Synthesis of Path Generating Compliant Mechanisms Using Initially Curved Frame Elements

2006 ◽  
Vol 129 (10) ◽  
pp. 1056-1063 ◽  
Author(s):  
Ashok Kumar Rai ◽  
Anupam Saxena ◽  
Nilesh D. Mankame
Keyword(s):  
Objective Function ◽  
Mechanical Response ◽  
Compliant Mechanisms ◽  
Element Formulation ◽  
Mechanical Responses ◽  
Design Variables ◽  
Lagrangian Finite Element ◽  
Synthesis Procedure ◽  
Synthesis Approach ◽  
Good Agreement

Initially curved frame elements are used in this paper within an optimization-based framework for the systematic synthesis of compliant mechanisms (CMs) that can trace nonlinear paths. These elements exhibit a significantly wider range of mechanical responses to applied loads than the initially straight frame elements, which have been widely used in the past for the synthesis of CMs. As a consequence, fewer elements are required in the design discretization to obtain a CM with a desired mechanical response. The initial slopes at the two nodes of each element are treated as design variables that influence not only the shape of the members in a CM, but also the mechanical response of the latter. Building on our prior work, the proposed synthesis approach uses genetic algorithms with both binary (i.e., 0/1) and continuous design variables in conjunction with a co-rotational total Lagrangian finite element formulation and a Fourier shape descriptors-based objective function. This objective function is chosen for its ability to provide a robust comparison between the actual path traced by a candidate CM design and the desired path. Two synthesis examples are presented to demonstrate the synthesis procedure. The resulting designs are fabricated as is, without any postprocessing, and tested. The fabricated prototypes show good agreement with the design intent.

Topology Synthesis of Large-Displacement Compliant Mechanisms

1999 ◽  
Author(s):  
Claus B. W. Pedersen ◽  
Thomas Buhl ◽  
Ole Sigmund
Keyword(s):  
Sensitivity Analysis ◽  
Optimization Problem ◽  
Adjoint Method ◽  
Compliant Mechanisms ◽  
Large Displacement ◽  
Element Formulation ◽  
Method Of Moving Asymptotes ◽  
Synthesis Tool ◽  
Lagrangian Finite Element ◽  
Moving Asymptotes

Abstract This paper describes the use of topology optimization as a synthesis tool for the design of large-displacement compliant mechanisms. An objective function for the synthesis of large-displacement mechanisms is proposed together with a formulation for synthesis of path-generating compliant mechanisms. The responses of the compliant mechanisms are modelled using a Total Lagrangian finite element formulation, the sensitivity analysis is performed using the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. Procedures to circumvent some numerical problems are discussed.

Melting and Resolidification of a Substrate Caused by Molten Microdroplet Impact

2001 ◽  
Vol 123 (6) ◽  
pp. 1110-1122 ◽  
Author(s):  
D. Attinger ◽  
D. Poulikakos
Keyword(s):  
Heat Transfer ◽  
Initial Conditions ◽  
Navier Stokes ◽  
Element Formulation ◽  
Material Transport ◽  
Melting Depth ◽  
Flat Substrate ◽  
Substrate Melting ◽  
Lagrangian Finite Element ◽  
Good Agreement

This paper describes the main features and results of a numerical investigation of molten microdroplet impact and solidification on a colder flat substrate of the same material that melts due to the energy input from the impacting molten material. The numerical model is based on the axisymmetric Lagrangian Finite-Element formulation of the Navier–Stokes, energy and material transport equations. The model accounts for a host of complex thermofluidic phenomena, exemplified by surface tension effects and heat transfer with solidification in a severely deforming domain. The dependence of the molten volume on time is determined and discussed. The influence of the thermal and hydrodynamic initial conditions on the amount of substrate melting is discussed for a range of superheat, Biot number, and impact velocity. Multidimensional and convective heat transfer effects, as well as material mixing between the droplet and the substrate are found and quantified and the underlying physics is discussed. Good agreement in the main features of the maximum melting depth boundary between the present numerical results and published experiments of other investigators for larger (mm-size) droplets was obtained, and a complex mechanism was identified, showing the influence of the droplet fluid dynamics on the substrate melting and re-solidification.

