A Finite Element Method for the Optimal Design of Variable Thickness Sheets

Rossow, M. P.; Taylor, John E.

doi:10.2514/3.50631

Cited by 100 publications

(28 citation statements)

References 8 publications

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“…When solving the problem of topology optimization, the following assumptions were adopted [9]: -Continuum medium will be tested, as a homogeneous and isotropic medium; -The material is linear-elastic (E = const. ); -It is assumed that the strain tensor is linear (analysis for small strains); -During the optimization process, the problem is considered for the permanent constructional space Ω (x, y, z) with dimensions of 0.250.251 m; -An approach is used of the finite element method, the updated Lagrangian description and the calculus of variations; -In the optimization process, a certain initial volume (w) V 0 is possessed of the body reduced by 25%; -The adopted optimization criterion is a maximized stiffness function of the component with restrictions imposed on the volume [10,11,12] -The change is examined in the operation length of internal forces (DDSW) in the output and the optimized construction with regard to the abovementioned criteria [13,14,15,16].…”

Section: Operation Length Of Internal Forces In Three Dimensional Dismentioning

confidence: 99%

Criteria for the Minimum Operation Length of Internal Forces as a Function of the Development of an Optimum Structure of Machinery Structural Components

Fligiel¹,

Patyk²

2016

International Journal of Applied Mechanics and Engineering

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The present study analyzes the operation length of internal forces (DDSW) understood as the length of the flow of internal forces along the shortest possible internal routes. The operation length of internal forces is determined on the basis of stresses and the given volume in the constructional space. The minimum DDSW of the structure satisfies the criterial conditions of the most rigid structure, where the potential energy of deformation and the deformation energy potential is the same in the whole volume and thus the potential gradient is zero.

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Section: Operation Length Of Internal Forces In Three Dimensional Dismentioning

confidence: 99%

Criteria for the Minimum Operation Length of Internal Forces as a Function of the Development of an Optimum Structure of Machinery Structural Components

Fligiel¹,

Patyk²

2016

International Journal of Applied Mechanics and Engineering

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“…The solution based on Berke's optimality criteria method with multiple constraints and a penalty parameter was used in the iterative formulation. The finite element based topology optimization was first explored in 1973 by Rossow and Taylor [18] and later Cheng and Olhoff [8]. In 1988 a new generation of problem formulation were created by Bendsoe and Kikuchi [3] using homogenization.…”

Section: J Lógómentioning

confidence: 99%

Topology optimization in the case of different boundary conditions by an iterative method

Lógó¹

2014

JCAM

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Optimal design with thousands of variables is a great challenge in engineering calculations. In this paper an iteration based topology design technique is introduced for the optimization of linearly elastic continuum type structures under single parametric static loading and different displacement boundary conditions. The support optimization is discussed briefly, as well. The investigated problem is utilized by minimization of the weight of the structure subjected to displacement constraints. The numerical procedure is based on an iterative formula which is formed by the use of the Kuhn-Tucker condition of the Lagrangian function of the constraint mathematical programming problem. The application is illustrated by numerical examples. Mathematical Subject Classification: 74P15Recently the topology optimization is one of the most "popular" topic in the expanding field of optimal design. A great number of papers indicates the importance of the topic [1,[3][4][5]7,9,11,23,25,27,28]. The popularity comes one part from the needs of the industry (car, airplane, etc.) and other part from the complexity of the problem which is a great challenging for the researchers. In present stage the field of topology optimization can be divided into two subfields: optimal design of skeletal structures (trusses, grids, etc.,) deals with the simultaneous optimization of the member sizes

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“…This latter technique aims at optimizing the material distribution in a link in order to satisfy performance criteria: a classical problem met in the literature is to minimize the link mass under compliance constraints [39]. The link shape is meshed, and deformation and vibration models are computed using Finite Element Methods (FEM) [40]. The presence of one element of material is parameterized by a design variable varying from 0 to 1, 1 means that there is material while 0 represents a void.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization of industrial robots: Application to a five-bar mechanism

Briot

Goldsztejn

2018

Mechanism and Machine Theory

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Recent works introduced topology optimization in the design of robots, but the proposed methodologies led to a local optimization of the performance. Moreover, most of performance indices used are not in strong relation with easy-to-understand technological requirements. We propose a methodology that is able to perform a topology optimization for robots, valid globally in the workspace or for a set of given trajectories, and which is based on the use of technology-oriented performance criteria. In order to enforce the chosen performance indices to be valid globally, optimal robot configurations or trajectories for which extreme performance will be attained are computed, and iteratively updated. In order to decrease the computational time associated with these performance indices, we exploit the structure of the elastic models in order to reduce their computational complexity. Finally, we use an optimization algorithm called the Linearization Method which gives results in a computational time equivalent to standard topology optimization algorithms, but its implementation is less complex and makes it quite easy to perform modification or improvement. The methodology is applied for the design of a five-bar mechanism. We show that our approach leaded to a robust optimization of the robot performance over the whole workspace.

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A Finite Element Method for the Optimal Design of Variable Thickness Sheets

Cited by 100 publications

References 8 publications

Criteria for the Minimum Operation Length of Internal Forces as a Function of the Development of an Optimum Structure of Machinery Structural Components

Criteria for the Minimum Operation Length of Internal Forces as a Function of the Development of an Optimum Structure of Machinery Structural Components

Topology optimization in the case of different boundary conditions by an iterative method

Topology optimization of industrial robots: Application to a five-bar mechanism

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