Diego Alexander Garzón

Topology Synthesis of Compliant Mechanisms Using the Hybrid Cellular Automaton Method with an Efficient Mass Control Strategy

Cellular automaton (CA) models have been used to simulate biological phenomena for over sixty years. In previous research, CA principles were applied to solve topology optimization problems using the hybrid cellular automaton (HCA) method. This method combines local evolutionary design rules with finite element analysis. Different control strategies, incorporated into the design rules, seek to minimize the error between a local mechanical signal and its optimum value. The HCA algorithm has demonstrated to be an efficient computational technique since optimal (black and white) topologies are obtained after a few iterations without checker-board patterns [4]. With a change in the objective function, the HCA method was also applied to compliant mechanisms design in a continuum design domain [3]. Nonlinear finite element analysis was incorporated into the algorithm [2]. Typically, a mass constraint is required to obtain slender flexible structures [1]. This constraint is satisfied by calculating the exact value of the associated Lagrange multiplier in every iteration. The objective of this work is to develop a new mass control strategy. In the proposed approach, the value of the Lagrange multiplier is corrected gradually during the iterative process and its final value is found at convergence. This strategy is implemented in both two- and three-dimensional models. The results are compared with the ones obtained using other approaches.

Mechanobiology of Oral Implantable Devices

A dental implant is a biomaterial device inserted in the jaw bone to replace the root of a missing tooth Adell et al. (1981); Hansson et al. (1983). With the implant insertion, a junction site between the biomaterial surface and the surrounding bone known as the bone-dental implant interface is created Branemark (1983). The formation of a new bone matrix in this interface allows the firm and long lasting connection between the bone and the implant in a process called osseointegration Albrektsson & Johansson (2001); Branemark (1983). The success of this contact depends on the restoration of the functional tissues around the implant providing it with mechanical support and anchorage Gapski et al. (2003); Hansson et al. (1983). This tissue restoration is conditioned to cell migration, cell proliferation and cell differentiation phenomena depending on the pathological conditions of the patient, the biological conditions of the host bone, the implant design and surface topography, and the distribution of mechanical loads between the bone and the implant Aukhil (2000); Ellingsen et al. (2006); Sikavitsas et al. (2001). The analysis of both biological and mechanical factors is known as mechanobiology Klein-Nulend et al. (2005); Van der Meulen & Huiskes (2002). Dental implants are widely used as anchorage devices for restoration and esthetical purposes Branemark (1983). However, in several orthodontic treatments where the anchorage is used, a higher control of treatment time and oral availability is needed Antoszewska et al. (2009); Gapski et al. (2003). In these cases, dental implants are not recommended since specific surgical procedures are required for their implantation usually demanding long lasting recovery times for insertion and loading Antoszewska et al. (2009). Furthermore, most of the orthodontic treatments are based on the temporary and direct application of loads for the movement of teeth Papadopoulos & Tarawneh (2007). This treatments rely on implantable devices capable of transmit immediate loading without the implicit need of being osseointegrated Papavasiliou (1996). Such devices, called mini-implants, reinforce the anchorage of orthodontic devices and speed up treatments given its relative simple insertion Mechanobiology of Oral Implantable Devices