Thermal diffusivity of polymers by modified angstrom method

The nature of the molecular structure of plastics makes the properties of such materials markedly temperature dependent. In addition, the continuous increase in the utilization of polymeric materials in many specific applications has demanded knowledge of their physical properties, both during their processing as raw material, as well as over the working temperature range of the final polymer product. Thermal conductivity, thermal diffusivity and specific heat, namely the thermal properties, are the three most important physical properties of a material that are needed for heat transfer calculations. Recently, among several different methods for the determination of the thermal diffusivity and thermal conductivity, transient techniques have become the preferable way for measuring thermal properties of materials. In this work, a very simple and low cost variation of the well known Angstrom method is employed in the experimental determination of the thermal diffusivity of some selected polymers. Cylindrical shaped samples 3 cm diameter and 7 cm high were prepared by cutting from long cylindrical commercial bars. The reproducibility is very good, and the results obtained were checked against results obtained by the hot wire technique, laser flash technique, and when possible, they were also compared with data found in the literature. Thermal conductivity may be then derived from the thermal diffusivity with the knowledge of the bulk density and the specific heat, easily obtained by differential scanning calorimetry. (C) 2009 Elsevier Ltd. All rights reserved.

Dual boundary element formulation applied to analysis of multi-fractured domains

This paper deals with analysis of multiple random crack propagation in two-dimensional domains using the boundary element method (BEM). BEM is known to be a robust and accurate numerical technique for analysing this type of problem. The formulation adopted in this work is based on the dual BEM, for which singular and hyper-singular integral equations are used. We propose an iterative scheme to predict the crack growth path and the crack length increment at each time step. The proposed scheme able us to simulate localisation and coalescence phenomena, which is the main contribution of this paper. Considering the fracture mechanics analysis, the displacement correlation technique is applied to evaluate the stress intensity factors. The propagation angle and the equivalent stress intensity factor are calculated using the theory of maximum circumferential stress. Examples of simple and multi-fractured domains, loaded up to the rupture, are considered to illustrate the applicability of the proposed scheme. (C) 2010 Elsevier Ltd. All rights reserved.

Chaos-Galerkin solution of stochastic Timoshenko bending problems

This paper presents an accurate and efficient solution for the random transverse and angular displacement fields of uncertain Timoshenko beams. Approximate, numerical solutions are obtained using the Galerkin method and chaos polynomials. The Chaos-Galerkin scheme is constructed by respecting the theoretical conditions for existence and uniqueness of the solution. Numerical results show fast convergence to the exact solution, at excellent accuracies. The developed Chaos-Galerkin scheme accurately approximates the complete cumulative distribution function of the displacement responses. The Chaos-Galerkin scheme developed herein is a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2011 Elsevier Ltd. All rights reserved.

A simple method for non-linear analysis of steel fiber reinforced concrete

This paper proposes a physical non-linear formulation to deal with steel fiber reinforced concrete by the finite element method. The proposed formulation allows the consideration of short or long fibers placed arbitrarily inside a continuum domain (matrix). The most important feature of the formulation is that no additional degree of freedom is introduced in the pre-existent finite element numerical system to consider any distribution or quantity of fiber inclusions. In other words, the size of the system of equations used to solve a non-reinforced medium is the same as the one used to solve the reinforced counterpart. Another important characteristic of the formulation is the reduced work required by the user to introduce reinforcements, avoiding ""rebar"" elements, node by node geometrical definitions or even complex mesh generation. Bounded connection between long fibers and continuum is considered, for short fibers a simplified approach is proposed to consider splitting. Non-associative plasticity is adopted for the continuum and one dimensional plasticity is adopted to model fibers. Examples are presented in order to show the capabilities of the formulation.

