scholarly journals Topology optimization incorporating external variables with metamodeling

2020 ◽  
Vol 62 (5) ◽  
pp. 2455-2466
Author(s):  
Shun Maruyama ◽  
Shintaro Yamasaki ◽  
Kentaro Yaji ◽  
Kikuo Fujita
Keyword(s):  
Topology Optimization ◽  
Design Problem ◽  
Optimization Problem ◽  
Design Domain ◽  
Material Distribution ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
External Variables ◽  
Multi Level ◽  
Dependence Relationship

Abstract The objective of conventional topology optimization is to optimize the material distribution for a prescribed design domain. However, solving the topology optimization problem strongly depends on the settings specified by the designer for the shape of the design domain or their specification of the boundary conditions. This contradiction indicates that the improvement of structures should be achieved by optimizing not only the material distribution but also the additional design variables that specify the above settings. We refer to the additional design variables as external variables. This paper presents our work relating to solving the design problem of topology optimization incorporating external variables. The approach we follow is to formulate the design problem as a multi-level optimization problem by focusing on the dominance-dependence relationship between external variables and material distribution. We propose a framework to solve the optimization problem utilizing the multi-level formulation and metamodeling. The metamodel approximates the relationship between the external variables and the performance of the corresponding optimized material distribution. The effectiveness of the framework is demonstrated by presenting three examples.

Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi ◽  
Sudhakar Arepally ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Multibody Dynamics ◽  
Optimization Problem ◽  
Finite Difference Methods ◽  
Analysis Method ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Rotational Motions

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

A Systems Approach to Structural Topology Optimization: Designing Optimal Connections

1996 ◽  
Author(s):  
Tao Jiang ◽  
Mehran Chirehdast
Keyword(s):  
Topology Optimization ◽  
Design Problem ◽  
Large Scale ◽  
Optimization Problem ◽  
Systems Design ◽  
Mathematical Programming Problem ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Topology Optimization Problem ◽  
Wide Range

Abstract In this paper, structural topology optimization is extended to systems design. Locations and patterns of connections in a structural system that consists of multiple components strongly affect its performance. Topology of connections is defined, and a new classification for structural optimization is introduced that includes the topology optimization problem for connections. A mathematical programming problem is formulated that addresses this design problem. A convex approximation method using analytical gradients is used to solve the optimization problem. This solution method is readily applicable to large-scale problems. The design problem presented and solved here has a wide range of applications in all areas of structural design. The examples provided here are for spot-weld and adhesive bond joints. Numerous other potential applications are suggested.

Topological design of freely vibrating bi-material structures to achieve the maximum band gap centering at a specified frequency

2021 ◽  
pp. 1-25
Author(s):  
Pai Liu ◽  
Xiaopeng Zhang ◽  
Yangjun Luo
Keyword(s):  
Topology Optimization ◽  
Band Gap ◽  
Optimization Problem ◽  
Excitation Frequency ◽  
Center Frequency ◽  
Solution Strategy ◽  
Topology Optimization Problem ◽  
Topological Design ◽  
Design Variables ◽  
Measure Index

Abstract The topological design of structures to avoid vibration resonance for a certain external excitation frequency is often desired. This paper considers the topology optimization of freely vibrating bi-material structures with fixed/varying attached mass positions, targeting at maximizing the frequency band gap centering at a specified frequency. A band gap measure index is proposed to measure the size of the band gap with a specified center frequency. Aiming at maximizing this measure index, the topology optimization problem is formulated on the basis of the material-field series-expansion (MFSE) method, which greatly reduces the number of design variables and at the same time keeps the capability to describe relatively complex structural topologies with clear boundaries. As the considered optimization problem is highly non-linear and may yield multiple local minima, a sequential Kriging-based optimization solution strategy is employed to effectively solve the optimization problem. This solution strategy exhibits a relatively strong global search capability and requires no sensitivity information. With the present topology optimization model and the gradient-free algorithm, relative large band gaps with specified center frequencies have been obtained for 2D beams and 3D plates, without specifying the frequency orders between which the desired band gap occurs in prior.

