Shape Optimization of Elastic Hollow Bars

1985 ◽  
Vol 107 (1) ◽  
pp. 100-105 ◽  
Author(s):  
J. W. Hou ◽  
J. L. Chen
Keyword(s):  
Shape Optimization ◽  
Optimum Design ◽  
Material Property ◽  
Torsional Rigidity ◽  
Bending Stiffness ◽  
Performance Criteria ◽  
Cross Sectional ◽  
Material Derivative ◽  
Numerical Examples ◽  
Design Scheme

In this paper a unified shape optimum design scheme, combining the material derivative and boundary parametrization is presented to find the optimal cross-sectional shapes of elastic hollow bars. Performance criteria can be the bending stiffness, the torsional rigidity, or the weight of the bar. The existence of a keyway (an example of geometric irregularity) can be considered as well. Material property can be either isotropic or anisotropic. Various numerical examples have been provided to show the validity of the presented approach.

Optimization of Cam-Follower Systems With Kinematic and Dynamic Constraints

1982 ◽  
Vol 104 (1) ◽  
pp. 29-33 ◽  
Author(s):  
N. Berzak
Keyword(s):  
Optimum Design ◽  
Dynamic Properties ◽  
Performance Criteria ◽  
Numerical Examples ◽  
Dynamic Constraints ◽  
Cam Follower ◽  
Independent Parameters ◽  
General Method

A general method for obtaining the optimum design of a cam-follower system is presented. This method, developed for polynomial output motions which satisfy prescribed terminal conditions, includes performance criteria related to kinematic, as well as dynamic properties of the system. The output motion and the performance coefficients are expressed as functions of independent parameters. Using a linear sum of the weighted performance coefficients, the optimum design is obtained by scanning a suitable family of polynomial output motions. The theory is illustrated by numerical examples for four-term polynomial output motions.

Grouping Concept in Optimum Sizing of Truss Structures

2018 ◽  
pp. 94-120
Author(s):  
Gebrail Bekdaş ◽  
Sinan Melih Nigdeli ◽  
Osman Hürol Türkakın
Keyword(s):  
Optimum Design ◽  
Interior Point ◽  
Computation Time ◽  
Total Weight ◽  
Truss Structures ◽  
Interior Point Algorithm ◽  
Structural Members ◽  
Cross Sectional ◽  
Design Constraints ◽  
Numerical Examples

In the optimum design of truss structures, the cross-sectional areas of structural members are optimized in order to minimize the total weight of the structures. This process is done by considering two design constraints, which are the limitation of stress of structural members and displacement of nodes of the structure. The members of truss structures are generally grouped for two reasons related to reduction of computation time and practical production of members. In this chapter, the optimum sizing of truss structures is found by using a non-linear programing tool considering the interior-point algorithm handling a Hessians for the nonlinear constrained multivariable problem. The aim of the chapter is to find the best grouping option for trusses by proposing a strategy. As a conclusion, the best grouping options for the numerical examples are found different from the existing groups in the documented methods.

Shape Optimization of Hydraulic Structures: an Example of an Optimum Design of a Fish Passage

10.29007/2k64 ◽  
2018 ◽  
Author(s):  
Pat Prodanovic ◽  
Cedric Goeury ◽  
Fabrice Zaoui ◽  
Riadh Ata ◽  
Jacques Fontaine ◽  
...  
Keyword(s):  
Numerical Model ◽  
Shape Optimization ◽  
Objective Function ◽  
Optimum Design ◽  
Optimization Problem ◽  
A Priori ◽  
Coupled System ◽  
Fish Passage ◽  
Hydraulic Structures ◽  
Design Variables

This paper presents a practical methodology developed for shape optimization studies of hydraulic structures using environmental numerical modelling codes. The methodology starts by defining the optimization problem and identifying relevant problem constraints. Design variables in shape optimization studies are configuration of structures (such as length or spacing of groins, orientation and layout of breakwaters, etc.) whose optimal orientation is not known a priori. The optimization problem is solved numerically by coupling an optimization algorithm to a numerical model. The coupled system is able to define, test and evaluate a multitude of new shapes, which are internally generated and then simulated using a numerical model. The developed methodology is tested using an example of an optimum design of a fish passage, where the design variables are the length and the position of slots. In this paper an objective function is defined where a target is specified and the numerical optimizer is asked to retrieve the target solution. Such a definition of the objective function is used to validate the developed tool chain. This work uses the numerical model TELEMAC- 2Dfrom the TELEMAC-MASCARET suite of numerical solvers for the solution of shallow water equations, coupled with various numerical optimization algorithms available in the literature.

