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.

scholarly journals Substructure-Based Topology Optimization for Symmetric Hierarchical Lattice Structures

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 678
Author(s):  
Zijun Wu ◽  
Renbin Xiao
Keyword(s):  
Topology Optimization ◽  
High Efficiency ◽  
Spline Interpolation ◽  
Optimization Method ◽  
Optimality Criteria ◽  
Lattice Structures ◽  
Hierarchical Lattice ◽  
B Spline ◽  
Design Variables ◽  
Optimality Criteria Method

This work presents a topology optimization method for symmetric hierarchical lattice structures with substructuring. In this method, we define two types of symmetric lattice substructures, each of which contains many finite elements. By controlling the materials distribution of these elements, the configuration of substructure can be changed. And then each substructure is condensed into a super-element. A surrogate model based on a series of super-elements can be built using the cubic B-spline interpolation. Here, the relative density of substructure is set as the design variable. The optimality criteria method is used for the updating of design variables on two scales. In the process of topology optimization, the symmetry of microstructure is determined by self-defined microstructure configuration, while the symmetry of macro structure is determined by boundary conditions. In this proposed method, because of the educing number of degree of freedoms on macrostructure, the proposed method has high efficiency in optimization. Numerical examples show that both the size and the number of substructures have essential influences on macro structure, indicating the effectiveness of the presented method.

Topology Optimization of Continuum Structures Based on SIMP

2011 ◽  
Vol 255-260 ◽  
pp. 14-19 ◽  
Author(s):  
Hong Zhang ◽  
Xiao Hui Ren
Keyword(s):  
Mathematical Model ◽  
Topology Optimization ◽  
Isotropic Material ◽  
Optimization Design ◽  
Optimality Criteria ◽  
Continuum Structures ◽  
Good Convergence ◽  
Minimum Compliance ◽  
Design Variables ◽  
Optimality Criteria Method

An Optimality Criteria method for topology optimization of continuum structures based on Solid Isotropic Material with Penalization (SIMP) was proposed. The minimum compliance of structures was selected as the objective function of the problem. A mathematical model for topology optimization design of statically loaded structures and the update scheme for the design variables were set. The examples showed that the algorithm has good convergence and application values.

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.

Topology Optimization Using Node-Based Smoothed Finite Element Method

2015 ◽  
Vol 07 (06) ◽  
pp. 1550085 ◽  
Author(s):  
Z. C. He ◽  
G. Y. Zhang ◽  
L. Deng ◽  
Eric Li ◽  
G. R. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Optimization Design ◽  
Solid Mechanics ◽  
Optimality Criteria ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Smoothed Finite Element Method ◽  
Element Method

The node-based smoothed finite element method (NS-FEM) proposed recently has shown very good properties in solid mechanics, such as providing much better gradient solutions. In this paper, the topology optimization design of the continuum structures under static load is formulated on the basis of NS-FEM. As the node-based smoothing domain is the sub-unit of assembling stiffness matrix in the NS-FEM, the relative density of node-based smoothing domains serves as design variables. In this formulation, the compliance minimization is considered as an objective function, and the topology optimization model is developed using the solid isotropic material with penalization (SIMP) interpolation scheme. The topology optimization problem is then solved by the optimality criteria (OC) method. Finally, the feasibility and efficiency of the proposed method are illustrated with both 2D and 3D examples that are widely used in the topology optimization design.

Topology Optimization of Electrostatically Actuated Micromechanical Structures With Accurate Electrostatic Modeling of the Interpolated Material Model

2006 ◽  
Author(s):  
Aravind Alwan ◽  
G. K. Ananthasuresh
Keyword(s):  
Topology Optimization ◽  
Electrostatic Force ◽  
Material Model ◽  
Optimality Criteria ◽  
Electrostatically Actuated ◽  
Optimality Criteria Method ◽  
Material State ◽  
Material Interpolation ◽  
New Formulation ◽  
Electrostatic Modeling

In this paper, we present a novel formulation for performing topology optimization of electrostatically actuated constrained elastic structures. We propose a new electrostatic-elastic formulation that uses the leaky capacitor model and material interpolation to define the material state at every point of a given design domain continuously between conductor and void states. The new formulation accurately captures the physical behavior when the material in between a conductor and a void is present during the iterative process of topology optimization. The method then uses the optimality criteria method to solve the optimization problem by iteratively pushing the state of the domain towards that of a conductor or a void in the appropriate regions. We present examples to illustrate the ability of the method in creating the stiffest structure under electrostatic force for different boundary conditions.

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.

Review of Methods of Mechanical Digital Design Based on Topology Optimization

2013 ◽  
Vol 288 ◽  
pp. 193-201
Author(s):  
Xiu Ye Wang ◽  
Han Zhao ◽  
Zu Fang Zhang ◽  
Yong Wang
Keyword(s):  
Topology Optimization ◽  
Optimization Algorithms ◽  
Optimality Criteria ◽  
Digital Design ◽  
Structural Topology ◽  
Optimality Criteria Method ◽  
Mathematical Programming Method ◽  
Pde Methods ◽  
Volume Method ◽  
Element Method

The basic mathematical model of topology optimization of continuum structures is introduced at first. Then the authors focus on reviewing the development of PDE methods and optimization algorithms. This paper details the development and applications of Finite Element Method, Boundary Element Method and Finite Volume Method. This paper also illustrates several typical applications and achievements of optimization algorithms, such as Optimality Criteria method, mathematical programming method and intelligent algorithm. Based on our research, this paper finally summarizes the process of the structural topology optimization and describes the directions of the topology optimization in the field of mechanical digital design.

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