Non-linear boundary element formulation with tangent operator to analyse crack propagation in quasi-brittle materials

This work deals with analysis of cracked structures using BEM. Two formulations to analyse the crack growth process in quasi-brittle materials are discussed. They are based on the dual formulation of BEM where two different integral equations are employed along the opposite sides of the crack surface. The first presented formulation uses the concept of constant operator, in which the corrections of the nonlinear process are made only by applying appropriate tractions along the crack surfaces. The second presented BEM formulation to analyse crack growth problems is an implicit technique based on the use of a consistent tangent operator. This formulation is accurate, stable and always requires much less iterations to reach the equilibrium within a given load increment in comparison with the classical approach. Comparison examples of classical problem of crack growth are shown to illustrate the performance of the two formulations. (C) 2009 Elsevier Ltd. All rights reserved.

A numerical model for the description of the nonlinear behaviour of multi-leaf masonry walls

A nonlinear finite element model was developed to simulate the nonlinear response of three-leaf masonry specimens, which were subjected to laboratory tests with the aim of investigating the mechanical behaviour of multiple-leaf stone masonry walls up to failure. The specimens consisted of two external leaves made of stone bricks and mortar joints, and an internal leaf in mortar and stone aggregate. Different loading conditions, typologies of the collar joints, and stone types were taken into account. The constitutive law implemented in the model is characterized by a damage tensor, which allows the damage-induced anisotropy accompanying the cracking process to be described. To follow the post-peak behaviour of the specimens with sufficient accuracy it was necessary to make the damage model non-local, to avoid mesh-dependency effects related to the strain-softening behaviour of the material. Comparisons between the predicted and measured failure loads are quite satisfactory in most of the studied cases. (c) 2007 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.

The random barrier-crossing problem

This paper addresses the time-variant reliability analysis of structures with random resistance or random system parameters. It deals with the problem of a random load process crossing a random barrier level. The implications of approximating the arrival rate of the first overload by an ensemble-crossing rate are studied. The error involved in this so-called ""ensemble-crossing rate"" approximation is described in terms of load process and barrier distribution parameters, and in terms of the number of load cycles. Existing results are reviewed, and significant improvements involving load process bandwidth, mean-crossing frequency and time are presented. The paper shows that the ensemble-crossing rate approximation can be accurate enough for problems where load process variance is large in comparison to barrier variance, but especially when the number of load cycles is small. This includes important practical applications like random vibration due to impact loadings and earthquake loading. Two application examples are presented, one involving earthquake loading and one involving a frame structure subject to wind and snow loadings. (C) 2007 Elsevier Ltd. All rights reserved.

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Analytical solutions for geometrically nonlinear trusses

This paper presents an analytical method for analyzing trusses with severe geometrically nonlinear behavior. The main objective is to find analytical solutions for trusses with different axial forces in the bars. The methodology is based on truss kinematics, elastic constitutive laws and equilibrium of nodal forces. The proposed formulation can be applied to hyper elastic materials, such as rubber and elastic foams. A Von Mises truss with two bars made by different materials is analyzed to show the accuracy of this methodology.

Multiobjective Particle Swarm Approach for the Design of a Brushless DC Wheel Motor

The roots of swarm intelligence are deeply embedded in the biological study of self-organized behaviors in social insects. Particle swarm optimization (PSO) is one of the modern metaheuristics of swarm intelligence, which can be effectively used to solve nonlinear and non-continuous optimization problems. The basic principle of PSO algorithm is formed on the assumption that potential solutions (particles) will be flown through hyperspace with acceleration towards more optimum solutions. Each particle adjusts its flying according to the flying experiences of both itself and its companions using equations of position and velocity. During the process, the coordinates in hyperspace associated with its previous best fitness solution and the overall best value attained so far by other particles within the group are kept track and recorded in the memory. In recent years, PSO approaches have been successfully implemented to different problem domains with multiple objectives. In this paper, a multiobjective PSO approach, based on concepts of Pareto optimality, dominance, archiving external with elite particles and truncated Cauchy distribution, is proposed and applied in the design with the constraints presence of a brushless DC (Direct Current) wheel motor. Promising results in terms of convergence and spacing performance metrics indicate that the proposed multiobjective PSO scheme is capable of producing good solutions.

An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 2: shells

Following the approach developed for rods in Part 1 of this paper (Pimenta et al. in Comput. Mech. 42:715-732, 2008), this work presents a fully conserving algorithm for the integration of the equations of motion in nonlinear shell dynamics. We begin with a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, allowing for an extremely simple update of the rotational variables within the scheme. The weak form is constructed via non-orthogonal projection, the time-collocation of which ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that general hyperelastic materials (and not only materials with quadratic potentials) are permitted in a totally consistent way. Spatial discretization is performed using the finite element method and the robust performance of the scheme is demonstrated by means of numerical examples.