A Study on Optimum Design Using Fuzzy Numbers As Design Variables

1995 ◽  
Author(s):  
Masao Arakawa ◽  
Hiroshi Yamakawa
Keyword(s):  
Fuzzy Sets ◽  
Optimum Design ◽  
Fuzzy Numbers ◽  
Fuzzy Optimization ◽  
Design Parameters ◽  
Numerical Examples ◽  
Design Variables ◽  
Conventional Methods

Abstract In this study, we summerize the method of fuzzy optimization using fuzzy numbers as design variables. In order to detect flaw in fuzzy calculation, we use LR-fuzzy numbers, which is known as its simplicity in calculation. We also use simple fuzzy numbers’ operations, which was proposed in the previous papers. The proposed method has unique characteristics that we can obtain fuzzy sets in design variables (results of the design) directly from single numerical optimizing process. Which takes a large number of numerical optimizing processes when we try to obtain similar results in the conventional methods. In the numerical examples, we compare the proposed method with several other methods taking imprecision in design parameters into account, and demonstrate the effectiveness of the proposed method.

Predicting the Benefits of Topology Optimization

2015 ◽  
Author(s):  
Shiguang Deng ◽  
Krishnan Suresh
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Shape Optimization ◽  
Systematic Method ◽  
Topological Sensitivity ◽  
Numerical Examples ◽  
Initial Design

Topology optimization is a systematic method of generating designs that maximize specific objectives. While it offers significant benefits over traditional shape optimization, topology optimization can be computationally demanding and laborious. Even a simple 3D compliance optimization can take several hours. Further, the optimized topology must typically be manually interpreted and translated into a CAD-friendly and manufacturing friendly design. This poses a predicament: given an initial design, should one optimize its topology? In this paper, we propose a simple metric for predicting the benefits of topology optimization. The metric is derived by exploiting the concept of topological sensitivity, and is computed via a finite element swapping method. The efficacy of the metric is illustrated through numerical examples.

Effects of surface tension and intraluminal fluid on mechanics of small airways

1997 ◽  
Vol 82 (1) ◽  
pp. 233-239 ◽  
Author(s):  
Mark J. Hill ◽  
Theodore A. Wilson ◽  
Rodney K. Lambert
Keyword(s):  
Surface Tension ◽  
Bending Stiffness ◽  
Liquid Interface ◽  
Cross Sectional Area ◽  
Pressure Curve ◽  
Small Airways ◽  
Sectional Area ◽  
Cross Sectional ◽  
Inner Surface ◽  
Air Liquid Interface

Hill, Mark J., Theodore A. Wilson, and Rodney K. Lambert.Effects of surface tension and intraluminal fluid on the mechanics of small airways. J. Appl. Physiol.82(1): 233–239, 1997.—Airway constriction is accompanied by folding of the mucosa to form ridges that run axially along the inner surface of the airways. The muscosa has been modeled (R. K. Lambert. J. Appl. Physiol. 71: 666–673, 1991) as a thin elastic layer with a finite bending stiffness, and the contribution of its bending stiffness to airway elastance has been computed. In this study, we extend that work by including surface tension and intraluminal fluid in the model. With surface tension, the pressure on the inner surface of the elastic mucosa is modified by the pressure difference across the air-liquid interface. As folds form in the mucosa, intraluminal fluid collects in pools in the depressions formed by the folds, and the curvature of the air-liquid interface becomes nonuniform. If the amount of intraluminal fluid is small, <2% of luminal volume, the pools of intraluminal fluid are small, the air-liquid interface nearly coincides with the surface of the mucosa, and the area of the air-liquid interface remains constant as airway cross-sectional area decreases. In that case, surface energy is independent of airway area, and surface tension has no effect on airway mechanics. If the amount of intraluminal fluid is >2%, the area of the air-liquid interface decreases as airway cross-sectional area decreases, and surface tension contributes to airway compression. The model predicts that surface tension plus intraluminal fluid can cause an instability in the area-pressure curve of small airways. This instability provides a mechanism for abrupt airway closure and abrupt reopening at a higher opening pressure.

Shape Optimum Design of Robotic Manipulators With Static Performance Criteria

1987 ◽  
Author(s):  
D. A. Saravanos ◽  
J. S. Lamancusa ◽  
H. J. Sommer
Keyword(s):  
Finite Element ◽  
Optimum Design ◽  
Robotic Manipulators ◽  
Performance Criterion ◽  
Performance Criteria ◽  
Robotic Arm ◽  
Mass Ratio ◽  
End Effector ◽  
Vibrational Response ◽  
Static Performance

Abstract The end effector deflections of robotic manipulators may be minimized by optimizing the geometric shape and the dimensions of their links. A multiple posture static performance criterion for the prediction of the shape optimum design is presented. An efficient optimization algorithm is developed for the solution of the problem using finite element modeling to predict the compliance of the robotic arm. The method is applied to an existing robotic arm, and the results demonstrate that simple alterations to the dimensions and the shape of the links can greatly improve, not only the stiffness, but also the stiffness/mass ratio and consequently the vibrational response of the manipulator structure.

