scholarly journals A pessimistic bilevel stochastic problem for elastic shape optimization

2021 ◽  
Author(s):  
Johanna Burtscheidt ◽  
Matthias Claus ◽  
Sergio Conti ◽  
Martin Rumpf ◽  
Josua Sassen ◽  
...  
Keyword(s):  
Shape Optimization ◽  
Risk Measure ◽  
Compact Convex ◽  
Quadratic Function ◽  
Goal Function ◽  
Bilevel Optimization ◽  
Material Distribution ◽  
Stochastic Programs ◽  
Alternate Model ◽  
Optimal Material

AbstractWe consider pessimistic bilevel stochastic programs in which the follower maximizes over a fixed compact convex set a strictly convex quadratic function, whose Hessian depends on the leader’s decision. This results in a random upper level outcome which is evaluated by a convex risk measure. Under assumptions including real analyticity of the lower-level goal function, we prove the existence of optimal solutions. We discuss an alternate model, where the leader hedges against optimal lower-level solutions, and show that solvability can be guaranteed under weaker conditions in both, a deterministic and a stochastic setting. The approach is applied to a mechanical shape optimization problem in which the leader decides on an optimal material distribution to minimize a tracking-type cost functional, whereas the follower chooses forces from an admissible set to maximize a compliance objective. The material distribution is considered to be stochastically perturbed in the actual construction phase. Computational results illustrate the bilevel optimization concept and demonstrate the interplay of follower and leader in shape design and testing.

Generative design and analysis of a double-wishbone suspension assembly: a methodology for developing constraint oriented solutions for optimum material distribution

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Aayush Bhat ◽  
Vyom Gupta ◽  
Savitoj Singh Aulakh ◽  
Renold S. Elsen
Keyword(s):  
Design Methodology ◽  
Manufacturing Industry ◽  
Optimization Technique ◽  
Design Solution ◽  
Material Distribution ◽  
Generative Design ◽  
Trade Off ◽  
Content Type ◽  
Life Study ◽  
Optimal Material

Purpose The purpose of this paper is to implement the generative design as an optimization technique to achieve a reasonable trade-off between weight and reliability for the control arm plate of a double-wishbone suspension assembly of a Formula Student race car. Design/methodology/approach The generative design methodology is applied to develop a low-weight design alternative to a standard control arm plate design. A static stress simulation and a fatigue life study are developed to assess the response of the plate against the loading criteria and to ensure that the plate sustains the theoretically determined number of loading cycles. Findings The approach implemented provides a justifiable outcome for a weight-factor of safety trade-off. In addition to optimal material distribution, the generative design methodology provides several design outcomes, for different materials and fabrication techniques. This enables the selection of the best possible outcome for several structural requirements. Research limitations/implications This technique can be used for applications with pre-defined constraints, such as packaging and loading, usually observed in load-bearing components developed in the automotive and aerospace sectors of the manufacturing industry. Practical implications Using this technique can provide an alternative design solution to long periods spent in the design phase, because of its ability to generate several possible outcomes in just a fraction of time. Originality/value The proposed research provides a means of developing optimized designs and provides techniques in which the design developed and chosen can be structurally analyzed.

Topology Optimization of Dynamic Systems Under Uncertain Loads: An H∞-Norm-Based Approach

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Paolo Venini
Keyword(s):  
Topology Optimization ◽  
Structural Parameters ◽  
Goal Function ◽  
Dynamic Compliance ◽  
Case Scenario ◽  
Worst Case ◽  
Original Definition ◽  
Optimal Material ◽  
The One ◽  
Definition Of

An innovative approach to topology optimization of dynamic system is introduced that is based on the system transfer-function H∞-norm. As for the structure, the proposed strategy allows to determine the optimal material distribution that ensures the minimization of a suitable goal function, such as (an original definition of) the dynamic compliance. Load uncertainty is accounted for by means of a nonprobabilistic convex-set approach (Ben-Haim and Elishakoff, 1990, Convex Models of Uncertainty in Applied Mechanics, Elsevier Science, Amsterdam). At each iteration, the worst load is determined as the one that maximizes the current dynamic compliance so that the proposed strategy fits the so-called worst case scenario (WCS) approach. The overall approach consists of the repeated solution of the two steps (minimization of the dynamic compliance with respect to structural parameters and maximization of the dynamic compliance with respect to the acting load) until convergence is achieved. Results from representative numerical studies are eventually presented along with extensions to the proposed approach that are currently under development.

