scholarly journals Towards solving large-scale topology optimization problems with buckling constraints at the cost of linear analyses

2020 ◽  
Vol 363 ◽  
pp. 112911 ◽  
Author(s):  
Federico Ferrari ◽  
Ole Sigmund
Keyword(s):  
Topology Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Buckling Constraints ◽  
The Cost

An Adaptive Continuation Method for Topology Optimization of Continuum Structures Considering Buckling Constraints

2017 ◽  
Vol 09 (07) ◽  
pp. 1750092 ◽  
Author(s):  
Xingjun Gao ◽  
Lijuan Li ◽  
Haitao Ma
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Continuation Method ◽  
Optimization Process ◽  
Continuum Structures ◽  
Design Evolution ◽  
Buckling Constraints ◽  
Load Factors ◽  
Structural Compliance ◽  
Parameter Values

This paper presents an adaptive continuation method for buckling topology optimization of continuum structures using the Solid Isotropic Material with Penalization (SIMP) model. For optimization problems of minimizing structural compliance subject to constraints on material volume and buckling load factors, it has been found that the conflict between the requirements for structural stiffness and stability may have an adverse impact on the performance of existing optimization algorithms. An automatic scheme for adjusting the penalization parameter is introduced to deal with this conflict and thus achieves better designs. Based on an investigation on the effect of the penalization parameter on design evolution during the optimization process, a rule is established to determine the appropriate penalization parameter values. Using this rule, an effective scheme is developed for determining the penalization parameter values such that the buckling constraints are appropriately considered throughout the optimization process. Numerical examples are presented to illustrate the effectiveness of the proposed method.

OPTIMAL TESTING RESOURCE ALLOCATION FOR MODULAR SOFTWARE CONSIDERING COST, TESTING EFFORT AND RELIABILITY USING GENETIC ALGORITHM

2009 ◽  
Vol 16 (06) ◽  
pp. 495-508 ◽  
Author(s):  
P. K. KAPUR ◽  
ANU. G. AGGARWAL ◽  
KANICA KAPOOR ◽  
GURJEET KAUR
Keyword(s):  
Genetic Algorithm ◽  
Resource Allocation ◽  
Software Development ◽  
Large Scale ◽  
Optimization Problems ◽  
Low Cost ◽  
Computer Software ◽  
Critical Issue ◽  
Software Systems ◽  
The Cost

The demand for complex and large-scale software systems is increasing rapidly. Therefore, the development of high-quality, reliable and low cost computer software has become critical issue in the enormous worldwide computer technology market. For developing these large and complex software small and independent modules are integrated which are tested independently during module testing phase of software development. In the process, testing resources such as time, testing personnel etc. are used. These resources are not infinitely large. Consequently, it is an important matter for the project manager to allocate these limited resources among the modules optimally during the testing process. Another major concern in software development is the cost. It is in fact, profit to the management if the cost of the software is less while meeting the costumer requirements. In this paper, we investigate an optimal resource allocation problem of minimizing the cost of software testing under limited amount of available resources, given a reliability constraint. To solve the optimization problem we present genetic algorithm which stands up as a powerful tool for solving search and optimization problems. The key objective of using genetic algorithm in the field of software reliability is its capability to give optimal results through learning from historical data. One numerical example has been discussed to illustrate the applicability of the approach.

A novel approach of reliability-based topology optimization for continuum structures under interval uncertainties

2019 ◽  
Vol 25 (9) ◽  
pp. 1455-1474 ◽  
Author(s):  
Lei Wang ◽  
Haijun Xia ◽  
Yaowen Yang ◽  
Yiru Cai ◽  
Zhiping Qiu
Keyword(s):  
Topology Optimization ◽  
Reliability Index ◽  
Large Scale ◽  
Optimization Problems ◽  
Uncertainty Propagation ◽  
Content Type ◽  
Continuum Structures ◽  
Novel Approach ◽  
Design Variables ◽  
Interval Uncertainties

Purpose The purpose of this paper is to propose a novel non-probabilistic reliability-based topology optimization (NRBTO) method for continuum structural design under interval uncertainties of load and material parameters based on the technology of 3D printing or additive manufacturing. Design/methodology/approach First, the uncertainty quantification analysis is accomplished by interval Taylor extension to determine boundary rules of concerned displacement responses. Based on the interval interference theory, a novel reliability index, named as the optimization feature distance, is then introduced to construct non-probabilistic reliability constraints. To circumvent convergence difficulties in solving large-scale variable optimization problems, the gradient-based method of moving asymptotes is also used, in which the sensitivity expressions of the present reliability measurements with respect to design variables are deduced by combination of the adjoint vector scheme and interval mathematics. Findings The main findings of this paper should lie in that new non-probabilistic reliability index, i.e. the optimization feature distance which is defined and further incorporated in continuum topology optimization issues. Besides, a novel concurrent design strategy under consideration of macro-micro integration is presented by using the developed RBTO methodology. Originality/value Uncertainty propagation analysis based on the interval Taylor extension method is conducted. Novel reliability index of the optimization feature distance is defined. Expressions of the adjoint vectors between interval bounds of displacement responses and the relative density are deduced. New NRBTO method subjected to continuum structures is developed and further solved by MMA algorithms.

scholarly journals Deep Learning-Based Accuracy Upgrade of Reduced Order Models in Topology Optimization

2021 ◽  
Vol 11 (24) ◽  
pp. 12005
Author(s):  
Nikos Ath. Kallioras ◽  
Alexandros N. Nordas ◽  
Nikos D. Lagaros
Keyword(s):  
Deep Learning ◽  
Topology Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Computational Effort ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Learning Techniques ◽  
Complex Models ◽  
Scale Design