An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 1: Rods

A fully conserving algorithm is developed in this paper for the integration of the equations of motion in nonlinear rod dynamics. The starting point is a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, which results in an extremely simple update of the rotational variables. The weak form is constructed with a non-orthogonal projection corresponding to the application of the virtual power theorem. Together with an appropriate time-collocation, it ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that nonlinear hyperelastic materials (and not only materials with quadratic potentials) are permitted without any prejudice on the conservation properties. Spatial discretization is performed via the finite element method and the performance of the scheme is assessed by means of several numerical simulations.

Hybrid and multi-field variational principles for geometrically exact three-dimensional beams

This paper addresses the development of several alternative novel hybrid/multi-field variational formulations of the geometrically exact three-dimensional elastostatic beam boundary-value problem. In the framework of the complementary energy-based formulations, a Legendre transformation is used to introduce the complementary energy density in the variational statements as a function of stresses only. The corresponding variational principles are shown to feature stationarity within the framework of the boundary-value problem. Both weak and linearized weak forms of the principles are presented. The main features of the principles are highlighted, giving special emphasis to their relationships from both theoretical and computational standpoints. (C) 2010 Elsevier Ltd. All rights reserved.

PERFORMANCE OF THE MODEL CALLED ACQUANETXL IN THE ALLOCATION OF WATER IN COMPLEX WATER RESOURCE SYSTEMS

This article presents a tool for the allocation analysis of complex systems of water resources, called AcquaNetXL, developed in the form of spreadsheet in which a model of linear optimization and another nonlinear were incorporated. The AcquaNetXL keeps the concepts and attributes of a decision support system. In other words, it straightens out the communication between the user and the computer, facilitates the understanding and the formulation of the problem, the interpretation of the results and it also gives a support in the process of decision making, turning it into a clear and organized process. The performance of the algorithms used for solving the problems of water allocation was satisfactory especially for the linear model.

Enlarging the domain of attraction of stable MPC controllers, maintaining the output performance

This work presents an alternative way to formulate the stable Model Predictive Control (MPC) optimization problem that allows the enlargement of the domain of attraction, while preserving the controller performance. Based on the dual MPC that uses the null local controller, it proposed the inclusion of an appropriate set of slacked terminal constraints into the control problem. As a result, the domain of attraction is unlimited for the stable modes of the system, and the largest possible for the non-stable modes. Although this controller does not achieve local optimality, simulations show that the input and output performances may be comparable to the ones obtained with the dual MPC that uses the LQR as a local controller. (C) 2009 Elsevier Ltd. All rights reserved.

Infinite horizon MPC with non-minimal state space feedback

In the MPC literature, stability is usually assured under the assumption that the state is measured. Since the closed-loop system may be nonlinear because of the constraints, it is not possible to apply the separation principle to prove global stability for the Output feedback case. It is well known that, a nonlinear closed-loop system with the state estimated via an exponentially converging observer combined with a state feedback controller can be unstable even when the controller is stable. One alternative to overcome the state estimation problem is to adopt a non-minimal state space model, in which the states are represented by measured past inputs and outputs [P.C. Young, M.A. Behzadi, C.L. Wang, A. Chotai, Direct digital and adaptative control by input-output, state variable feedback pole assignment, International journal of Control 46 (1987) 1867-1881; C. Wang, P.C. Young, Direct digital control by input-output, state variable feedback: theoretical background, International journal of Control 47 (1988) 97-109]. In this case, no observer is needed since the state variables can be directly measured. However, an important disadvantage of this approach is that the realigned model is not of minimal order, which makes the infinite horizon approach to obtain nominal stability difficult to apply. Here, we propose a method to properly formulate an infinite horizon MPC based on the output-realigned model, which avoids the use of an observer and guarantees the closed loop stability. The simulation results show that, besides providing closed-loop stability for systems with integrating and stable modes, the proposed controller may have a better performance than those MPC controllers that make use of an observer to estimate the current states. (C) 2008 Elsevier Ltd. All rights reserved.

Robust model predictive control with zone control

Model predictive control (MPC) is usually implemented as a control strategy where the system outputs are controlled within specified zones, instead of fixed set points. One strategy to implement the zone control is by means of the selection of different weights for the output error in the control cost function. A disadvantage of this approach is that closed-loop stability cannot be guaranteed, as a different linear controller may be activated at each time step. A way to implement a stable zone control is by means of the use of an infinite horizon cost in which the set point is an additional variable of the control problem. In this case, the set point is restricted to remain inside the output zone and an appropriate output slack variable is included in the optimisation problem to assure the recursive feasibility of the control optimisation problem. Following this approach, a robust MPC is developed for the case of multi-model uncertainty of open-loop stable systems. The controller is devoted to maintain the outputs within their corresponding feasible zone, while reaching the desired optimal input target. Simulation of a process of the oil re. ning industry illustrates the performance of the proposed strategy.

Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming

This paper addresses the non-preemptive single machine scheduling problem to minimize total tardiness. We are interested in the online version of this problem, where orders arrive at the system at random times. Jobs have to be scheduled without knowledge of what jobs will come afterwards. The processing times and the due dates become known when the order is placed. The order release date occurs only at the beginning of periodic intervals. A customized approximate dynamic programming method is introduced for this problem. The authors also present numerical experiments that assess the reliability of the new approach and show that it performs better than a myopic policy.