A linear optimization approach to the combined production planning model

Two fundamental processes usually arise in the production planning of many industries. The first one consists of deciding how many final products of each type have to be produced in each period of a planning horizon, the well-known lot sizing problem. The other process consists of cutting raw materials in stock in order to produce smaller parts used in the assembly of final products, the well-studied cutting stock problem. In this paper the decision variables of these two problems are dependent of each other in order to obtain a global optimum solution. Setups that are typically present in lot sizing problems are relaxed together with integer frequencies of cutting patterns in the cutting problem. Therefore, a large scale linear optimizations problem arises, which is exactly solved by a column generated technique. It is worth noting that this new combined problem still takes the trade-off between storage costs (for final products and the parts) and trim losses (in the cutting process). We present some sets of computational tests, analyzed over three different scenarios. These results show that, by combining the problems and using an exact method, it is possible to obtain significant gains when compared to the usual industrial practice, which solve them in sequence. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

A positional FEM Formulation for geometrical non-linear analysis of shells

This work presents a fully non-linear finite element formulation for shell analysis comprising linear strain variation along the thickness of the shell and geometrically exact description for curved triangular elements. The developed formulation assumes positions and generalized unconstrained vectors as the variables of the problem, not displacements and finite rotations. The full 3D Saint-Venant-Kirchhoff constitutive relation is adopted and, to avoid locking, the rate of thickness variation enhancement is introduced. As a consequence, the second Piola-Kirchhoff stress tensor and the Green strain measure are employed to derive the specific strain energy potential. Curved triangular elements with cubic approximation are adopted using simple notation. Selected numerical simulations illustrate and confirm the objectivity, accuracy, path independence and applicability of the proposed technique.

GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

Non-linear boundary element formulation applied to contact analysis using tangent operator

This work presents a non-linear boundary element formulation applied to analysis of contact problems. The boundary element method (BEM) is known as a robust and accurate numerical technique to handle this type of problem, because the contact among the solids occurs along their boundaries. The proposed non-linear formulation is based on the use of singular or hyper-singular integral equations by BEM, for multi-region contact. When the contact occurs between crack surfaces, the formulation adopted is the dual version of BEM, in which singular and hyper-singular integral equations are defined along the opposite sides of the contact boundaries. The structural non-linear behaviour on the contact is considered using Coulomb`s friction law. The non-linear formulation is based on the tangent operator in which one uses the derivate of the set of algebraic equations to construct the corrections for the non-linear process. This implicit formulation has shown accurate as the classical approach, however, it is faster to compute the solution. Examples of simple and multi-region contact problems are shown to illustrate the applicability of the proposed scheme. (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.

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 solid-like FEM for geometrically non-linear 3D frames

This study presents a solid-like finite element formulation to solve geometric non-linear three-dimensional inhomogeneous frames. To achieve the desired representation, unconstrained vectors are used instead of the classic rigid director triad; as a consequence, the resulting formulation does not use finite rotation schemes. High order curved elements with any cross section are developed using a full three-dimensional constitutive elastic relation. Warping and variable thickness strain modes are introduced to avoid locking. The warping mode is solved numerically in FEM pre-processing computational code, which is coupled to the main program. The extra calculations are relatively small when the number of finite elements. with the same cross section, increases. The warping mode is based on a 2D free torsion (Saint-Venant) problem that considers inhomogeneous material. A scheme that automatically generates shape functions and its derivatives allow the use of any degree of approximation for the developed frame element. General examples are solved to check the objectivity, path independence, locking free behavior, generality and accuracy of the proposed formulation. (C) 2009 Elsevier B.V. All rights reserved.

A FEM procedure based on positions and unconstrained vectors applied to non-linear dynamic of 3D frames

This study presents an alternative three-dimensional geometric non-linear frame formulation based on generalized unconstrained vector and positions to solve structures and mechanisms subjected to dynamic loading. The formulation is classified as total Lagrangian with exact kinematics description. The resulting element presents warping and non-constant transverse strain modes, which guarantees locking-free behavior for the adopted three-dimensional constitutive relation, Saint-Venant-Kirchhoff, for instance. The application of generalized vectors is an alternative to the use of finite rotations and rigid triad`s formulae. Spherical and revolute joints are considered and selected dynamic and static examples are presented to demonstrate the accuracy and generality of the proposed technique. (C) 2010 Elsevier B.V. All rights reserved.

Optimal synthesis of Fenton reactor networks for phenol degradation

There is an increasing need to treat effluents contaminated with phenol with advanced oxidation processes (AOPs) to minimize their impact on the environment as well as on bacteriological populations of other wastewater treatment systems. One of the most promising AOPs is the Fenton process that relies on the Fenton reaction. Nevertheless, there are no systematic studies on Fenton reactor networks. The objective of this paper is to develop a strategy for the optimal synthesis of Fenton reactor networks. The strategy is based on a superstructure optimization approach that is represented as a mixed integer non-linear programming (MINLP) model. Network superstructures with multiple Fenton reactors are optimized with the objective of minimizing the sum of capital, operation and depreciation costs of the effluent treatment system. The optimal solutions obtained provide the reactor volumes and network configuration, as well as the quantities of the reactants used in the Fenton process. Examples based on a case study show that multi-reactor networks yield decrease of up to 45% in overall costs for the treatment plant. (C) 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Non-linear modal analysis for beams subjected to axial loads: Analytical and finite-element solutions

