Otimização de forma aplicando B-splines sob critério integral de tensões

This work proposes a computational methodology to solve problems of optimization in structural design. The application develops, implements and integrates methods for structural analysis, geometric modeling, design sensitivity analysis and optimization. So, the optimum design problem is particularized for plane stress case, with the objective to minimize the structural mass subject to a stress criterion. Notice that, these constraints must be evaluated at a series of discrete points, whose distribution should be dense enough in order to minimize the chance of any significant constraint violation between specified points. Therefore, the local stress constraints are transformed into a global stress measure reducing the computational cost in deriving the optimal shape design. The problem is approximated by Finite Element Method using Lagrangian triangular elements with six nodes, and use a automatic mesh generation with a mesh quality criterion of geometric element. The geometric modeling, i.e., the contour is defined by parametric curves of type B-splines, these curves hold suitable characteristics to implement the Shape Optimization Method, that uses the key points like design variables to determine the solution of minimum problem. A reliable tool for design sensitivity analysis is a prerequisite for performing interactive structural design, synthesis and optimization. General expressions for design sensitivity analysis are derived with respect to key points of B-splines. The method of design sensitivity analysis used is the adjoin approach and the analytical method. The formulation of the optimization problem applies the Augmented Lagrangian Method, which convert an optimization problem constrained problem in an unconstrained. The solution of the Augmented Lagrangian function is achieved by determining the analysis of sensitivity. Therefore, the optimization problem reduces to the solution of a sequence of problems with lateral limits constraints, which is solved by the Memoryless Quasi-Newton Method It is demonstrated by several examples that this new approach of analytical design sensitivity analysis of integrated shape design optimization with a global stress criterion purpose is computationally efficient

Otimização topológica de estruturas termoelásticas tridimensionais

This work presents an optimization technique based on structural topology optimization methods, TOM, designed to solve problems of thermoelasticity 3D. The presented approach is based on the adjoint method of sensitivity analysis unified design and is intended to loosely coupled thermomechanical problems. The technique makes use of analytical expressions of sensitivities, enabling a reduction in the computational cost through the use of a coupled field adjoint equation, defined in terms the of temperature and displacement fields. The TOM used is based on the material aproach. Thus, to make the domain is composed of a continuous distribution of material, enabling the use of classical models in nonlinear programming optimization problem, the microstructure is considered as a porous medium and its constitutive equation is a function only of the homogenized relative density of the material. In this approach, the actual properties of materials with intermediate densities are penalized based on an artificial microstructure model based on the SIMP (Solid Isotropic Material with Penalty). To circumvent problems chessboard and reduce dependence on layout in relation to the final optimal initial mesh, caused by problems of numerical instability, restrictions on components of the gradient of relative densities were applied. The optimization problem is solved by applying the augmented Lagrangian method, the solution being obtained by applying the finite element method of Galerkin, the process of approximation using the finite element Tetra4. This element has the ability to interpolate both the relative density and the displacement components and temperature. As for the definition of the problem, the heat load is assumed in steady state, i.e., the effects of conduction and convection of heat does not vary with time. The mechanical load is assumed static and distributed

Otimização Topológica com Termo-elasticidade Utilizando Elementos Tri3

This work proposes a formulation for optimization of 2D-structure layouts submitted to mechanic and thermal shipments and applied an h-adaptive filter process which conduced to computational low spend and high definition structural layouts. The main goal of the formulation is to minimize the structure mass submitted to an effective state of stress of von Mises, with stability and lateral restriction variants. A criterion of global measurement was used for intents a parametric condition of stress fields. To avoid singularity problems was considerate a release on the stress restriction. On the optimization was used a material approach where the homogenized constructive equation was function of the material relative density. The intermediary density effective properties were represented for a SIMP-type artificial model. The problem was simplified by use of the method of finite elements of Galerkin using triangles with linear Lagrangian basis. On the solution of the optimization problem, was applied the augmented Lagrangian Method, that consists on minimum problem sequence solution with box-type restrictions, resolved by a 2nd orderprojection method which uses the method of the quasi-Newton without memory, during the problem process solution. This process reduces computational expends showing be more effective and solid. The results materialize more refined layouts with accurate topologic and shape of structure definitions. On the other hand formulation of mass minimization with global stress criterion provides to modeling ready structural layouts, with violation of the criterion of homogeneous distributed stress

Desenvolvimento da célula base de microestruturas periódicas de compósitos sob otimização topológica

This thesis develops a new technique for composite microstructures projects by the Topology Optimization process, in order to maximize rigidity, making use of Deformation Energy Method and using a refining scheme h-adaptative to obtain a better defining the topological contours of the microstructure. This is done by distributing materials optimally in a region of pre-established project named as Cell Base. In this paper, the Finite Element Method is used to describe the field and for government equation solution. The mesh is refined iteratively refining so that the Finite Element Mesh is made on all the elements which represent solid materials, and all empty elements containing at least one node in a solid material region. The Finite Element Method chosen for the model is the linear triangular three nodes. As for the resolution of the nonlinear programming problem with constraints we were used Augmented Lagrangian method, and a minimization algorithm based on the direction of the Quasi-Newton type and Armijo-Wolfe conditions assisting in the lowering process. The Cell Base that represents the composite is found from the equivalence between a fictional material and a preescribe material, distributed optimally in the project area. The use of the strain energy method is justified for providing a lower computational cost due to a simpler formulation than traditional homogenization method. The results are presented prescription with change, in displacement with change, in volume restriction and from various initial values of relative densities.

An augmented reality pipeline to create scenes with coherent illumination using textured cuboids

Shadows and illumination play an important role when generating a realistic scene in computer graphics. Most of the Augmented Reality (AR) systems track markers placed in a real scene and retrieve their position and orientation to serve as a frame of reference for added computer generated content, thereby producing an augmented scene. Realistic depiction of augmented content with coherent visual cues is a desired goal in many AR applications. However, rendering an augmented scene with realistic illumination is a complex task. Many existent approaches rely on a non automated pre-processing phase to retrieve illumination parameters from the scene. Other techniques rely on specific markers that contain light probes to perform environment lighting estimation. This study aims at designing a method to create AR applications with coherent illumination and shadows, using a textured cuboid marker, that does not require a training phase to provide lighting information. Such marker may be easily found in common environments: most of product packaging satisfies such characteristics. Thus, we propose a way to estimate a directional light configuration using multiple texture tracking to render AR scenes in a realistic fashion. We also propose a novel feature descriptor that is used to perform multiple texture tracking. Our descriptor is an extension of the binary descriptor, named discrete descriptor, and outperforms current state-of-the-art methods in speed, while maintaining their accuracy.