A Material-Mask Overlay Strategy for Continuum Topology Optimization of Compliant Mechanisms Using Honeycomb Discretization

2008 ◽  
Vol 130 (8) ◽  
Author(s):  
Anupam Saxena
Keyword(s):  
Compliant Mechanisms ◽  
Large Strain ◽  
Optimal Solutions ◽  
Free Rotation ◽  
Hexagonal Cell ◽  
Rectangular Cell ◽  
New Material ◽  
Single Material ◽  
Assignment Approach ◽  
The Continuum

This paper proposes novel honeycomb tessellation and material-mask overlay methods to obtain optimal single-material compliant topologies free from checkerboard and point-flexure pathologies. The presence of strain-free rotation regions in rectangular cell based discretization is identified to be a cardinal cause for appearance of such singularities. With each hexagonal cell sharing an edge with its neighboring cells, strain-free displacements are not permitted anywhere in the continuum. The new material assignment approach manipulates material within a subregion of cells as opposed to a single cell thereby reducing the number of variables making optimization efficient. Cells are allowed to get filled with only the chosen material or they can remain void. Optimal solutions obtained are free from intermediate material states and can be manufactured requiring no material interpretation and less postprocessing. Though the hexagonal cells do not allow strain-free rotations, some subregions undergoing large strain deformations can still be present within the design. The proposed procedure is illustrated using three classical examples in compliant mechanisms solved using genetic algorithm.

On Optimization of 2D Compliant Mechanisms Using Honeycomb Discretization With Material-Mask Overlay Strategy

2007 ◽  
Author(s):  
Anupam Saxena
Keyword(s):  
Genetic Algorithm ◽  
Compliant Mechanisms ◽  
Optimal Solutions ◽  
Free Rotation ◽  
Post Processing ◽  
Hexagonal Cell ◽  
Rectangular Cell ◽  
New Material ◽  
Assignment Approach ◽  
The Continuum

Novel honeycomb tessellation and material mask overlay methods are proposed in this paper to obtain optimal planar compliant topologies free from checkerboard and point flexure pathologies. A cardinal reason, namely the presence of strain-free rotation regions in rectangular cell based discretization is identified to be a cause in appearance of such singularities. With each hexagonal cell sharing an edge with its neighboring cells, strain-free displacements are not permitted anywhere in the continuum. The new material assignment approach manipulates material within a group of cells as opposed to a single cell thereby reducing the number of variables making optimization efficient. Optimal solutions obtained are free from intermediate material states and can be manufactured directly after design, without requiring any post processing. The proposed procedure is illustrated using two classical examples in 2D compliant mechanisms solved using genetic algorithm.

Efficient Development of Continuum/Compliant Planar Linkage Mechanisms

2019 ◽  
Author(s):  
Woo Rib Suh ◽  
J. Michael McCarthy ◽  
Edwin A. Peraza Hernandez
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Parameters ◽  
Element Analysis ◽  
Initial Node ◽  
Synthesis Of Mechanisms ◽  
Efficient Alternative ◽  
Computationally Intensive ◽  
The Given ◽  
The Continuum

Abstract This paper presents a method to develop continuum/compliant mechanisms based on planar bar-node linkage precursors. The method takes as inputs the initial node positions and connectivity data of a given bar-node linkage and converts it into a continuum/compliant mechanism having the same targeted motion. The line bars of the given bar-node linkage are thickened into trapezoidal planar members and the nodes are thickened by introducing fillets at each intersection of bars. The thicknesses of the bars and the shape parameters of the fillets in the continuum/compliant linkage are optimized to obtain the same targeted motion of the given bar-node linkage while keeping stresses below a maximum allowable value. Each design generated during the optimization process is evaluated using finite element analysis. The present method allows for the synthesis of mechanisms having the following advantages over conventional bar-node linkages: 1) They do not require complex ball or pin joints; 2) they can be readily 3-D printed and size-scaled, and 3) they can be optimized to decrease stresses below a maximum allowable value. Furthermore, the method uses a relatively small number of optimization variables (thicknesses of the members, shape-parameters of the fillets), making it an efficient alternative to more complex and computationally intensive methods for synthesizing compliant mechanisms such as those incorporating topology optimization.

An Improved Material-Mask Overlay Strategy for Topology Optimization of Structures and Compliant Mechanisms

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Chandini Jain ◽  
Anupam Saxena
Keyword(s):  
Topology Optimization ◽  
Multiple Solutions ◽  
Compliant Mechanisms ◽  
Single Point ◽  
Topology Design ◽  
Small Displacement ◽  
Rectangular Cell ◽  
Black And White ◽  
Overlay Method ◽  
Free Material

The honeycomb-based domain representation directly yields checkerboard and point flexure free optimal solutions to various topology design problems without requiring any supplementary suppression method. This is because the root cause behind the appearance of these pathologies, namely, the permitted single-point connectivity between contiguous subregions in rectangular-cell-based representation, is eliminated. The mesh-free material-mask overlay method further promises unadulterated “black and white” solutions in contrast to density interpolation schemes where the material is modeled between the “void” and “filled” states. Here, we propose improvements to the material-mask overlay method by judiciously increasing the number of material masks during a sequence of subsearches for the best solution. We used an alternative, mutation-based zero-order stochastic search, which, through a small population of solution vectors, can yield multiple solutions from a single search for nonconvex topology optimization formulations. Wachspress hexagonal cells are used as finite elements since they offer rich displacement interpolation functions. Singular solutions are penalized and filtered. With the improved material-mask overlay method, we showcase the synthesis using two classical small displacement problems each on optimal stiff structures and compliant mechanisms to illustrate the extraction of pathology-free, “black and white,” and multiple solutions.

