This paper presents an efficient and compact MATLAB code to solve three-dimensional topology optimization problems. The 169 lines comprising this code include finite element analysis, sensitivity analysis, density filter, optimality criterion optimizer, and display of results. The basic code solves minimum compliance problems. A systematic approach is presented to easily modify the definition of supports and external loads. The paper also includes instructions to define multiple load cases, active and passive elements, continuation strategy, synthesis of compliant mechanisms, and heat conduction problems, as well as the theoretical and numerical elements to implement general non-linear programming strategies such as SQP and MMA. The code is intended for students and newcomers in the topology optimization. The complete code is provided in Appendix C and it can be downloaded from http://top3dapp. com.

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The hybrid cellular automaton (HCA) algorithm is a methodology developed to simulate the process of structural adaptation in bones. This methodology incorporates a distributed control loop within a structure in which ideally localized sensor cells activate local processes of the formation and resorption of material. With a proper control strategy, this process drives the overall structure to an optimal configuration. The controllers developed in this investigation include two-position, proportional, integral and derivative strategies. The HCA algorithm combines elements of the cellular automaton (CA) paradigm with finite element analysis (FEA). This methodology has proved to be computationally efficient to solve topology optimization problems. The resulting optimal structures are free of numerical instabilities such as the checkerboarding effect. This investigation presents the main features of the HCA algorithm and the influence of different parameters applied during the iterative optimization process.

Crashworthiness design is an evolving discipline that combines vehicle crash simulation and design synthesis. The goal is to increase passenger safety subject to manufacturing cost constraints. The crashworthiness design process requires modeling of the complex interactions involved in a crash event. Current approaches utilize a parametrized optimization approach that requires response surface approximations of the design space. This is due to the expensive nature of numerical crash simulations and the high nonlinearity and noisiness in the design space. These methodologies usually require a significant effort to determine an initial design concept. In this paper, a heuristic approach to continuum-based topology optimization is developed for crashworthiness design. The methodology utilizes the cellular automata paradigm to generate three-dimensional design concepts. Furthermore, a constraint on maximum displacement is implemented to maintain a desired performance of the structures synthesized. Example design problems are used to demonstrate that the proposed methodology converges to a final topology in an efficient manner.

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An emerging approach in biofabrication is the creation of 3D tissue constructs through scaffold-free, cell spheroid-only methods. The basic mechanism in this technology is spheroid fusion, which is driven by the minimization of energy, the same biophysical mechanism that governs spheroid formation. However, other factors such as oxygen and metabolite accessibility within spheroids impact on spheroid properties and their ability to form larger-scale structures. The goal of our work is to develop a simulation platform eventually capable of predicting the conditions that minimize metabolism-related cell loss within spheroids. To describe the behavior and dynamic properties of the cells in response to their neighbors and to transient nutrient concentration fields, we developed a hybrid discrete-continuous heuristic model, combining a cellular Potts-type approach with field equations applied to a randomly populated spheroid cross-section of prescribed cell-type constituency. This model allows for the description of: (i) cellular adhesiveness and motility; (ii) interactions with concentration fields, including diffusivity and oxygen consumption; and (iii) concentration-dependent, stochastic cell dynamics, driven by metabolite-dependent cell death. Our model readily captured the basic steps of spheroid-based biofabrication (as specifically dedicated to scaffold-free bioprinting), including intra-spheroid cell sorting (both in 2D and 3D implementations), spheroid defect closure, and inter-spheroid fusion. Moreover, we found that when hypoxia occurring at the core of the spheroid was set to trigger cell death, this was amplified upon spheroid fusion, but could be mitigated by external oxygen supplementation. In conclusion, optimization and further development of scaffold-free bioprinting techniques could benefit from our computational model which is able to simultaneously account for both cellular dynamics and metabolism in constructs obtained by scaffold-free biofabrication.

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