Galerkin Solution of Stochastic Beam Bending on Winkler Foundations

In this paper, the Askey-Wiener scheme and the Galerkin method are used to obtain approximate solutions to stochastic beam bending on Winkler foundation. The study addresses Euler-Bernoulli beams with uncertainty in the bending stiffness modulus and in the stiffness of the foundation. Uncertainties are represented by parameterized stochastic processes. The random behavior of beam response is modeled using the Askey-Wiener scheme. One contribution of the paper is a sketch of proof of existence and uniqueness of the solution to problems involving fourth order operators applied to random fields. From the approximate Galerkin solution, expected value and variance of beam displacement responses are derived, and compared with corresponding estimates obtained via Monte Carlo simulation. Results show very fast convergence and excellent accuracies in comparison to Monte Carlo simulation. The Askey-Wiener Galerkin scheme presented herein is shown to be a theoretically solid and numerically efficient method for the solution of stochastic problems in engineering.

Inverse analysis FOR two-dimensional structures using the boundary element method

Inverse analysis is currently an important subject of study in several fields of science and engineering. The identification of physical and geometric parameters using experimental measurements is required in many applications. In this work a boundary element formulation to identify boundary and interface values as well as material properties is proposed. In particular the proposed formulation is dedicated to identifying material parameters when a cohesive crack model is assumed for 2D problems. A computer code is developed and implemented using the BEM multi-region technique and regularisation methods to perform the inverse analysis. Several examples are shown to demonstrate the efficiency of the proposed model. (C) 2010 Elsevier Ltd. All rights reserved,

A coupled boundary element/differential equation method formulation for plate-beam interaction analysis

In this work, a new boundary element formulation for the analysis of plate-beam interaction is presented. This formulation uses a three nodal value boundary elements and each beam element is replaced by its actions on the plate, i.e., a distributed load and end of element forces. From the solution of the differential equation of a beam with linearly distributed load the plate-beam interaction tractions can be written as a function of the nodal values of the beam. With this transformation a final system of equation in the nodal values of displacements of plate boundary and beam nodes is obtained and from it, all unknowns of the plate-beam system are obtained. Many examples are analyzed and the results show an excellent agreement with those from the analytical solution and other numerical methods. (C) 2009 Elsevier Ltd. All rights reserved.

A boundary element formulation for analysis of elastoplastic plates with geometrical nonlinearity

In this paper a new boundary element method formulation for elastoplastic analysis of plates with geometrical nonlinearities is presented. The von Mises criterion with linear isotropic hardening is considered to evaluate the plastic zone. Large deflections are assumed but within the context of small strain. To derive the boundary integral equations the von Karman`s hypothesis is taken into account. An initial stress field is applied to correct the true stresses according to the adopted criterion. Isoparametric linear elements are used to approximate the boundary unknown values while triangular internal cells with linear shape function are adopted to evaluate the domain value influences. The nonlinear system of equations is solved by using an implicit scheme together with the consistent tangent operator derived along the paper. Numerical examples are presented to demonstrate the accuracy and the validity of the proposed formulation.

A BEM model applied to failure analysis of multi-fractured structures

Due to manufacturing or damage process, brittle materials present a large number of micro-cracks which are randomly distributed. The lifetime of these materials is governed by crack propagation under the applied mechanical and thermal loadings. In order to deal with these kinds of materials, the present work develops a boundary element method (BEM) model allowing for the analysis of multiple random crack propagation in plane structures. The adopted formulation is based on the dual BEM, for which singular and hyper-singular integral equations are used. An iterative scheme to predict the crack growth path and crack length increment is proposed. This scheme enables us to simulate the localization and coalescence phenomena, which are the main contribution of this paper. Considering the fracture mechanics approach, the displacement correlation technique is applied to evaluate the stress intensity factors. The propagation angle and the equivalent stress intensity factor are calculated using the theory of maximum circumferential stress. Examples of multi-fractured domains, loaded up to rupture, are considered to illustrate the applicability of the proposed method. (C) 2011 Elsevier Ltd. All rights reserved.

