Hybrid Cellular Automata: a biologically-inspired structural optimization technique (original) (raw)
Related papers
Proceedings of 6th World …, 2005
In previous investigations, the functional adaptation process in bones was modeled using the hybrid cellular automaton (HCA) algorithm. In this algorithm, the structural analysis is performed using the finite element method, while the cellular communication within the bone structure and its adaptation process are modeled using cellular automaton (CA) principles. This model of bone functional adaptation also demonstrated to be an effective technique for topology optimization of continuum structures. The optimization problem used for the bone adaptation process was defined as minimizing mass while maximizing strength. Using optimality conditions, it was possible to demonstrate the existence of a local equilibrium state where the bone structure is adapted to the environment and no further structural change is required. Inspired by phenomenological approaches to simulating bone functional adaptation, the HCA algorithm makes use of control rules in order to obtain an optimal configuration. Four different control strategies has been implemented, including two-position, proportional, integral and derivative control. The combination of proportional, integral and derivative (PID) control has shown improved convergence in comparison to other topology optimization approaches. This algorithm has been successfully applied to a variety of two-and three-dimensional structural models. The objective of this investigation is to enhance the flexibility of the HCA algorithm. This work introduces a new methodology for setting various types of constraints in the HCA optimization problem formulation. These constraints include mass, deflection, stress and strain energy density. Different strategies based on control theory and optimality conditions are implemented to achieve fast and reliable convergence. 2.
Optimality conditions of the hybrid cellular automata for structural optimization
AIAA journal, 2007
The hybrid cellular automaton (HCA) method has been successfully applied to topology optimization using a uniform strain energy density distribution approach. In this work, a new set of design rules is derived from the first order optimality conditions of a multiobjective problem. In this new formulation, the final topology is derived to minimize both mass and strain energy. In the HCA algorithm, local design rules based on the cellular automaton paradigm are used to efficiently drive the design to optimality. In addition to the control-based techniques previously introduced, a new ratio technique is derived in this investigation. This work also compares the performance of the control strategies and the ratio technique. * Associate Professor, AIAA Member,
Topology Optimization of Structures using Cellular Automata with Constant Strain Triangles
International Journal of Civil Engineering
Due to the algorithmic simplicity, cellular automata (CA) models are useful and simple methods in structural optimization. In this paper, a cellular-automaton-based algorithm is presented for simultaneous shape and topology optimization of continuum structures, using five-step optimization procedure. Two objective functions are considered and the optimization process is converted to the single objective optimization problem (SOOP) using weighted sum method (WSM). A novel triangle neighborhood is proposed and the design domain is divided into small triangle elements, considering each cell as the finite element. The finite element formulation for constant strain triangles using three-node triangular elements is developed in this article. Topological parameters and shape of the design space are taken as the design variables, which for the purpose of this paper are continuous variables. The paper reports the results of several design experiments, comparing them with the currently available results obtained by CA and genetic algorithm in the literature. The outcomes of the developed scheme show the accuracy and efficiency of the method as well as its timesaving behavior in achieving better results
Frontiers in Heat and Mass Transfer, 2019
A hybrid cellular automaton model combined with finite element method for structural topology optimization with mechanical and heat constraints is developed. The effect of thermal stress on structural optimization is taken into account. Higher order 8-node element and von Neumann strategy are employed for the finite element and the cellular element, respectively. The validating studies of standard testing structure for topological optimization are carried out. The structure evolution, stress evolution and thermal evolution of topology optimization with mechanical and heat constraints are investigated. The results show the developed hybrid method is more efficient for structural topology optimization. Meanwhile, the topology optimization can eliminate most of the thermal stress in the structure.
Cellular Automata in Topology Optimization of Continuum Structures
In this paper, an optimization algorithm based on cellular automata (CA) is developed for topology optimization of continuum structures with shear and flexural behavior. The design domain is divided into small triangle elements and each cell is considered as a finite element. The stress analysis is performed by the Constant Strain Triangles (CST) finite elements method. The thicknesses of the individual cells are taken as the design variables, while the weight of the structure and the ratio of the Von Mises equivalent stress to the yield stress in each cell are considered as the two objective functions to minimize. Using the weighted sum method, the multi-objective optimization problem (MOOP) is converted to the single-objective optimization problem (SOOP) and then the optimization problem is solved by the developed method. The paper reports the results of several design experiments, comparing with the existing reported results.
Topology optimization using a hybrid cellular automaton method with local control rules
Journal of Mechanical Design, 2006
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.
A multi-objective structural optimization using optimality criteria and cellular automata
Asian Journal of Civil Engineering (Building and …, 2007
This paper is devoted to the simultaneous weight and stiffness optimization of two dimensional structures. The necessary optimality conditions are derived and the obtained optimality criterion is briefly explained. Based on the paradigm of cellular automata, a local rule is constructed which alleviates the well known problems of mesh dependency and checker-boarding in topological structural optimization. It is shown that implementation of this algorithm is useful in prevention of the formation of undesirable members in the resulting layouts. In this approach, contrary to the conventional topological structural optimization methods, the shape and boundaries of the two dimensional continuum are not fixed and can undergo considerable changes during the optimization process. Hence, This approach may be considered as a generalized structural optimization method. To demonstrate the advantages of the method a couple of examples are presented.
Topology Synthesis of Structures Under Impact Loading Using a Hybrid Cellular Automaton Algorithm
11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2006
In this paper, a Hybrid Cellular Automaton (HCA) algorithm has been utilized to develop an efficient methodology for synthesizing structures under a dynamic loading event. Previous work in topology optimization in structural design have concentrated on modeling assuming static loading conditions due the complexities associated with dynamic/impact loading. The assumption of small deformations is a simplification that is also often used. These simplifications are due to the sensitivities required for gradient-based methods that dominate the field of topology optimization. However, this neglects the effects of material and geometric nonlinearities, contact between elements, and strain rate effects, among other phenomena. The HCA method is a non-gradient method that has been used in traditional topology optimization. This technique is used in this research to tackle more complicated problems that involve dynamic events, such as impacts and collisions. By applying the HCA method to impact problems, the resulting structure will account for all phenomena involved. In this paper, the design of structures subject to impact loading is investigated by utilizing the HCA method to develop an efficient methodology that quickly converges to a final design, reducing the computational time required.