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On filtered “conservatism” in direct topology design
Published in Alphose Zingoni, Insights and Innovations in Structural Engineering, Mechanics and Computation, 2016
Dirk Munro, Albert A. Groenwold
Distinguished algorithms in this class include CONLIN (Fleury and Braibant 1986, Fleury 1989), the Method of Moving Asymptotes (MMA) (Svanberg 1987), followed by SCPIP (Zillober 2002) and SAOi (Groenwold et al. 2009, Groenwold and Etman 2011). SAO methods in topology design (and structural optimization in general) are typically based on subproblems constructed from truncated linear Taylor series expansions, but, in order to model the nonlinear response of the structure, reciprocal-like intervening variables are used. In Groenwold and Etman (2010b) it is demonstrated that separable approximation functions with intervening variables can be replaced with simple diagonal quadratic Taylor series expansions; the form of the resulting subproblemis independent of the specific form of the approximations, the subproblems are easily convexified and conservatism is easily controlled (Groenwold et al. 2007, Groenwold et al. 2010).
Topology Optimisation Techniques
Published in Richard Leach, Simone Carmignato, Precision Metal Additive Manufacturing, 2020
Rajit Ranjan, Can Ayas, Matthijs Langelaar, Fred van Keulen
A given TO problem can be solved using gradient-based optimisation techniques. Commonly used techniques are the optimality criteria (OC) method, sequential linear programming (SLP) methods and the method of moving asymptotes (MMA). Among these, MMA and its variant, globally convergent MMA, are the most popular (Svanberg 1987).
A multi-material topology optimization with temperature-dependent thermoelastic properties
Published in Engineering Optimization, 2022
Yuan Chen, Lin Ye, Y. X. Zhang, Chunhui Yang
When incorporating the temperature-dependent thermoelastic properties into multi-material topology optimization, an updating of Te is calculated and called iteratively, leading to a simultaneous iterative updating of thermoelastic properties when implementing Equations (8)–(10). This updating is iteratively carried out until the convergence has been reached by a maximum fractional change in all elemental design variables between two consecutive iterations. If the change is less than 1%, then the design optimization is converged. In optimization, the method of moving asymptotes (MMA), developed by Svanberg (1987), is utilized for solving the optimization problem, i.e. Equation (1), owing to its stability and computational efficiency (Jung et al. 2020; Lin, Luo, and Tong 2010). The sensitivity analysis and filtering methods for multi-material temperature-dependent thermoelastic topology optimization (TTTO) are accordingly introduced in Appendix A2.
Adaptive optimal control of pneumatic suspensions for comfort improvement of flexible railway vehicles using Monte Carlo simulations
Published in Vehicle System Dynamics, 2022
E. Palomares, A. L. Morales, A. J. Nieto, M. Félix, J. M. Chicharro, P. Pintado
The Method of Moving Asymptotes is a gradient descent method that must be provided with the sensitivities (gradients) of both the cost function and the constraints. These are calculated using the classical adjoint method [27,28], stated as where is the vector of state variables, represents the right-hand terms of the state system (), and is the Lagrangian restriction multiplier. This Lagrangian is the Hamiltonian that appears in Pontryagin's maximum principle [27], so that and the multiplier is also the adjoint state vector, solution of the adjoint system obtained by differentiating with respect to the state vector , with the transversality end-time condition .
Topology optimisation for large-scale additive manufacturing: generating designs tailored to the deposition nozzle size
Published in Virtual and Physical Prototyping, 2021
E. Fernández, C. Ayas, M. Langelaar, P. Duysinx
The reference and the maximum-size-constrained problems, i.e. Equations (6) and (8), are implemented in free access codes. Here, we use the 88-line code (Andreassen et al. 2011) and the TopOpt code (Aage, Andreassen, and Lazarov 2015). The first one is written in MATLAB aimed at solving 2D problems, whereas the latter is a C++ code intended to solve large scale 3D problems. These codes use the density method, the SIMP interpolation scheme and the density filter. Therefore, the Heaviside projection that builds the eroded, intermediate and dilated designs has been added, along with the maximum size restriction and the robust topology optimisation formulation. The optimisation problems are solved using the Method of Moving Asymptotes (MMA) (Svanberg 1987).