixtures approximation. The elastic domain for ductile phases is defined through the Von Mises yield criterion. The mathematical problem consists of a variational equation that represents the equilibrium of the body and a variational inequality expressing the plastic strain rate evolution. An iterative method for solving this nonlinear system, combining a finite element approximation and an incremental‐iterative scheme, is proposed. The results of some numerical experiments comparing the plastic response of tubes with abrupt transition to different configurations obtained using smooth transitions containing FGM layers between the two dissimilar materials are provided.

Calibration of adhesion models based on the extended Kalman filtering

ABSTRACT This paper presents a strategy to be used for the calibration of adhesion models using a modified extended Kalman filter algorithm. A constitutive model coupling unilateral contact, adhesion and damage is considered for the analysis. The effect of the uncertainties in the constitutive adhesion parameters onto the adhesion reaction force is performed considering four uncertain scenarios. Furthermore, the effect of the speed in the loading-unloading of the system is also taken into account for these analyses. The parameter estimation strategy is assessed considering noise-corrupted synthetic data, two loading profiles and two possible measurement scenarios. The results indicate the key-role played by the sensitivity analysis when estimating the constitutive adhesion parameters and highlights the low sensitivity of system responses with respect to the viscous parameter when compared to the elastic parameter and also to the parameter associated with the energy of decohesion.

Calibration of adhesion models based on Bayesian inference

The use of composite materials in a myriad of applications fostered the development of reliable procedures to connect components with adhesives. This led to a demand for reliable adhesion models to be used in engineering designs that are based on computer simulations. This paper presents a strategy to be used for calibration of adhesion models. The proposed methodology is built on the formalism of Statistical Inverse Problems. Uncertainties about the unknowns are inferred using Population-Based Markov Chain Monte Carlo and Adaptive Metropolis. It is proposed to perform model assessments based on the analysis of a validation metric. Realizations of the validation metric are computed with the posterior densities of model parameters that are provided by the calibration process. The analysis of the validation metric allows for model selection to be performed. Some numerical experiments are presented with noise-contaminated data. The calibration strategy proved effective when dealing with both the nonlinearity and nondifferentiability of the adhesion constitutive equation.

A Bayesian framework for the calibration of cohesive zone models

ABSTRACT Adhesively bonded joints are used in several industrial sectors. Cohezive Zone Modes can be used to predict the adhesive mechanical behaviour. This work presents an approach to calibrate Cohesive Zone Models (CZM) by means of Statistical Inverse Analysis. The Bayesian framework for Inverse Problems is used to infer about the CZM model parameters. The solution corresponds to the exploration of the posterior probability density function of the model parameters. The exploration of the posterior density is performed by means of Markov Chain Monte Carlo (MCMC) methods mixing Population-Based MCMC with Adaptive Metropolis (AD) strategies. The assessment of the approach is performed using measured data from a single-lap shear experimental set-up. Measured data from 5 test-specimens is used for calibration and measured data from five other test-specimens is used for model validation. It is proposed a stochastic effective model for the CZM parameters. The predictions of maximum force and maximum displacement that are provided by the effective model are in accordance with measured data that is used for validation.

The Mechanical Behavior of Viscoelastic Materials in the Frequency Domain

In the last few decades, a growing need for new materials for several applications led to the development and increase of studies in new theories such as viscoelasticity. Many efforts have been done to understand and characterize the mechanical behavior of these materials. The purpose of this work is to determine the viscoelastic Poisson’s ratio in the frequency domain, \(\nu ^*(\omega )\), for a viscoelastic material in order to characterize its three-dimensional behavior. To do so, the work is based on the elastic-viscoelastic correspondence principle (EVCP) and the time-temperature superposition principle (TTSP). Measurements of the complex shear modulus, \(G^*(\omega )\), and the complex modulus, \(E^*(\omega )\), were performed using a dynamic mechanical analyzer (DMA). To consider eventual uncertainties, each specific mechanical test was carried out using three test-specimens.