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

Modelagem Matemática e Computacional de fenômenos eletrocinéticos em meios porosos carregados eletricamente

In this work we present a mathematical and computational modeling of electrokinetic phenomena in electrically charged porous medium. We consider the porous medium composed of three different scales (nanoscopic, microscopic and macroscopic). On the microscopic scale the domain is composed by a porous matrix and a solid phase. The pores are filled with an aqueous phase consisting of ionic solutes fully diluted, and the solid matrix consists of electrically charged particles. Initially we present the mathematical model that governs the electrical double layer in order to quantify the electric potential, electric charge density, ion adsorption and chemical adsorption in nanoscopic scale. Then, we derive the microscopic model, where the adsorption of ions due to the electric double layer and the reactions of protonation/ deprotanaç~ao and zeta potential obtained in modeling nanoscopic arise in microscopic scale through interface conditions in the problem of Stokes and Nerst-Planck equations respectively governing the movement of the aqueous solution and transport of ions. We developed the process of upscaling the problem nano/microscopic using the homogenization technique of periodic structures by deducing the macroscopic model with their respectives cell problems for effective parameters of the macroscopic equations. Considering a clayey porous medium consisting of kaolinite clay plates distributed parallel, we rewrite the macroscopic model in a one-dimensional version. Finally, using a sequential algorithm, we discretize the macroscopic model via the finite element method, along with the interactive method of Picard for the nonlinear terms. Numerical simulations on transient regime with variable pH in one-dimensional case are obtained, aiming computational modeling of the electroremediation process of clay soils contaminated

Modelagem dos efeitos da irradiação luminosa no cérebro de camundongos e rastreamento de neurônios durante experimentos de microscopia de fluorescência

The fluorescent proteins are an essential tool in many fields of biology, since they allow us to watch the development of structures and dynamic processes of cells in living tissue, with the aid of fluorescence microscopy. Optogenectics is another technique that is currently widely used in Neuroscience. In general, this technique allows to activate/deactivate neurons with the radiation of certain wavelengths on the cells that have ion channels sensitive to light, at the same time that can be used with fluorescent proteins. This dissertation has two main objectives. Initially, we study the interaction of light radiation and mice brain tissue to be applied in optogenetic experiments. In this step, we model absorption and scattering effects using mice brain tissue characteristics and Kubelka-Munk theory, for specific wavelengths, as a function of light penetration depth (distance) within the tissue. Furthermore, we model temperature variations using the finite element method to solve Pennes’ bioheat equation, with the aid of COMSOL Multiphysics Modeling Software 4.4, where we simulate protocols of light stimulation tipically used in optogenetics. Subsequently, we develop some computational algorithms to reduce the exposure of neuron cells to the light radiation necessary for the visualization of their emitted fluorescence. At this stage, we describe the image processing techniques developed to be used in fluorescence microscopy to reduce the exposure of the brain samples to continuous light, which is responsible for fluorochrome excitation. The developed techniques are able to track, in real time, a region of interest (ROI) and replace the fluorescence emitted by the cells by a virtual mask, as a result of the overlay of the tracked ROI and the fluorescence information previously stored, preserving cell location, independently of the time exposure to fluorescent light. In summary, this dissertation intends to investigate and describe the effects of light radiation in brain tissue, within the context of Optogenetics, in addition to providing a computational tool to be used in fluorescence microscopy experiments to reduce image bleaching and photodamage due to the intense exposure of fluorescent cells to light radiation.

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.