A Topology Optimization Problem in Control of Structures Using Modal Disparity

2005 ◽  
Vol 128 (3) ◽  
pp. 536-541 ◽  
Author(s):  
A. R. Diaz ◽  
R. Mukherjee
Keyword(s):  
Topology Optimization ◽  
Optimization Problem ◽  
Flexible Structures ◽  
Three Dimensional ◽  
Vibration Energy ◽  
Frame Structures ◽  
Topology Optimization Problem ◽  
Small Set ◽  
Simulation Results ◽  
External Forces

Modal disparity and a topology optimization problem seeking to maximize this disparity are introduced, with the goal of developing a new methodology for control of vibration in flexible structures. Modal disparity is generated in a structure by the application of external forces that vary the stiffness of the structure. When the forces are switched on and off and, as a result, the structure is switched between two stiffness states, modal disparity results in vibration energy being transferred from a set of not-controlled modes to a set of controlled modes. This allows the vibration of the structure to be completely attenuated by removing energy only from a small set of controlled modes. A topology optimization problem determines the best locations for application of the external forces. Simulation results are presented to demonstrate control of vibration exploiting modal disparity in two three-dimensional (3D) frame structures.

A Topology Optimization Problem in Control of Structures Using Modal Disparity

2005 ◽  
Author(s):  
Alejandro Diaz ◽  
Ranjan Mukherjee
Keyword(s):  
Topology Optimization ◽  
Optimization Problem ◽  
Flexible Structures ◽  
Vibration Energy ◽  
Topology Optimization Problem ◽  
Small Set ◽  
Simulation Results

Towards the goal of developing a new methodology for control of vibration in flexible structures, this paper introduces the concept of modal disparity and addresses the topology optimization problem for maximizing the disparity. The modal disparity in a structure is generated by the application of forces that vary the stiffness of the structure and a topology optimization problem determines the best locations for application of these forces. When the forces are switched on and off and, as a result, the structure is switched between two stiffness states, modal disparity results in vibration energy being transferred from a set of uncontrolled modes to a set of controlled modes. This allows the vibration of the structure to be completely attenuated by removing energy from the small set of controlled modes. Simulation results are presented to demonstrate control of vibration in two truss-like structures exploiting modal disparity.

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.

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.

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.

Weight Selection and PSO Based Three-Dimensional Localization for Wireless Sensor Networks

2013 ◽  
Vol 427-429 ◽  
pp. 2540-2544 ◽  
Author(s):  
Jia Liang Lv ◽  
Ying Long Wang ◽  
Huan Qing Cui ◽  
Nuo Wei
Keyword(s):  
Wireless Sensor Networks ◽  
Particle Swarm Optimization ◽  
Sensor Networks ◽  
Optimization Problem ◽  
Three Dimensional ◽  
Wireless Sensor ◽  
Swarm Optimization ◽  
Localization Algorithms ◽  
Key Technologies ◽  
Simulation Results

Localization is one of the key technologies of wireless sensor networks, and the problem of localization is always formulated as an optimization problem. Particle swarm optimization (PSO) is easy to implement and requires moderate computing resources, which is feasible for localization of sensor networks. To improve the efficiency and precision of PSO-based localization methods, this paper proposes a novel three-dimensional PSO method based on weight selection (WSPSO). Simulation results show that the proposed method outperforms standard PSO and existing localization algorithms.

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.

Multi-material topology optimization of compliant mechanisms via solid isotropic material with penalization approach and alternating active phase algorithm

2020 ◽  
Vol 234 (13) ◽  
pp. 2631-2642
Author(s):  
Behzad Majdi ◽  
Arash Reza
Keyword(s):  
Topology Optimization ◽  
Isotropic Material ◽  
Close Agreement ◽  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Active Phase ◽  
Maximum Displacement ◽  
Topology Optimization Problem ◽  
Solid Phases ◽  
Ansys Workbench

The present study aims at providing a topology optimization of multi-material compliant mechanisms using solid isotropic material with penalization (SIMP) approach. In this respect, three multi-material gripper, invertor, and cruncher compliant mechanisms are considered that consist of three solid phases, including polyamide, polyethylene terephthalate, and polypropylene. The alternating active-phase algorithm is employed to find the distribution of the materials in the mechanism. In this case, the multiphase topology optimization problem is divided into a series of binary phase topology optimization sub-problems to be solved partially in a sequential manner. Finally, the maximum displacement of the multi-material compliant mechanisms was validated against the results obtained from the finite element simulations by the ANSYS Workbench software, and a close agreement between the results was observed. The results reveal the capability of the SIMP method to accurately conduct the topology optimization of multi-material compliant mechanisms.

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