Design 3D Thermo-Mechanical Structures with Multidisciplinary Topology Optimization

2012 ◽  
Vol 466-467 ◽  
pp. 1212-1216
Author(s):  
San Bao Hu ◽  
Li Ping Chen ◽  
Yu Zhang ◽  
Ming Jiang
Keyword(s):  
Heat Transfer ◽  
Topology Optimization ◽  
Design Variable ◽  
Optimization Problem ◽  
Three Dimensional ◽  
Topology Design ◽  
Design Domain ◽  
3D Design ◽  
Topology Optimization Problem ◽  
The Common

This paper presents an approach for solving the multidisciplinary topology optimization (MTO). To simplifying the description, a three-dimensional (3D) “heat transfer-thermal stress” coupling topology design problem is used as an instance to interpret the solving scheme. Unlike the common multiphysics topology optimization problem which usually modeled in a 3D domain or a 2D domain alternatively, the topology optimization problem mentioned in this paper has a 3D design domain (the design variable is referred as ρ1) and two 2D design domains (the design variable is referred as ρ2and ρ3) together in one mathematical model. Although all the model and solving method are based on a certain design instance, the solving scheme presented in this paper can be used as an efficient method for solving the boundary coupling MTO.

A Systems Approach to Structural Topology Optimization: Designing Optimal Connections

1997 ◽  
Vol 119 (1) ◽  
pp. 40-47 ◽  
Author(s):  
T. Jiang ◽  
M. Chirehdast
Keyword(s):  
Topology Optimization ◽  
Design Problem ◽  
Large Scale ◽  
Optimization Problem ◽  
Systems Design ◽  
Mathematical Programming Problem ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Topology Optimization Problem ◽  
Wide Range

In this paper, structural topology optimization is extended to systems design. Locations and patterns of connections in a structural system that consists of multiple components strongly affect its performance. Topology of connections is defined, and a new classification for structural optimization is introduced that includes the topology optimization problem for connections. A mathematical programming problem is formulated that addresses this design problem. A convex approximation method using analytical gradients is used to solve the optimization problem. This solution method is readily applicable to large-scale problems. The design problem presented and solved here has a wide range of applications in all areas of structural design. The examples provided here are for spot-weld and adhesive bond joints. Numerous other potential applications are suggested.

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 for the Single Phase Flow Using Two Point Flux Approximation Model

2013 ◽  
Author(s):  
Guang Dong ◽  
Yulan Song
Keyword(s):  
Porous Media ◽  
Topology Optimization ◽  
Optimization Problem ◽  
Single Phase ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Approximation Model ◽  
Single Phase Flow ◽  
Topology Optimization Problem ◽  
Flux Approximation

The topology optimization method is extended to solve a single phase flow in porous media optimization problem based on the Two Point Flux Approximation model. In particular, this paper discusses both strong form and matrix form equations for the flow in porous media. The design variables and design objective are well defined for this topology optimization problem, which is based on the Solid Isotropic Material with Penalization approach. The optimization problem is solved by the Generalized Sequential Approximate Optimization algorithm iteratively. To show the effectiveness of the topology optimization in solving the single phase flow in porous media, the examples of two-dimensional grid cell TPFA model with impermeable regions as constrains are presented in the numerical example section.

Topology Optimization Under Independent Multi-Load With Uncertainty

2016 ◽  
Author(s):  
Hae Chang Gea ◽  
Xing Liu ◽  
Euihark Lee ◽  
Limei Xu
Keyword(s):  
Topology Optimization ◽  
Optimization Problem ◽  
Optimization Method ◽  
Engineering Practice ◽  
Worst Case ◽  
Load Uncertainty ◽  
Topology Optimization Problem ◽  
Level Problem ◽  
Upper Level ◽  
Mean Compliance

In this paper, topology optimization under multiple independent loadings with uncertainty is presented. In engineering practice, load uncertainty can be found in many applications. From the literature, researchers have focused mainly on problems containing only a single uncertain external load. However, such idealistic problems may not be very useful in engineering practice. Problems involving multi-loadings with uncertainty are more commonly found in engineering applications. This paper presents a method to solve a system which contains multiple independent loadings with load uncertainty. First, a two-level optimization problem is formulated. The upper level problem is a typical topology optimization problem to minimize the mean compliance in the design using the worst case conditions. The lower level optimization problem is to solve for the worst loadings corresponding to the critical structure response. At the lower level formulation, an unknown-but-bounded model is used to define uncertain loadings. There are two challenges in finding the worst loading case: non-convexity and multi-loadings. The non-convexity problem is addressed by reformulating the problem as an inhomogeneous eigenvalue problem by applying the KKT optimality conditions and the multi-uncertain loadings problem is solved by an iterative method. After the worst loadings are generated, the upper level problem can be solved by a general topology optimization method. The effectiveness of the proposed method is demonstrated by numerical examples.

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