GENERALIZED FINITE ELEMENT METHOD FOR NONLINEAR THREE-DIMENSIONAL ANALYSIS OF SOLIDS

The Generalized Finite Element Method (GFEM) is employed in this paper for the numerical analysis of three-dimensional solids tinder nonlinear behavior. A brief summary of the GFEM as well as a description of the formulation of the hexahedral element based oil the proposed enrichment strategy are initially presented. Next, in order to introduce the nonlinear analysis of solids, two constitutive models are briefly reviewed: Lemaitre`s model, in which damage and plasticity are coupled, and Mazars`s damage model suitable for concrete tinder increased loading. Both models are employed in the framework of a nonlocal approach to ensure solution objectivity. In the numerical analyses carried out, a selective enrichment of approximation at regions of concern in the domain (mainly those with high strain and damage gradients) is exploited. Such a possibility makes the three-dimensional analysis less expensive and practicable since re-meshing resources, characteristic of h-adaptivity, can be minimized. Moreover, a combination of three-dimensional analysis and the selective enrichment presents a valuable good tool for a better description of both damage and plastic strain scatterings.

Analysis of stiffened plates by the boundary element method

In this paper, a formulation for representation of stiffeners in plane stress by the boundary elements method (BEM) in linear analysis is presented. The strategy is to adopt approximations for the displacements in the central line of the stiffener. With this simplification the Spurious oscillations in the stress along stiffeners with small thickness is prevented. Worked examples are analyzed to show the efficiency of these techniques, especially in the insertion of very narrow sub-regions, in which quasi-singular integrals are calculated, with stiffeners that are much stiffer than the main domain. The results obtained with this formulation are very close to those obtained with other formulations. (C) 2007 Elsevier Ltd. All rights reserved.

Consolidation of elastic-plastic saturated porous media by the boundary element method

This paper presents a domain boundary element formulation for inelastic saturated porous media with rate-independent behavior for the solid skeleton. The formulation is then applied to elastic-plastic behavior for the solid. Biot`s consolidation theory, extended to include irreversible phenomena is considered and the direct boundary element technique is used for the numerical solution after time discretization by the implicit Euler backward algorithm. The associated nonlinear algebraic problem is solved by the Newton-Raphson procedure whereby the loading/unloading conditions are fully taken into account and the consistent tangent operator defined. Only domain nodes (nodes defined inside the domain) are used to represent all domain values and the corresponding integrals are computed by using an accurate sub-elementation scheme. The developments are illustrated through the Drucker-Prager elastic-plastic model for the solid skeleton and various examples are analyzed with the proposed algorithms. (c) 2008 Elsevier B.V. All rights reserved.

On the analysis of notched concrete beams: From measurement with digital image correlation to identification with boundary element method of a cohesive model

A way of coupling digital image correlation (to measure displacement fields) and boundary element method (to compute displacements and tractions along a crack surface) is presented herein. It allows for the identification of Young`s modulus and fracture parameters associated with a cohesive model. This procedure is illustrated to analyze the latter for an ordinary concrete in a three-point bend test on a notched beam. In view of measurement uncertainties, the results are deemed trustworthy thanks to the fact that numerous measurement points are accessible and used as entries to the identification procedure. (C) 2010 Elsevier Ltd. All rights reserved.

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.

Solution of a heterogeneous modeling of a horizontal-flow anaerobic immobilized biomass (HAIB) reactor by the sequencing method

A modeling study was completed to develop a methodology that combines the sequencing and finite difference methods for the simulation of a heterogeneous model of a tubular reactor applied in the treatment of wastewater. The system included a liquid phase (convection diffusion transport) and a solid phase (diffusion reaction) that was obtained by completing a mass balance in the reactor and in the particle, respectively. The model was solved using a pilot-scale horizontal-flow anaerobic immobilized biomass (HAIB) reactor to treat domestic sewage, with the concentration results compared with the experimental data. A comparison of the behavior of the liquid phase concentration profile and the experimental results indicated that both the numerical methods offer a good description of the behavior of the concentration along the reactor. The advantage of the sequencing method over the finite difference method is that it is easier to apply and requires less computational time to model the dynamic simulation of outlet response of HAIB.