scholarly journals A performance-based optimization method for topology design of continuum structures with mean compliance constraints

2002 ◽  
Vol 191 (13-14) ◽  
pp. 1471-1489 ◽  
Author(s):  
Qing Quan Liang ◽  
Grant P Steven
Keyword(s):  
Optimization Method ◽  
Topology Design ◽  
Continuum Structures ◽  
Mean Compliance ◽  
Compliance Constraints ◽  
A Performance

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.

Are Circular Shaped Masks Adequate in Adaptive Mask Overlay Topology Synthesis Method?

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Anupam Saxena
Keyword(s):  
Resource Constraints ◽  
Synthesis Method ◽  
Design Procedure ◽  
Topology Design ◽  
Two Dimensional ◽  
Closed Curves ◽  
Compliance Minimization ◽  
Topological Features ◽  
Mean Compliance ◽  
Material Layout

Previous versions of the material mask overlay strategy (MMOS) for topology synthesis primarily employ circular masks to simulate voids within the design region. MMOS operates on the photolithographic principle by appropriately positioning and sizing a group of negative masks and thus iteratively improves the material layout to meet the desired objective. The fundamental notion is that a group of circular masks can represent a local void of any shape. The question whether masks of more general shapes (e.g., any two-dimensional closed, nonself intersecting polygon) would offer significant enhancements in efficiently attaining the appropriate topological features in a continuum remains. This paper investigates the performance of two other mask types; elliptical and rectangular masks are compared with that of the circular ones. These are the respective modest representatives of closed curves and their polygonal approximations. First, two mean compliance minimization examples under resource constraints are solved. Thereafter, compliant pliers are synthesized using the three mask types. It is observed that the use of elliptical or rectangular masks do not offer significant advantages over the use of circular ones. On the contrary, the examples suggest that less number of circular masks are adequate to model the topology design procedure more efficiently. Thus, it is postulated that using generic simple closed curves or polygonal masks will not introduce significant benefits over circular ones in the MMOS based topology design algorithms.

Robust topology optimization for continuum structures with random loads

2018 ◽  
Vol 35 (2) ◽  
pp. 710-732 ◽  
Author(s):  
Jie Liu ◽  
Guilin Wen ◽  
Qixiang Qing ◽  
Fangyi Li ◽  
Yi Min Xie
Keyword(s):  
Topology Optimization ◽  
Optimization Method ◽  
Computational Time ◽  
Optimization Approach ◽  
Random Load ◽  
Content Type ◽  
Continuum Structures ◽  
Robust Topology Optimization ◽  
Random Loads ◽  
Expansion Technique

Purpose This paper aims to tackle the challenge topic of continuum structural layout in the presence of random loads and to develop an efficient robust method. Design/methodology/approach An innovative robust topology optimization approach for continuum structures with random applied loads is reported. Simultaneous minimization of the expectation and the variance of the structural compliance is performed. Uncertain load vectors are dealt with by using additional uncertain pseudo random load vectors. The sensitivity information of the robust objective function is obtained approximately by using the Taylor expansion technique. The design problem is solved using bi-directional evolutionary structural optimization method with the derived sensitivity numbers. Findings The numerical examples show the significant topological changes of the robust solutions compared with the equivalent deterministic solutions. Originality/value A simple yet efficient robust topology optimization approach for continuum structures with random applied loads is developed. The computational time scales linearly with the number of applied loads with uncertainty, which is very efficient when compared with Monte Carlo-based optimization method.