The Analysis of a Simplified 2R Pseudo-Rigid-Body Model with Moment Load

2012 ◽  
Vol 224 ◽  
pp. 18-23
Author(s):  
Yun Jiao Zhang ◽  
Guo Wu Wei ◽  
Jian Sheng Dai
Keyword(s):  
Rigid Body ◽  
Objective Function ◽  
Compliant Mechanisms ◽  
Three Dimensional ◽  
Body Model ◽  
Design Variables ◽  
Characteristic Radius ◽  
Rigid Body Model ◽  
Analysis And Synthesis ◽  
Moment Load

Pseudo-rigid-body model (PRBM) method, which simplifies the geometrical nonlinear analysis, has become an important tool for the analysis and synthesis of compliant mechanisms. In this paper, a simplified 2R PRBM with two rigid links and two torsion springs is proposed. The characteristic radius factor and stiffness coefficients are selected as the design variables; in order to be better to simulate the tip point and tip slope, a three-dimensional objective function is formulated to optimize the new pseudo-rigid-body model. It is revealed in this paper that the precision of the tip point simulation can be improved when the coefficient of the tip slope error in the objective function is reduced.

Topology Optimization of Large-Displacement Flexure Hinges

2015 ◽  
Author(s):  
Min Liu ◽  
Xianmin Zhang ◽  
Sergej Fatikow
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Optimization Method ◽  
Large Displacement ◽  
Element Formulation ◽  
Nonlinear Behaviour ◽  
Geometrically Nonlinear ◽  
Flexure Hinges ◽  
Lagrangian Finite Element ◽  
Moving Asymptotes

Research on topology optimization of compliant mechanisms is extensive but the design of flexure hinges using topology optimization method is comparatively rare. This paper deals with topology optimization of flexure hinges undergoing large-displacement. The basic optimization model is developed for topology optimization of the revolute hinge. The objective function for the synthesis of large-displacement flexure hinges are proposed together with constraints function. The geometrically nonlinear behaviour of flexure hinge is modelled using the total Lagrangian finite element formulation. The equilibrium is found by using a Newton-Raphson iterative scheme. The sensitivity analysis of the objective functions are calculated by the adjoint method and the optimization problem is solved using the method of moving asymptotes (MMA). Numerical examples are used to show the validity of the proposed method and the differences between the results obtained by linear and nonlinear modelling are large.

Parameterization Strategy for Optimization of Shape Morphing Compliant Mechanisms Using Load Path Representation

2003 ◽  
Author(s):  
Kerr-Jia Lu ◽  
Sridhar Kota
Keyword(s):  
Compliant Mechanisms ◽  
Element Model ◽  
Structural Deformation ◽  
Load Path ◽  
Aircraft Wings ◽  
Shape Morphing ◽  
Design Variables ◽  
Path Representation ◽  
Flexible Antenna ◽  
Synthesis Approach

The distributed compliance and smooth deformation field of compliant mechanisms provide a viable means to achieve shape morphing in many systems, such as flexible antenna reflectors and morphing aircraft wings. We previously developed a systematic synthesis approach to design shape morphing compliant mechanisms using Genetic Algorithm (GA). However, the design variable definition, in fact, allows the generation of invalid designs (disconnected structures) within the GA. In this research, we developed a load path representation to include the structure connectivity information into the design variables, thus improving the GA efficiency. The number of design variables is also independent of the number of elements in the finite element model that is used to solve for the structural deformation. The shape morphing synthesis approach, incorporating this path representation, is demonstrated through two examples, followed by discussions on further refinements.

Topology synthesis of a 3-kink contact-aided compliant switch

2020 ◽  
pp. 1-47
Author(s):  
B V S Nagendra Reddy ◽  
Anupam Saxena
Keyword(s):  
Compliant Mechanisms ◽  
Synthesis Process ◽  
Quadrilateral Elements ◽  
Design Variables ◽  
Rigid Contact ◽  
Contact Surfaces ◽  
Output Characteristics ◽  
Line Elements ◽  
Mechanical Switch ◽  
Synthesis Approach

Abstract A topology synthesis approach to design 2D Contact-aided Compliant Mechanisms (CCMs) to trace output paths with three or more kinks is presented. Synthesis process uses three different types of external, rigid contact surfaces – circular, elliptical and rectangular – which in combination, offer intricate local curvatures that CCMs can benefit from, to deliver desired, complex output characteristics. A network of line elements is employed to generate topologies. A set of circular subregions is laid over this network, and external contact surfaces are generated within each subregion. Both, discrete and continuous design variables are employed – the former set controls the CCM topology, appearance and type of external contact surfaces, whereas the latter set governs shapes and sizes of the CCM constituents, and sizes of contact surfaces. All contact types are permitted with contact modeling made significantly easier through identification of outer and inner loops. Line topologies are fleshed out via a user-defined number of quadrilateral elements along lateral and longitudinal directions. Candidate CCM designs are carefully preprocessed before analysis via a commercial software and evolution using a stochastic search. The process is exemplified via a contact-aided, 3-kink mechanical switch which is thoroughly analysed in presence of friction and wear.

