scholarly journals Concurrent topological optimization of two bodies sharing design space: problem formulation and numerical solution

2018 ◽  
Vol 59 (3) ◽  
pp. 745-757 ◽  
Author(s):  
Giorgio Previati ◽  
Federico Ballo ◽  
Massimiliano Gobbi
Keyword(s):  
Numerical Solution ◽  
Design Space ◽  
Problem Formulation ◽  
Topological Optimization ◽  
Space Problem ◽  
Two Bodies

scholarly journals A sensitivity interpolation algorithm for the concurrent optimization of bodies sharing a common design space

2021 ◽  
Author(s):  
Giorgio Previati ◽  
Massimiliano Gobbi ◽  
Federico Ballo
Keyword(s):  
Design Problem ◽  
Design Space ◽  
Three Dimensional ◽  
Simultaneous Optimization ◽  
Topological Optimization ◽  
Dimensional System ◽  
Concurrent Optimization ◽  
Load Carrying ◽  
Three Dimensional System ◽  
Two Bodies

AbstractIn this paper the problem of the concurrent topological optimization of two different bodies sharing a region of the design space is dealt with. This design problem focuses on the simultaneous optimization of two bodies (components) where not only the material distribution of each body has to be optimized but also the design space has to be divided among the two bodies. This novel optimization formulation represents a design problem in which more than one component have to be located inside a limited allowable room. Each component has its own function and load carrying requirements. In the paper a novel development solution algorithm is presented. With respect to previously published papers, the new algorithm comprises an interpolation of the density fields which allows a complete independence of the meshes of the two bodies. As the bodies can be meshed with any arbitrary mesh, this new algorithm can be applied to any real geometry. The developed algorithm is used to design a complex three dimensional system, namely a multi-component arm for a tube bending machine.

Concurrent Topological Optimization of a Wheel and Brake Caliper Assembly

2019 ◽  
Author(s):  
Massimiliano Gobbi ◽  
Giorgio Previati ◽  
Federico Ballo
Keyword(s):  
Optimization Problem ◽  
Design Space ◽  
Complex Geometry ◽  
Topological Optimization ◽  
Real Problem ◽  
Concurrent Optimization ◽  
New Development ◽  
The Common ◽  
Actual Shape ◽  
Two Bodies

Abstract The paper deals with the topological optimization of a wheel and brake caliper assembly. In this system, the design of each components is influenced by the actual shape of the other component. In fact, a conflict exists in the room requirements of the two components. In the design process, therefore, not only the material distribution of the two bodies has to be optimized, but also the design space has to be divided in most effective way. The design of the wheel and brake caliper assembly can be seen as a special class of topological optimization problem. Such problem of concurrent topological optimization of two components sharing part of the design space has been already addressed by the authors in previous papers under the restriction that the two bodies have the same mesh in the shared part of the domain. In this paper, a novel development of the presented optimization algorithm is described. The algorithm is modified in order to allow the concurrent optimization of two bodies with different meshes in the common part of the domain. This new development allows the methodology to be applied to any real problem with arbitrarily complex geometry. The application to the case of the wheel and brake assembly is shown.

Concurrent Topological Optimisation of Two Bodies Sharing Design Space

2020 ◽  
pp. 215-231
Author(s):  
Federico Maria Ballo ◽  
Massimiliano Gobbi ◽  
Giampiero Mastinu ◽  
Giorgio Previati
Keyword(s):  
Design Space ◽  
Two Bodies

scholarly journals Quantitative Comparison of High- and Low-Performing Teams in a Design Task Subject to Drastic Changes

2014 ◽  
Author(s):  
Christopher McComb ◽  
Jonathan Cagan ◽  
Kenneth Kotovsky
Keyword(s):  
Design Space ◽  
New Technology ◽  
Problem Formulation ◽  
Target Area ◽  
Design Data ◽  
Design Task ◽  
High Performing ◽  
Engineering Teams ◽  
Solution Strategies ◽  
The Face

Many design tasks are subject to changes in goals or constraints. For instance, a client might modify specifications after design has commenced, or a competitor may introduce a new technology or feature. A design team often cannot anticipate such changes, yet they pose a considerable challenge. This paper presents a study where engineering teams sought to solve a design task that was subject to two large, unexpected changes in problem formulation that occurred during problem solving. Continuous design data was collected to observe how the designers responded to the changes. We show that high- and low-performing teams demonstrated very different approaches to solving the problem and overcoming the changes. In particular, high-performing teams achieved simple designs and extensively explored small portions of the design space; low-performing teams explored complex designs with little exploration around a target area of the design space. These strategic differences are interpreted with respect to cognitive load theory and goal theory. The results raise questions as to the relationship between characteristics of design problems and solution strategies. In addition, an attempt at increasing the teams’ resilience in the face of unexpected changes is introduced by encouraging early divergent search.