Topological Optimization of Coronary Stents

2015 ◽  
Author(s):  
Shijia Zhao ◽  
Linxia Gu
Keyword(s):  
Radial Stress ◽  
Optimization Method ◽  
Homogenization Method ◽  
Topology Design ◽  
Topological Optimization ◽  
Optimal Topology ◽  
Patient Specific ◽  
Stent Design ◽  
Restenosis Rate ◽  
Radial Stiffness

The structural topological optimization method is an effective way to find the optimal topology of stents, which could be tailored for targeted stent performance, such as scaffolding ability, foreshortening, potential restenosis rate, etc. The radial stiffness is one of the major characteristics about stent performance. In this work, the homogenization method was utilized for the optimization of stent designs with the objective of maximizing the scaffolding ability of stent, i.e. its radial stiffness. A few design choices were presented by changing the number and distribution of strut connectors while keeping the void volume as 80%. The obtained optimal topology illustrated that the material distribution was mainly determined by the radial stress applied onto the stent. The optimal topology design in this work paves the way for the following dimension design, which can be targeted to the customized stent design for patient-specific lesions.

scholarly journals Layout optimization of multi-material continuum structures with the isolines topology design method

2014 ◽  
Vol 47 (2) ◽  
pp. 221-237 ◽  
Author(s):  
Osvaldo M. Querin ◽  
Mariano Victoria ◽  
Concepción Díaz ◽  
Pascual Martí
Keyword(s):  
Design Method ◽  
Layout Optimization ◽  
Topology Design ◽  
Continuum Structures

Early-Stage Naval Ship Distributed System Design Using Architecture Flow Optimization

2020 ◽  
pp. 1-19
Author(s):  
Mark A. Parsons ◽  
Mustafa Y. Kara ◽  
Kevin M. Robinson ◽  
Nicholas T. Stinson ◽  
Alan J. Brown
Keyword(s):  
System Design ◽  
Energy Flow ◽  
Early Stage ◽  
Linear Optimization ◽  
Optimization Method ◽  
Topology Design ◽  
Flow Optimization ◽  
Naval Ship ◽  
The Time Domain ◽  
Power And Energy Systems

This article describes an architecture flow optimization (AFO) method for naval ship System design. AFO is a network-based method. It is used to design and analyze naval ship Mission, Power, and Energy Systems (MPES) in a naval ship Concept and Requirements Exploration (C&RE) process at a sufficient level of detail to better understand system energy flow, define MPES architecture and sizing, reduce system vulnerability, and improve system reliability. This method decomposes MPES into three architectures: logical, physical, and operational which describe the system’s spatial, functional, and temporal characteristics, respectively. Using this framework, the AFO incorporates system topologies, input/output energy coefficient component models, preliminary arrangements, and (nominal and damaged) steady-state operational scenarios into a linear optimization method to minimize the energy flow cost required to satisfy all operational scenario demands and constraints. AFO results are used to inform system topology design and assess the feasibly and survivability of representative designs in the C&RE process. AFO results may also be used in physics-based vital component sizing, calculation of vulnerability/effectiveness metrics in the C&RE process, and subsequent linear optimization formulations to assess recoverability and operational effectiveness in the time domain.

A Design Method of Beads in Shell Structure Using Non-Parametric Shape Optimization Method

2014 ◽  
Author(s):  
Kohei Shintani ◽  
Hideyuki Azegami
Keyword(s):  
Shape Optimization ◽  
Shell Structure ◽  
Parametric Design ◽  
Design Method ◽  
Optimization Method ◽  
Adjoint Problem ◽  
Sigmoid Function ◽  
Out Of Plane ◽  
Mean Compliance ◽  
Non Parametric

The present paper describes a method finding bead shapes in shell structure to increase the stiffness using a solution to shape optimization method. Variation of the shell structure in out-of-plane direction is chosen as a non-parametric design variable. To create beads, the out-of-plane variation is restricted by using the sigmoid function. Mean compliance is used as objective function. The main problem is defined as a linear elastic problem for shell structure. The Fréchet derivative with respect to the out-of-plane variation of the mean compliance is evaluated with the solutions of the main problem and an adjoint problem which is derived theoretically by the adjoint variable method. To solve the bead design problem, an iterative algorithm based on the H1 gradient method is used. Numerical results show the effectiveness of the method.

Sign in / Sign up

Export Citation Format

Share Document