Eder Lima de Albuquerque

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.

Fast BEM multi-domain approach for the elastostatic analysis of short fibre composites

Abstract Composite materials are usually treated as homogeneous when carrying out structural design. However, failure in these materials often originated at their heterogeneous microstructure or constituents; hence, the different materials should be considered in the analysis. The use of composite materials has increased considerably over the years due to their relative superior properties. The accurate determination of their mechanical properties and behaviour is thus of great practical significance. The Boundary Element Method (BEM) has demonstrated to be a powerful computational technique for the analysis of many physical and engineering problems. The present work deals with the use of the multi-domain BEM to obtain a more appropriate characterisation of fibre–matrix composites. The generally anisotropic fundamental solution based on a double-Fourier series is employed together with a fast BEM approach, namely, the Adaptive Cross Approximation (ACA) technique. The ACA technique is aimed at speeding up the process required to generate the BEM matrices. Some numerical examples are presented to demonstrate its applicability. The present work is a precursor to treating problems involving anisotropic inclusions in general composites.

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.