Computational Issues Associated With Gear Rattle Analysis: Part I — Problem Formulation

1992 ◽  
Author(s):  
C. Padmanabhan ◽  
T. E. Rook ◽  
Rajendra Singh
Keyword(s):  
Numerical Solution ◽  
Mathematical Formulation ◽  
Order Reduction ◽  
Problem Formulation ◽  
Reduction Gear ◽  
Type Problem ◽  
Contact Ratio ◽  
Processing Stage ◽  
Gear Contact ◽  
Gear Rattle

Abstract This paper proposes a new procedure for formulating the gear rattle type problem analytically before attempting a numerical solution. This step is necessary due to the nature of the mathematical formulation with vibro-impacts, which is non-analytical and hence causes numerical “stiffness”. The procedure is essentially an “intelligent” pre-processing stage and is based on our vast experience in simulating such systems. Important concepts such as order reduction, gear contact ratio, appropriate choice of non-dimensionalization parameters are illustrated through several examples.

Dimensionless Solution to the Optimal Design of Spur Gear Sets

1989 ◽  
Vol 111 (2) ◽  
pp. 290-296 ◽  
Author(s):  
R. K. Carroll ◽  
G. E. Johnson
Keyword(s):  
Optimal Design ◽  
Material Properties ◽  
Design Space ◽  
Problem Formulation ◽  
Stress Constraints ◽  
Spur Gear ◽  
Minimum Size ◽  
New Approach ◽  
Materials Used ◽  
Standard Sets

In some earlier papers (Savage, Coy, and Townsend, 1982; Carroll and Johnson, 1984), the design of spur gear sets based on minimum size has been addressed considering the interaction of bending and contact stress constraints. In this paper, we present a new approach to the spur gear problem. The new method makes use of some newly defined dimensionless parameters. In the resulting design space, the optimal dimensionless design (which defines the optimal tooth geometry) is independent of load and speed requirements of the gear set. However the optimum is dependent on the physical properties of the materials used. We introduce a new quantity called the Material Properties Relationship Factor, CMP. In the problem formulation presented here, we show that the optimum will always be constraint bound and it will occur at one of three possible constraint intersections. CMP is used to identify which of three possible constraint intersections is the correct one. After the dimensionless optimum is found, we present an example which shows how to transform the solution back into the real design space considering the load and speed requirements of the gear set along with discrete value constraints on the number of teeth and the diametral pitch. Tabulated optimal dimensionless designs are included for some standard sets of tooth proportions.

Optimal Topologies of Structures

1989 ◽  
Vol 42 (8) ◽  
pp. 223-239 ◽  
Author(s):  
Uri Kirsch
Keyword(s):  
Numerical Methods ◽  
Analytical Methods ◽  
Solution Process ◽  
Problem Formulation ◽  
Present Review ◽  
Topological Optimization ◽  
Solution Approach ◽  
Structural Applications ◽  
Practical Design ◽  
Discrete Structures

Topological design, where the member connectivity is sought in addition to member sizing, is perhaps the most challenging and economically the most rewarding of the structural optimization tasks. Due to the basic difficulties involved in the solution process, various simplifications and approximations are often considered. The present review introduces first the typical characteristics and properties of the problem. Two main solution approaches are surveyed: (a) analytical methods for optimization of gridlike continua; (b) numerical methods for optimization of discrete structures. The various difficulties involved in the solution process are presented and the common approximations and simplifications assumed in the problem formulation are discussed. Some fundamental problems that have not yet been solved are emphasized. The significant progress that has been made recently in optimization of gridlike continua by analytical methods provides insight into the design problem and it is often possible to find the theoretical lower bound. However, these methods have limitations in practical design. Numerical methods for topological optimization of discrete structures are still in the stage of early development. Progress is much needed in this area and the development of a general solution approach for practical design of structures remains a challenge. Although both analytical and numerical methods are intended for similar structural applications, a wide gap between researchers of the two groups does exist. It is believed that the present review will contribute to bridge this gap.

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