scholarly journals A New Compliance-function-shapeoriented Robust Approach for Volume-constrained Continuous Topology Optimization with Uncertain Loading Directions

2017 ◽  
Author(s):  
Anikó Csébfalvi
Keyword(s):  
Topology Optimization ◽  
Variational Problems ◽  
Feasible Directions ◽  
Robust Approach ◽  
Compliance Function ◽  
Equality Relation ◽  
Material Volume ◽  
Area Minimizing ◽  
Continuous Topology ◽  
Function Shape

The paper presents a new compliance-function-shape-oriented robust approach for the volume-constrained continuous topology optimization with uncertain loading directions. The pure set-based algorithm try to rearrange (take away) some amount of the material volume, originally used to minimize the nominal-compliance, to make a more balanced compliance-function-shape on the set of feasible directions which is less sensitive to the directional fluctuation. The objective is the area of the compliance function shape defined on the set of feasible directions. The area-minimal shape searching process is controlled by the maximum allowable increase of the nominal-compliance. The result will be a more robust compliance function shape which can be characterized by a higher nominal-compliance but a smaller curvature about it in any direction. Using the terminology of the classical variational problems, the proposed approach can be classified as a curve-length or surface-area minimizing inner-value problem where the inner condition, namely the maximum allowable increase of the nominal-compliance, expressed as a percentage of the original nominal compliance, the searching domain is defined implicitly as integration limits in the objective formulation and a usual equality relation is used to prescribe the allowable material volume expressed as a percentage of the total material volume. Two examples are presented to demonstrate the viability and efficiency of the proposed robust approach.

Topological Optimum Design Considering Stress Constraint Using Approximate Function

2009 ◽  
Vol 419-420 ◽  
pp. 25-28
Author(s):  
Chien Jong Shih ◽  
Kuang You Chen
Keyword(s):  
Topology Optimization ◽  
Numerical Optimization ◽  
Volume Fraction ◽  
Stress Constraint ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Integrated Process ◽  
Approximate Function ◽  
Material Volume ◽  
Element Technique

This paper presents an integrated process of structural topology optimization in minimizing both compliance and structural weight. The material volume fraction acts an additional design variable subjected to the empirical approximate stress constraint in terms of material volume fraction. This explicitly approximate function can provide a convenient way to calculate its gradient information for numerical optimization. An engineer does not require advanced topology optimization and superior finite element technique in applying proposed method.

Topology Optimization on the Material Distribution of Track Segment for Heavy Machinery

2011 ◽  
Vol 346 ◽  
pp. 460-470
Author(s):  
Yong Li ◽  
Guo Qiang Wang ◽  
Zhen Hua Yan
Keyword(s):  
Topology Optimization ◽  
Variable Density ◽  
Material Distribution ◽  
Distribution Law ◽  
Track Segment ◽  
Heavy Machinery ◽  
Maximum Stiffness ◽  
Material Volume ◽  
Optimal Material ◽  
Optimal Area

To achieve the rational shape and structure of large or super-large track segment, this paper investigated the optimal material distribution law of the track segment with topology optimization by variable density method. In this method the element density of the optimal area is the design variable, the maximum stiffness between the track segment and the terrain is the object, and the material volume per centum of the optimal area is the constraint. In this study, we obtained the topology optimal results of a track segment for a certain heavy-machinery by OPTISTRUCT software. The paper also presented the transitional geometrical distribution law of the optimal material from solid state to hollow state at the same constraint of the material volume percentum and at the different terrain stiffness. Finally, the optimal shape was put into application.

scholarly journals Critical Investigation of the Combined Compliance Average and Spreading Measures in the Robust Topology Optimization with Uncertain Loading Magnitude and Direction

2020 ◽  
Author(s):  
Anikó Csébfalvi
Keyword(s):  
Topology Optimization ◽  
Robust Design ◽  
Response Variable ◽  
Robust Solution ◽  
Robust Approach ◽  
Robust Topology Optimization ◽  
Design Variables ◽  
Bridge Problem ◽  
Creative Contribution

The paper critically investigates the role of the combined compliance average and spreading measures in the volume-constrained continuous robust topology optimization with uncertain loading magnitude and direction. In the robust topology optimization the generally expected and most popular robustness measure is the expected compliance, In the expectancy oriented approach, the compliance increment which is needed to get the robust design is an implicitly defined response variable. In order to open the possibility of the creative contribution of the designer to the best robust design searching process, this measure is sometimes combined with a spreading-oriented measure, which may be the variance or standard deviation. The best weighting schema can be done by a try-and-error-like algorithm in which the weights are design variables and the compliance-increment remains an implicitly defined response variable. In this paper, it will be shown that all of the compliance oriented approaches which are based on a single or combined statistical measure can be replaced by a new compliance-function-shape-oriented robust approach in which the allowed-compliance-increment will be an explicitly defined design variable and for a given increment value the robust solution will be the theoretically best one. A popular volume-constrained symmetric bridge problem with uncertain loading magnitude and direction will be presented to demonstrate the viability and efficiency of the proposed robust approach.