Genesis of Ribbed Plate and Shells With Isotropic Density Dependent Material

1993 ◽  
Author(s):  
Hans P. Mlejnek
Keyword(s):  
Working Conditions ◽  
Isotropic Material ◽  
Material Model ◽  
Elastic Behaviour ◽  
Material Distribution ◽  
Isotropic Model ◽  
Material Density ◽  
Layer Structures ◽  
Optimal Material ◽  
Theoretical Considerations

Abstract An essential part in the genesis of structures or optimal material distribution is the relation between elastic behaviour and material density. This approach makes use of a isotropic material model, which leads to very simple working conditions. The isotropic model is directly formulated and utilized without employing homogenization based on an artificial microstructure. It is shown in theoretical considerations and demonstrated by examples, that this idea works also very easily with plate and shells, even for very general layer structures.

Topological Optimization Technique for Free Vibration Problems

1995 ◽  
Vol 62 (1) ◽  
pp. 200-207 ◽  
Author(s):  
Zheng-Dong Ma ◽  
Noboru Kikuchi ◽  
Hsien-Chie Cheng ◽  
Ichiro Hagiwara
Keyword(s):  
Free Vibration ◽  
Optimization Algorithm ◽  
Optimization Problem ◽  
Optimization Technique ◽  
Topological Optimization ◽  
Material Distribution ◽  
Eigenvalue Optimization ◽  
Shift Parameter ◽  
Vibration Problems ◽  
Optimal Material

A topological optimization technique using the conception of OMD (Optimal Material Distribution) is presented for free vibration problems of a structure. A new objective function corresponding to multieigenvalue optimization is suggested for improving the solution of the eigenvalue optimization problem. An improved optimization algorithm is then applied to solve these problems, which is derived by the authors using a new convex generalized-linearization approach via a shift parameter which corresponds to the Lagrange multiplier and the use of the dual method. Finally, three example applications are given to substantiate the feasibility of the approaches presented in this paper.

Distribution Parameter Optimization of an FGM Pressure Vessel

2011 ◽  
Vol 320 ◽  
pp. 404-409
Author(s):  
Ze Wu Wang ◽  
Shu Juan Gao ◽  
Qian Zhang ◽  
Pei Qi Liu ◽  
Xiao Long Jiang
Keyword(s):  
Analytical Solution ◽  
Pressure Vessel ◽  
Material Properties ◽  
Optimization Design ◽  
Optimal Solution ◽  
Functionally Graded ◽  
Material Distribution ◽  
Optimization Scheme ◽  
Graded Material ◽  
Optimal Material

Functionally graded material (FGM) is well-known as one of the most promising materials in the 21stcentury, which has become the hot issue on its mechanical behavior and composition design. The optimization design of the material distribution properties for an FGM hollow vessel subjected to internal pressure were investigated in this paper. By constructing an exponentially function determining the material properties, the general analytical solution of the stresses of the FGM pressure vessel was given based on the Euler-Cauchy formula. And then, an optimization model for obtaining the optimal material distribution of FGM vessel was proposed coupling the general finite element (FE) code. The discrepancy between the analytical solution and the numerical solution was about 2%, which verified the reliability of the proposed models, and the optimization results also proved the feasibility of proposed optimization scheme because of arriving at the optimal solution in a few iterations. Results obtained would be helpful in designing an FGM pressure vessel.

scholarly journals Optimization of Grillage-like Continuum by Triangle Plate Element

2012 ◽  
Vol 6 (1) ◽  
pp. 8-14
Author(s):  
Kemin Zhou ◽  
Xia Li
Keyword(s):  
Optimization Procedure ◽  
Material Model ◽  
Stress Constraints ◽  
Design Domain ◽  
Material Distribution ◽  
Plate Element ◽  
Design Variables ◽  
Plate Elements ◽  
Discrete Structures ◽  
Optimal Material

The volume of grillages with stress constraints is minimized. An optimal beams system or plate with reinforced ribs is obtained to present the optimal structure. A grillage-like continuum material model is adapted. Structure is analyzed by finite element method with triangle plate elements. The geometric matrix of triangle plate element in explicit formulation about area coordinates is presented. The stiffness matrix of grillage-like continuum material model is derived. The material distribution field in design domain is optimized by fully-stressed criterion. The densities and orientations of the beam or reinforced ribs at nodes in grillages are taken as design variables. The densities and orientations vary in design domain continuously. The optimal distribution fields of bend moments, flexure displacement and material are obtained simultaneously. Subsequently the discrete structures are founded based on the optimal material distribution fields. The performances of different elements are compared. The optimization procedure is accomplished by computer program automatically.

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.

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