A rigorous derivation of non-linear equations governing the dynamics of an axially loaded beam is given with a clear focus to develop robust low-dimensional models. Two important loading scenarios were considered, where a structure is subjected to a uniformly distributed axial and a thrust force. These loads are to mimic the main forces acting on an offshore riser, for which an analytical methodology has been developed and applied. In particular, non-linear normal modes (NNMs) and non-linear multi-modes (NMMs) have been constructed by using the method of multiple scales. This is to effectively analyse the transversal vibration responses by monitoring the modal responses and mode interactions. The developed analytical models have been crosschecked against the results from FEM simulation. The FEM model having 26 elements and 77 degrees-of-freedom gave similar results as the low-dimensional (one degree-of-freedom) non-linear oscillator, which was developed by constructing a so-called invariant manifold. The comparisons of the dynamical responses were made in terms of time histories, phase portraits and mode shapes. (C) 2008 Elsevier Ltd. All rights reserved.

Non-linear pathways of corporate environmental management: a survey of ISO 14001-certified companies in Brazil

A study was conducted to verify whether the theory on the evolution of corporate environmental management (CEM) is applicable to organizations located in Brazil. Some of the most important proposals pertaining to the evolution of CEM were evaluated in a systematic fashion and integrated into a typical theoretical framework containing three evolutionary stages: reactive, preventive and proactive. The validity of this framework was tested by surveying 94 companies located in Brazil with ISO 14001 certification. Results indicated that the evolution of CEM tends to occur in a manner that is counter to what has generally been described in the literature. Two evolutionary stages were identified: 1) synergy for eco-efficiency and 2) environmental legislation view, which combine variables that were initially categorized into different theoretical CEM stages. These data, obtained from a direct study of Brazilian companies, suggest that the evolution of environmental management in organizations tends to occur in a non-linear fashion, requiring a re-analysis of traditional perceptions of CEM development, as suggested by Kolk and Mauser (2002). (C) 2010 Elsevier Ltd. All rights reserved.

The constrained compartmentalized knapsack problem: mathematical models and solution methods

The constrained compartmentalized knapsack problem can be seen as an extension of the constrained knapsack problem. However, the items are grouped into different classes so that the overall knapsack has to be divided into compartments, and each compartment is loaded with items from the same class. Moreover, building a compartment incurs a fixed cost and a fixed loss of the capacity in the original knapsack, and the compartments are lower and upper bounded. The objective is to maximize the total value of the items loaded in the overall knapsack minus the cost of the compartments. This problem has been formulated as an integer non-linear program, and in this paper, we reformulate the non-linear model as an integer linear master problem with a large number of variables. Some heuristics based on the solution of the restricted master problem are investigated. A new and more compact integer linear model is also presented, which can be solved by a branch-and-bound commercial solver that found most of the optimal solutions for the constrained compartmentalized knapsack problem. On the other hand, heuristics provide good solutions with low computational effort. (C) 2011 Elsevier BM. All rights reserved.

A hybrid Particle Swarm Optimization - Simplex algorithm (PSOS) for structural damage identification

This study proposes a new PSOS-model based damage identification procedure using frequency domain data. The formulation of the objective function for the minimization problem is based on the Frequency Response Functions (FRFs) of the system. A novel strategy for the control of the Particle Swarm Optimization (PSO) parameters based on the Nelder-Mead algorithm (Simplex method) is presented; consequently, the convergence of the PSOS becomes independent of the heuristic constants and its stability and confidence are enhanced. The formulated hybrid method performs better in different benchmark functions than the Simulated Annealing (SA) and the basic PSO (PSO(b)). Two damage identification problems, taking into consideration the effects of noisy and incomplete data, were studied: first, a 10-bar truss and second, a cracked free-free beam, both modeled with finite elements. In these cases, the damage location and extent were successfully determined. Finally, a non-linear oscillator (Duffing oscillator) was identified by PSOS providing good results. (C) 2009 Elsevier Ltd. All rights reserved

Real time optimization (RTO) with model predictive control (MPC)

This paper studies a simplified methodology to integrate the real time optimization (RTO) of a continuous system into the model predictive controller in the one layer strategy. The gradient of the economic objective function is included in the cost function of the controller. Optimal conditions of the process at steady state are searched through the use of a rigorous non-linear process model, while the trajectory to be followed is predicted with the use of a linear dynamic model, obtained through a plant step test. The main advantage of the proposed strategy is that the resulting control/optimization problem can still be solved with a quadratic programming routine at each sampling step. Simulation results show that the approach proposed may be comparable to the strategy that solves the full economic optimization problem inside the MPC controller where the resulting control problem becomes a non-linear programming problem with a much higher computer load. (C) 2010 Elsevier Ltd. All rights reserved.

Ressonância não linear de uma bússola em campos magnéticos

Fenômenos oscilatórios e ressonantes são explorados em vários cursos experimentais de física. Em geral os experimentos são interpretados no limite de pequenas oscilações e campos uniformes. Neste artigo descrevemos um experimento de baixo custo para o estudo da ressonância em campo magnético da agulha de uma bússola fora dos limites acima. Nesse caso, termos não lineares na equação diferencial são responsáveis por fenômenos interessantes de serem explorados em laboratórios didáticos.