Generating support structures for additive manufacturing with continuum topology optimization methods

2019 ◽  
Vol 25 (2) ◽  
pp. 232-246 ◽  
Author(s):  
Yang Liu ◽  
Zuyu Li ◽  
Peng Wei ◽  
Shikui Chen
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Rapid Development ◽  
Load Condition ◽  
Practical Significance ◽  
Heaviside Function ◽  
Optimal Topology ◽  
Support Structures ◽  
Content Type ◽  
Material Volume

PurposeThe purpose of this paper is to explore the possibility of combining additive manufacturing (AM) with topology optimization to generate support structures for addressing the challenging overhang problem. The overhang problem is considered as a constraint, and a novel algorithm based on continuum topology optimization is proposed.Design/methodology/approachA mathematical model is formulated, and the overhang constraint is embedded implicitly through a Heaviside function projection. The algorithm is based on the Solid Isotropic Material Penalization (SIMP) method, and the optimization problem is solved through sensitivity analysis.FindingsThe overhang problem of the support structures is fixed. The optimal topology of the support structures is developed from a mechanical perspective and remains stable as the material volume of support structures changes, which allows engineers to adjust the material volume to save cost and printing time and meanwhile ensure sufficient stiffness of the support structures. Three types of load conditions for practical application are considered. By discussing the uniform distributive load condition, a compromise result is achieved. By discussing the point load condition, the removal work of support structures after printing is alleviated. By discussing the most unfavorable load condition, the worst collapse situation of the printing model during printing process is sufficiently considered. Numerical examples show feasibility and effectiveness of the algorithm.Research limitations/implicationsThe proposed algorithm involves time-consuming finite element analysis and iterative solution, which increase the computation burden. Only the overhang constraint and the minimum compliance problem are discussed, while other constraints and objective functions may be of interest.Practical implicationsCompared with most of the existing heuristic or geometry-based support-generating algorithms, the proposed algorithm develops support structures for AM from a mechanical perspective, which is necessary for support structures particularly used in AM for mega-scale construction such as architectures and sculptures to ensure printing success and accuracy of the printed model.Social implicationsWith the rapid development of AM, complicated structures result from topology optimization are available for fabrication. The present paper demonstrates a combination of AM and topology optimization, which is the trend of fabricating manner in the future.Originality/valueThis paper remarks the first of attempts to use continuum topology optimization method to generate support structures for AM. The methodology used in this work is theoretically meaningful and conclusions drawn in this paper can be of important instruction value and practical significance.

Topology Optimization of Thermo-Mechanical Structure Using the Hybrid Celluar Automata Method

2013 ◽  
Vol 365-366 ◽  
pp. 111-116
Author(s):  
Jin Qing Zhan
Keyword(s):  
Topology Optimization ◽  
Cellular Automata ◽  
Optimization Problem ◽  
Control Law ◽  
Local Rule ◽  
Hybrid Cellular Automata ◽  
Material Volume ◽  
The Mean ◽  
Mean Compliance ◽  
Single Material

Topology optimization of thermo-elastic structures using the hybrid cellular automata method is investigated in this paper. The objective is to minimize the mean compliance of a structure with a single material volume constraint. The hybrid cellular automata method is used to solve the optimization problem. The local change in the design variable is determined by a local rule based on the proportional control law. The numerical example is presented to show the feasibility of the present approach.

Topology Optimization of Piezoelectric Energy Harvesting Strap Buckle

2009 ◽  
Author(s):  
Bin Zheng ◽  
Hong-Zhong Huang ◽  
Hae Chang Gea
Keyword(s):  
Topology Optimization ◽  
Energy Harvesting ◽  
Electric Energy ◽  
Optimization Method ◽  
Piezoelectric Energy Harvesting ◽  
Wearable Electronics ◽  
Design Constraint ◽  
Piezoelectric Energy ◽  
Material Volume ◽  
Topology Optimization Method

In the past decades, the stagnant growth of battery technology becomes the bottle-neck of new generation of portable and wearable electronics which ask for longer work time and higher power consumption. Energy harvesting device based on the direct piezoelectric effect that converts ambient mechanical energy to usable electric energy is a very attractive energy source for portable and wearable electronics. This paper discusses the design of piezoelectric energy harvesting strap buckle that can generate as much as possible electric energy from the differential forces applying on the buckle. Topology optimization method is employed to improve the efficiency of piezoelectric energy harvesting strap buckle in a limited design space. A stiffness or displacement constraint is introduced to substitute material volume constraint in this problem formulation to avoid useless optimum result with nearly zero material volume. The sensitivities of both objective function and design constraint are derived from the adjoint method. A design example of piezoelectric energy harvesting strap buckle using the proposed topology optimization method is presented and the result is discussed.

Topology Optimization of Truss-Like Continuum under Stress Constraints by Sequence Linear Program

2012 ◽  
Vol 151 ◽  
pp. 327-331
Author(s):  
Ke Min Zhou ◽  
Xia Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Iterative Procedure ◽  
Material Model ◽  
Stress Constraints ◽  
Linear Program ◽  
Stress Constraint ◽  
Design Domain ◽  
Material Volume

A method to minimize material volume of truss-like continuum with stress constraint under multi-loads cases by sequence linear program was presented. It is assumed that there were infinite numbers of members with infinitesimal spaces along two orthotropic orientations at any position. A truss-like material model was employed to simulate the topological optimal structures. Members were assumed as distributed continuously in design domain. Structure was analyzed by finite element method. The densities and orientations of members at nodes were taken as designed variables. Their values in elements vary continuously. An iterative procedure was suggested to optimize the distributed field of members. The sensitivities of stresses constraints were derived. Truss-like continuum was built by the method in this paper.

Sign in / Sign up

Export Citation Format

Share Document