Area Moment of Inertia for Comparison of Implant Cross-Sectional Geometry and Bending Stiffness

1995 ◽  
Vol 08 (03) ◽  
pp. 146-152 ◽  
Author(s):  
P. Muir ◽  
M. D. Markel ◽  
K. A. Johnson
Keyword(s):  
Modulus Of Elasticity ◽  
316L Stainless Steel ◽  
Bending Stiffness ◽  
Moment Of Inertia ◽  
Cross Sectional ◽  
Implant Selection ◽  
Principal Factors ◽  
Mathematical Equations ◽  
Selection For ◽  
Object Area

Area moment of inertia for an object can be calculated by use of mathematical equations, and is defined by the dimensions of the object. Area moment of inertia and modulus of elasticity are principal factors determining bending stiffness. Because the majority of veterinary orthopaedic implants are made of 316L stainless steel, and therefore have a similar modulus of elasticity, comparison of area moment of inertia for different implants provides an estimate of relative bending stiffness and can assist implant selection for a particular fracture. Knowledge of this parameter may help avoid treatment complications, such as implant failure.

OPTIMUM DESIGN OF CANTILEVERED MICROPROBES FOR INSPECTING LCD PANELS AND MEASUREMENT OF CONTACTING FORCES

2010 ◽  
Vol 24 (15n16) ◽  
pp. 2429-2434 ◽  
Author(s):  
CHEOL KIM ◽  
KWANG-JOONG KIM
Keyword(s):  
Shape Optimization ◽  
Optimum Design ◽  
Measuring Equipment ◽  
Optimization Technique ◽  
Experimental Results ◽  
Design Requirement ◽  
Fine Pitch ◽  
Mems Fabrication ◽  
Topology And Shape Optimization ◽  
Design Requirements

Fine pitch microprobe arrays are microneedle-like probes for inspecting the pixels of LCD panels or IC. They are usually made of multi-layers of metallic, nonmetallic, or combination of the two. The design requirement for a contacting force is less than 2 gf and a deflection should be less than 100 µm. Many microprobe shapes satisfying the design requirements are possible. A cantilever-type microprobe having many needles was chosen and optimized in this study. Several candidate shapes were chosen using topology and shape optimization technique subjected to design requirements. Then, the microprobe arrays were fabricated using the process applied for MEMS fabrication and they were made of BeNi , BeCu , or Si . The contact probing forces and deflections were measured for checking the results from optimum design by newly developed measuring equipment in our laboratory. Numerical and experimental results were compared and both showed a good correlation.

A Study on Shape Optimization Using Affine Transformation

2001 ◽  
Author(s):  
Satoshi Kitayama ◽  
Hiroshi Yamakawa
Keyword(s):  
Shape Optimization ◽  
Cantilever Beam ◽  
Coordinate Transformation ◽  
Affine Transformation ◽  
Sufficient Conditions ◽  
Optimal Shape ◽  
Design Domain ◽  
Shape Transformation ◽  
Numerical Examples ◽  
Inclined Beam

Abstract This paper presents a new method to determine an optimal shape using affine transformation which is used in the field of Computer Aided Design (CAD), linear programming, and etc. We use affine transformation as coordinate transformation. Affine transformation is a linear transformation, so that shapes transformed must be linearly. Shape optimization of a inclined beam for example, we can deal with in the following manner. We define a simple cantilever beam first in initial design domain, and calculate an optimal shape. Then we use affine transformation remaining with optimal shape calculated in simple design domain and get to an optimal shape of the inclined beam. To compare with an optimal shape obtained by our proposed method, we calculate an optimal shape directly by conventional method in the same design domain after coordinate transformation. We show that affine transformation plays a role as scaling to structural optimization by finite element method and that necessary and sufficient conditions between design variables and shape transformation matrix may exist to get an exact optimal shape. We treat some numerical examples by our proposed method. In numerical examples, we consider shape optimization of inclined cantilever beam for simplicity. We show that some stepwise linear optimal shapes could be expressed from an optimal shape of a simple cantilever beam by using affine transformation. Optimal shape calculated by our method can obtain easily and speedy. Through some numerical examples, we could examine effectiveness of our proposed method.

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