scholarly journals Influence of Density-Based Topology Optimization Parameters on the Design of Periodic Cellular Materials

Materials ◽  
2019 ◽  
Vol 12 (22) ◽  
pp. 3736
Author(s):  
Hugo A. Alvarez ◽  
Habib R. Zambrano ◽  
Olavo M. Silva
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Optimization Procedure ◽  
Optimality Criteria ◽  
Cellular Materials ◽  
Initial Guess ◽  
Method Of Moving Asymptotes ◽  
Optimization Parameters ◽  
Common Technique ◽  
Moving Asymptotes

The density based topology optimization procedure represented by the SIMP (Solid isotropic material with penalization) method is the most common technique to solve material distribution optimization problems. It depends on several parameters for the solution, which in general are defined arbitrarily or based on the literature. In this work the influence of the optimization parameters applied to the design of periodic cellular materials were studied. Different filtering schemes, penalization factors, initial guesses, mesh sizes, and optimization solvers were tested. In the obtained results, it was observed that using the Method of Moving Asymptotes (MMA) can be achieved feasible convergent solutions for a large amount of parameters combinations, in comparison, to the global convergent method of moving asymptotes (GCMMA) and optimality criteria. The cases of studies showed that the most robust filtering schemes were the sensitivity average and Helmholtz partial differential equation based filter, compared to the Heaviside projection. The choice of the initial guess demonstrated to be a determining factor in the final topologies obtained.

scholarly journals Generalized Optimality Criteria Method for Topology Optimization

2021 ◽  
Vol 11 (7) ◽  
pp. 3175
Author(s):  
Nam H. Kim ◽  
Ting Dong ◽  
David Weinberg ◽  
Jonas Dalidd
Keyword(s):  
Topology Optimization ◽  
Lagrange Multipliers ◽  
Inequality Constraints ◽  
Optimality Criteria ◽  
Multiple Constraints ◽  
Numerical Examples ◽  
Method Of Moving Asymptotes ◽  
Design Variables ◽  
Optimality Criteria Method ◽  
Moving Asymptotes

In this article, a generalized optimality criteria method is proposed for topology optimization with arbitrary objective function and multiple inequality constraints. This algorithm uses sensitivity information to update both the Lagrange multipliers and design variables. Different from the conventional optimality criteria method, the proposed method does not satisfy constraints at every iteration. Rather, it improves the Lagrange multipliers and design variables such that the optimality criteria are satisfied upon convergence. The main advantages of the proposed method are its capability of handling multiple constraints and computational efficiency. In numerical examples, the proposed method was found to be more than 100 times faster than the optimality criteria method and more than 1000 times faster than the method of moving asymptotes.

Advanced Primal-Dual Interior-Point Method for the Method of Moving Asymptotes

2018 ◽  
Author(s):  
Daozhong Li ◽  
Stephen Roper ◽  
Il Yong Kim
Keyword(s):  
Topology Optimization ◽  
Interior Point ◽  
Interior Point Method ◽  
Optimization Problems ◽  
Point Method ◽  
Topology Optimization Problem ◽  
Method Of Moving Asymptotes ◽  
Primal Dual ◽  
Numerical Performance ◽  
Moving Asymptotes

The Method of Moving Asymptotes (MMA) is one of the well-known optimization algorithms for topology optimization due to its stable numerical performance. Here, this paper simplifies the MMA algorithm by considering the features of topology optimization problem statements and presents a strategy to solve the necessary subproblems based on the primal-dual-interior-point method to further enhance numerical performance. A new scaling mechanism is also introduced to improve searching quality by utilizing the sensitivities of the original problems at the beginning of each MMA iteration. Numerical examples of solving both mathematical problems and topology optimization problems demonstrate the success of this method.

Finding Better Local Optima in Topology Optimization via Tunneling

2018 ◽  
Author(s):  
Shanglong Zhang ◽  
Julián A. Norato
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Structural Response ◽  
Free Form ◽  
Local Optima ◽  
Design Representation ◽  
Tunneling Method ◽  
Optimization Parameters ◽  
Gradient Based ◽  
Geometric Primitives

Topology optimization problems are typically non-convex, and as such, multiple local minima exist. Depending on the initial design, the type of optimization algorithm and the optimization parameters, gradient-based optimizers converge to one of those minima. Unfortunately, these minima can be highly suboptimal, particularly when the structural response is very non-linear or when multiple constraints are present. This issue is more pronounced in the topology optimization of geometric primitives, because the design representation is more compact and restricted than in free-form topology optimization. In this paper, we investigate the use of tunneling in topology optimization to move from a poor local minimum to a better one. The tunneling method used in this work is a gradient-based deterministic method that finds a better minimum than the previous one in a sequential manner. We demonstrate this approach via numerical examples and show that the coupling of the tunneling method with topology optimization leads to better designs.

Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Hong Zhou
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Diagonal Element ◽  
Initial Guess ◽  
Stress Constraint ◽  
Design Variables ◽  
Hybrid Discretization

The hybrid discretization model for topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. Each design cell is further subdivided into triangular analysis cells. This hybrid discretization model allows any two contiguous design cells to be connected by four triangular analysis cells whether they are in the horizontal, vertical, or diagonal direction. Topological anomalies such as checkerboard patterns, diagonal element chains, and de facto hinges are completely eliminated. In the proposed topology optimization method, design variables are all binary, and every analysis cell is either solid or void to prevent the gray cell problem that is usually caused by intermediate material states. Stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum and to avoid the need to choose the initial guess solution and conduct sensitivity analysis. The obtained topology solutions have no point connection, unsmooth boundary, and zigzag member. No post-processing is needed for topology uncertainty caused by point connection or a gray cell. The introduced hybrid discretization model and the proposed topology optimization procedure are illustrated by two classical synthesis examples of compliant mechanisms.

Topology optimization of continuum structures with uncertain-but-bounded parameters for maximum non-probabilistic reliability of frequency requirement

2015 ◽  
Vol 23 (16) ◽  
pp. 2557-2566 ◽  
Author(s):  
Bin Xu ◽  
Lei Zhao ◽  
Yi Min Xie ◽  
Jiesheng Jiang
Keyword(s):  
Topology Optimization ◽  
Reliability Index ◽  
Optimization Problems ◽  
Mass Density ◽  
Limit State ◽  
Optimization Procedure ◽  
State Equation ◽  
Outer Loop ◽  
Continuum Structures ◽  
Beso Method

A method for the non-probabilistic reliability optimization on frequency of continuum structures with uncertain-but-bounded parameters is proposed. The objective function is to maximize the non-probabilistic reliability index of frequency requirement.The corresponding bi-level optimization model is built, where the constraints are applied on the material volume in the outer loop and the limit state equation in the inner loop. The non-probabilistic reliability index of frequency requirement is derived by the analytical method for the continuum structure with the uncertain elastic module and mass density. Further, the sensitivity of the non-probabilistic reliability index with respect to the design variables is analyzed. The topology optimization in the outer loop is performed by a bi-directional evolutionary structural optimization (BESO) method, where the numerical techniques and the optimization procedure of BESO method are presented. Numerical results show that the proposed BESO method is efficient, and convergent optimal solutions can be achieved for a variety of optimization problems on frequency non-probabilistic reliability of continuum structures.

A Continuous Protein Design Model Using Artificial Power Law in Topology Optimization

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Sung K. Koh ◽  
Guangjun Liu ◽  
Wen-Hong Zhu
Keyword(s):  
Protein Synthesis ◽  
Topology Optimization ◽  
Power Law ◽  
Protein Design ◽  
Optimization Problems ◽  
Design Method ◽  
Minimum Energy ◽  
Initial Guess ◽  
Design Methods ◽  
Structural Topology

A continuous protein synthesis formulation based on the design principles applied to topology optimization problems is proposed in this paper. In contrast to conventional continuous protein design methods, the power law (PL) protein design formulation proposed in this paper can handle any number of residue types to accomplish the goal of protein synthesis, and hence provides a general continuous formulation for protein synthesis. Moreover, a discrete sequence with minimum energy can be determined by the PL design method as it inherits the feature of material penalization used in designing a structural topology. Since a continuous optimization method is implemented to solve the PL design formulation, the entire design process is more efficient and robust than conventional design methods employing stochastic or enumerative search methods. The performance of the proposed PL design formulation is explored by designing simple lattice protein models, for which an exhaustive search can be carried out to identify a sequence with minimum energy. We used residue probabilities as an initial guess for the design optimization to enhance the capability and efficiency of the PL design formulation. The comparison with the exchange replica method indicates that the PL design method is millions of times more efficient than the conventional stochastic protein design method.

An Improved Alternating Active-Phase Algorithm for Multi-Material Topology Optimization Problems

2014 ◽  
Vol 635-637 ◽  
pp. 105-111 ◽  
Author(s):  
Ming Tao Cui ◽  
Hong Fang Chen
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Active Phase ◽  
Optimality Criteria ◽  
Numerical Examples ◽  
Original Algorithm ◽  
Minimum Compliance ◽  
Object Based ◽  
The Mathematical Model ◽  
Improved Algorithm

For the multi-material topology optimization problems which take structural minimum compliance as the object, based on the weight function and optimality criteria, an improvement to the original alternating active-phase algorithm is achieved in establishing and calculating the mathematical model of multi-material topology optimization problems. Simulations of numerical examples are implemented respectively by the improved alternating active-phase algorithm and the original algorithm. It can be found that the minimum compliance obtained by the improved algorithm is generally lower than that obtained by the original algorithm in each numerical example, whereupon the feasibility and efficiency of the improved algorithm are manifested.

Topology Optimization of 3-D Nonlinear Magnetic Field Problem Using the Method of Moving Asymptotes

2016 ◽  
Vol 2016.12 (0) ◽  
pp. 2206
Author(s):  
Yoshifumi Okamoto ◽  
Hiroshi Masuda ◽  
Yutaro Kanda ◽  
Reona Hoshino ◽  
Shinji Wakao
Keyword(s):  
Magnetic Field ◽  
Topology Optimization ◽  
Field Problem ◽  
Method Of Moving Asymptotes ◽  
Moving Asymptotes
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