Carla Tatiana Mota Anflor

A Quadratic Boundary Implementation for Solving 2D Problems of Elasticity by Topology Optimization

The main goal of this work relies on implementing discontinuous quadratic elements on a previous existent optimization code. The existent code refers to problems of topology optimization using a standard Boundary Element Method (BEM) formulation. A Topological Derivative (DT) is used for determining the domains sensitivity. The implicit cost function used for DT derivation is based on the total potential energy. A fixed amount of material with less efficiency is progressively removed during the optimization process. It is expected that the quadratic elements implementation increases the accuracy of the final solution, since the previous code were implemented by using linear elements. Despite of this code is still under development the final topology presents a good agreement when compared with those presented in the literature.

Structural optimization using the boundary element method and topological derivative applied to a suspension trailing arm

ABSTRACT This work investigates the optimization of elasticity problems using the boundary element method (BEM) as a numerical solver. A topological shape sensitivity approach is used to select the points showing the lowest sensitivities. As the iterative process evolves, the original domain has portions of material progressively removed in the less efficient areas until a given stop criterion is achieved. Two benchmark tests are investigated to demonstrate the influence of the boundary conditions on the final topology. Following this, a suspension trailing arm is optimized and a new design is proposed as an alternative to commercially available methods. A postprocedure of smoothing using Bézier curves was employed for the final topology of the trailing arm. This process allowed the external irregular shapes to be overcome. The BEM coupled with the topological derivative was shown to be an alternative to traditional optimization techniques using the finite element method. The present methodology was shown to be efficient for delivering optimal topologies with few iterations. All routines used were written in open code.

Numerical and experimental analysis of a RVE condition for heterogeneous materials using BEM and thermal images

espanolEste trabajo se enfoca en el estudio numerico y experimental de los efectos de la conductividad termica en materiales heterogeneos. El analisis numerico se basa en la formulacion de Metodo de los Elementos de Contorno (MEC) basada en la tecnica de subregiones con el fin de simular un dominio bidimensional con inclusiones de material distribuidas aleatoriamente. Las condiciones de contorno fueron seleccionadas adecuadamente con el fin de obtener condiciones de conductividad termica unidireccional. La Teoria de los Campos Medios (TCM) es aplicada para determinar el elemento de volumen representativo (EVR) para los casos estudiados. Finalmente, el coeficiente de conductividad termica efectivo es obtenido a partir del EVR. Para la verificacion de los resultados numericos obtenidos es propuesto un procedimiento experimental basado en imagenes termicas. El montaje experimental replica la condicion de flujo de calor unidireccional en una placa de acero. La conductividad termica efectiva experimental es obtenida a partir del analisis de las imagenes termicas del campo de temperatura resultante en la superficie de la placa las cuales fueron tomadas con una camara infrarroja. La comparacion entre los resultados numericos y experimentales resulto en una diferencia de 3% entre los dos resultados, apuntando el buen desempeno de la metodologia propuesta. EnglishThis work focuses on the numerical and experimental study of the effective thermal conductivity in materials with heterogeneous composition. The numerical analysis relies in the Boundary Element method (BEM) formulation assisted by the sub-regions technique to simulate a two-dimensional square domain, with randomly distributed material inclusions. The boundary conditions are set to achieve a unidirectional heat flux condition. The Average Field Theory (AFT) is applied to determinate the representative volume element (RVE) condition for the studied cases. Finally, the effective heat conduction coefficient is obtained from the defined RVE’s. To verify the obtained numerical results, it is proposed an experimental procedure based on thermal images. The experimental assembly replicates the unidirectional heat flux condition over a steel plate. The experimental effective thermal conductivity is obtained from the analysis of the resultant temperature field on the surface of the plate taken by an infrared camera. The comparison between the numerical and experimental results showed a 3% difference between both results, pointing out for the successfulness of the proposed methodology.

The fast multipole boundary element method performance evaluation for topological optimization procedure

espanolEl objetivo de este trabajo es evaluar el rendimiento de un Metodo de elementos de contorno (BEM) acelerado por el Metodo Multipolar Rapido (FMM), en comparacion con un BEM directo en un problema de optimizacion de topologia. La formulacion del Metodo de elementos de contorno multipolar rapido (FMBEM) se introduce con el fin de hacer que el proceso de optimizacion sea mas atractivo desde el punto de vista del coste computacional. La formulacion del metodo multipolar rapido se resume brevemente. Un enfoque al respecto de la sensibilidad topologica-forma es empleado para seleccionar los puntos que muestran las sensibilidades mas bajas, a la cual se le retirara material mediante la apertura de una cavidad en el mismo. A medida que el proceso iterativo evoluciona, el dominio original tiene agujeros eliminadas progresivamente, hasta que se alcanza un criterio determinado de parada. Para la comparacion, se utiliza la topologia resultante de un proceso de optimizacion directa BEM. El tiempo de CPU x GDL tambien es investigado. El BEM acelerado muestra un buen rendimiento en una rutina de optimizacion. EnglishThe objective of this work is to evaluate the performance of a Boundary Element Method (BEM) accelerated by the Fast Multipole Method (FMM) compared with a direct (BEM) in an optimization topology problem. The formulation of the Fast Multipole Boundary Element Method (FMBEM) is introduced in order to make the optimization process more attractive from the point of view of the computational cost. The fast multipole formulation is briefly summarized. A topological-shape sensitivity approach is used to select the points showing the lowest sensitivities, where material is removed by opening a cavity. As the iterative process evolves, the original domain has holes progressively removed, until a given stop criteria is achieved. For comparison, the topology resulting from a direct BEM optimization process is used. The CPU time x DOFs is also investigated. The accelerated BEM shows good performance in an optimization routine.