Topology optimization problems pose substantial requirements in computing resources, which become prohibitive in cases of large-scale design domains discretized with fine finite element meshes. A Deep Learning-assisted Topology OPtimization (DLTOP) methodology was previously developed by the authors, which employs deep learning techniques to predict the optimized system configuration, thus substantially reducing the required computational effort of the optimization algorithm and overcoming potential bottlenecks. Building upon DLTOP, this study presents a novel Deep Learning-based Model Upgrading (DLMU) scheme. The scheme utilizes reduced order (surrogate) modeling techniques, which downscale complex models while preserving their original behavioral characteristics, thereby reducing the computational demand with limited impact on accuracy. The novelty of DLMU lies in the employment of deep learning for extrapolating the results of optimized reduced order models to an optimized fully refined model of the design domain, thus achieving a remarkable reduction of the computational demand in comparison with DLTOP and other existing techniques. The effectiveness, accuracy and versatility of the novel DLMU scheme are demonstrated via its application to a series of benchmark topology optimization problems from the literature.

Application of Topology Optimization in Product Design and Manufacturing

2011 ◽  
Author(s):  
Ihab Ragai ◽  
Harry Tempelman ◽  
David Kirby
Keyword(s):  
Topology Optimization ◽  
Conceptual Design ◽  
Design Process ◽  
Development Time ◽  
Optimization Problems ◽  
Mathematical Formulation ◽  
Design Stage ◽  
Conceptual Design Stage ◽  
Structural Design Optimization ◽  
The Cost

This paper deals with the utilization of topology optimization in the design process. Topology optimization is considered the most challenging task in the structural design optimization problems because the general layout of the structure is not known; however, implementing it in the conceptual design stage has proven to reduce the cost and development time. In this paper, the design process is briefly discussed emphasizing the use of topology optimization in the conceptual design stage. Also, the mathematical formulation for topology optimization with material density contours is presented. Furthermore, two industrial case studies, related to off-road mining and construction trucks, are discussed where the use of topology optimization has proven to dramatically improve an existing design and significantly decrease the development time of a new design.

scholarly journals Structural Topology Design Optimization Using the Binary Bat Algorithm

2020 ◽  
Vol 10 (4) ◽  
pp. 1481 ◽  
Author(s):  
Abdulkhaliq A. Jaafer ◽  
Mustafa Al-Bazoon ◽  
Abbas O. Dawood
Keyword(s):  
Topology Optimization ◽  
Penalty Function ◽  
Large Scale ◽  
Optimization Problems ◽  
Bat Algorithm ◽  
Topology Design ◽  
Benchmark Problems ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Filtering Algorithm

In this study, the binary bat algorithm (BBA) for structural topology optimization is implemented. The problem is to find the stiffest structure using a certain amount of material and some constraints using the bit-array representation method. A new filtering algorithm is proposed to make BBA find designs with no separated objects, no checkerboard patterns, less unusable material, and higher structural performance. A volition penalty function for topology optimization is also proposed to accelerate the convergence toward the optimal design. The main effect of using the BBA lies in the fact that the BBA is able to handle a large number of design variables in comparison with other well-known metaheuristic algorithms. Based on the numerical results of four benchmark problems in structural topology optimization for minimum compliance, the following conclusions are made: (1) The BBA with the proposed filtering algorithm and penalty function are effective in solving large-scale numerical topology optimization problems (fine finite elements mesh). (2) The proposed algorithm produces solid-void designs without gray areas, which makes them practical solutions that are applicable in manufacturing.

Minimization of Cost and Print Time of Additive Manufacturing via Topology Optimization

2018 ◽  
Author(s):  
Graeme Sabiston ◽  
Luke Ryan ◽  
Il Yong Kim
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Surface Area ◽  
Large Scale ◽  
Time Factors ◽  
Design Tool ◽  
Support Material ◽  
Manufacturing Operations ◽  
Volume Yield ◽  
The Cost

As the field of design for additive manufacturing continues to evolve and accelerate towards admitting more robust designs requiring fewer instances of user-intervention, we will see the conventional design cycle evolve dramatically. However, to fully take advantage of this emerging technology — particularly with respect to large scale manufacturing operations — considerations of productivity from a fiscal perspective are sure to become of the utmost importance. A mathematical model incorporating the cost and time factors associated with additive manufacturing processes has been developed and implemented as a multi-weighted single-objective topology optimization algorithm. The aforementioned factors have been identified as component surface area and volume of support material. These quantities are optimized alongside compliance, producing a design tool that gives the user the option to choose the relative weighting of performance over cost. In two academic examples, minimization of compliance alongside surface area and support structure volume yield geometries demonstrating that considerable decreases in support material in particular can be achieved without sacrificing significant part compliance.

Assembly-Free Buckling Analysis for Topology Optimization

2015 ◽  
Author(s):  
Xiang Bian ◽  
Praveen Yadav ◽  
Krishnan Suresh
Keyword(s):  
Topology Optimization ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Optimization Problems ◽  
Buckling Analysis ◽  
Inverse Iteration ◽  
Analysis Method ◽  
Linear Buckling ◽  
3D Topology ◽  
Linear Buckling Analysis

Linear buckling analysis entails the solution of a generalized eigenvalue problem. Popular methods for solving such problems tend to be memory-hungry, and therefore slow for large degrees of freedom. The main contribution of this paper is a low-memory assembly-free linear buckling analysis method. In particular, we employ the classic inverse iteration, in conjunction with an assembly-free deflated linear solver. The resulting implementation is simple, fast and particularly well suited for parallelization. The proposed method is used here to solve large scale 3D topology optimization problems subject to buckling constraints, where buckling problems must be solved repeatedly.

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