Topology and Dimensional Synthesis of Compliant Mechanisms Using Discrete Optimization

2005 ◽  
Vol 128 (5) ◽  
pp. 1080-1091 ◽  
Author(s):  
Kerr-Jia Lu ◽  
Sridhar Kota
Keyword(s):  
Discrete Optimization ◽  
Optimization Problem ◽  
Compliant Mechanisms ◽  
Discrete Optimization Problem ◽  
Dimensional Synthesis ◽  
Load Path ◽  
Design Variables ◽  
Gray Areas ◽  
Path Synthesis ◽  
Synthesis Approach

A unified approach to topology and dimensional synthesis of compliant mechanisms is presented in this paper as a discrete optimization problem employing both discrete (topology) and continuous (size) variables. The synthesis scheme features a design parameterization method that treats load paths as discrete design variables to represent various topologies, thereby ensuring structural connectivity among the input, output, and ground supports. The load path synthesis approach overcomes certain design issues, such as “gray areas” and disconnected structures, inherent in previous design schemes. Additionally, multiple gradations of structural resolution and a variety of configurations can be generated without increasing the number of design variables. By treating topology synthesis as a discrete optimization problem, the synthesis approach is incorporated in a genetic algorithm to search for feasible topologies for single-input single-output compliant mechanisms. Two design examples, commonly seen in the compliant mechanisms literature, are included to illustrate the synthesis procedure and to benchmark the performance. The results show that the load path synthesis approach can effectively generate well-connected compliant mechanism designs that are free of gray areas.

Toward a Unified Design Approach for Both Compliant Mechanisms and Rigid-Body Mechanisms: Module Optimization

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Lin Cao ◽  
Allan T. Dolovich ◽  
Arend L. Schwab ◽  
Just L. Herder ◽  
Wenjun (Chris) Zhang
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Optimization Approach ◽  
Structure Model ◽  
Dimensional Synthesis ◽  
Beam Elements ◽  
Compliant Joints ◽  
Design Variables ◽  
Rigid Joints ◽  
Synthesis Approach

Rigid-body mechanisms (RBMs) and compliant mechanisms (CMs) are traditionally treated in significantly different ways. In this paper, we present a synthesis approach that is appropriate for both RBMs and CMs. In this approach, RBMs and CMs are generalized into modularized mechanisms that consist of five basic modules, including compliant links (CLs), rigid links (RLs), pin joints (PJs), compliant joints (CJs), and rigid joints (RJs). The link modules and joint modules are modeled through beam elements and hinge elements, respectively, in a geometrically nonlinear finite-element solver, and subsequently a beam-hinge ground structure model is proposed. Based on this new model, a link and joint determination approach—module optimization—is developed for the type and dimensional synthesis of both RBMs and CMs. In the module optimization approach, the states (both presence or absence and sizes) of joints and links are all design variables, and one may obtain an RBM, a partially CM, or a fully CM for a given mechanical task. Three design examples of path generators are used to demonstrate the effectiveness of the proposed approach to the type and dimensional synthesis of RBMs and CMs.

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.

scholarly journals Hybrid Seven-bar Press Mechanism

2018 ◽  
Vol 12 (3) ◽  
pp. 181-187
Author(s):  
M. Erkan Kütük ◽  
L. Canan Dülger
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Design Optimization ◽  
Hybrid System ◽  
Degrees Of Freedom ◽  
Dimensional Synthesis ◽  
Design Variables ◽  
Optimization Study ◽  
Metal Stamping

An optimization study with kinetostatic analysis is performed on hybrid seven-bar press mechanism. This study is based on previous studies performed on planar hybrid seven-bar linkage. Dimensional synthesis is performed, and optimum link lengths for the mechanism are found. Optimization study is performed by using genetic algorithm (GA). Genetic Algorithm Toolbox is used with Optimization Toolbox in MATLAB®. The design variables and the constraints are used during design optimization. The objective function is determined and eight precision points are used. A seven-bar linkage system with two degrees of freedom is chosen as an example. Metal stamping operation with a dwell is taken as the case study. Having completed optimization, the kinetostatic analysis is performed. All forces on the links and the crank torques are calculated on the hybrid system with the optimized link lengths

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