On an Adaptive Multi-Mask Overlay Strategy for Topology Optimization of Structures and Compliant Mechanisms

2009 ◽  
Author(s):  
Chandini Jain ◽  
Anupam Saxena
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Optimal Solution ◽  
Small Population ◽  
Topology Design ◽  
Optimal Solutions ◽  
Black And White ◽  
Mesh Free ◽  
Overlay Method ◽  
Free Material

The honeycomb based discretization shows promise in yielding checkerboard and point flexure free optimal solutions to various topology design problems. The mesh-free material mask overlay method further promises unadulterated “black and white” optimal solutions as opposed to schemes where material is interpolated between the “void” and “filled” states in a cell [26]. Here, we propose improvements in the material mask overlay method by judiciously choosing the number of masks during a sequence of sub-searches for the optimal solution. We use an alternative mutation based zero order search which allows the use of a small population of solutions and also maintains diversity between them. Thus, multiple solutions can be simultaneously obtained for non-convex topology optimization formulations. We solve two classical problems each on optimal stiff structures and compliant mechanisms to illustrate pathology free, “black and white” topology synthesis.

A Novel Compliant Mechanism for Converting Reciprocating Translation Into Enclosing Curved Paths

2004 ◽  
Vol 126 (4) ◽  
pp. 667-672 ◽  
Author(s):  
Nilesh D. Mankame ◽  
G. K. Ananthasuresh
Keyword(s):  
Large Deformations ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Two Dimensional ◽  
Contact Interactions ◽  
Macro Scale ◽  
Potential Applications ◽  
Curved Paths ◽  
Single Material ◽  
Flexural Joints

This paper introduces a novel contact-aided compliant mechanism that uses intermittent contacts to convert a single translatory reciprocating input into two output curves, which intersect to enclose a two dimensional region. Contact interactions endow contact-aided compliant mechanisms with enhanced kinematic and kinetostatic capabilities. The mechanism described in this paper is designed to undergo large deformations repeatedly, without yielding by avoiding flexural joints and by using contacts to obtain the desired deformation. A single-material, joint-free and planar design makes the mechanism easy and economical to fabricate at the macro or micro scales. The design is validated experimentally by manufacturing and testing macro scale prototypes. Two potential applications that motivated this mechanism are also noted.

Synthesis of C0 Path-Generating Contact-Aided Compliant Mechanisms Using the Material Mask Overlay Method

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Prabhat Kumar ◽  
Roger A. Sauer ◽  
Anupam Saxena
Keyword(s):  
Compliant Mechanisms ◽  
Synthesis Method ◽  
Mean Value ◽  
Contact Boundary ◽  
Element Formulation ◽  
Active Set ◽  
Set Constraints ◽  
Mean Value Coordinates ◽  
Augmented Lagrange Multiplier ◽  
The Continuum

Contact-aided compliant mechanisms (CCMs) are synthesized via the material mask overlay strategy (MMOS) to trace desired nonsmooth paths. MMOS employs hexagonal cells to discretize the design region and engages negative circular masks to designate material states. To synthesize CCMs, the modified MMOS presented herein involves systematic mutation of five mask parameters through a hill climber search to evolve not only the continuum topology but also to position the rigid, interacting surfaces within some masks. To facilitate analysis with contact, boundary smoothing is performed by shifting boundary nodes of the evolving continuum. Various geometric singularities are subdued via hexagonal cells, and the V-notches at the continuum boundaries are alleviated. Numerous hexagonal cells get morphed into concave subregions as a consequence. Large deformation finite-element formulation with mean-value coordinates based shape functions is used to cater to the generic hexagonal shapes. Contact analysis is accomplished via the Newton–Raphson (NR) iteration with load incrementing in conjunction with the augmented Lagrange multiplier method and active set constraints. An objective function based on Fourier shape descriptors (FSDs) is minimized subject to suitable design constraints. Two examples of path-generating CCMs are presented, their performance compared with a commercial software and fabricated to establish the efficacy of the proposed synthesis method.

An Adaptive Material Mask Overlay Method: Modifications and Investigations on Binary, Well Connected Robust Compliant Continua

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Anupam Saxena
Keyword(s):  
Compliant Mechanisms ◽  
Search Algorithm ◽  
Reaction Force ◽  
Small Deformation ◽  
Mesh Dependency ◽  
Overlay Method ◽  
Contour Boundary ◽  
Mutation Strategies ◽  
Effective Use ◽  
Single Material

The material mask overlay strategy employs negative masks to create material voids within the design region to synthesize perfectly binary (0-1), well connected continua. Previous implementations use either a constant number of circular masks or increase the latter via a sequence of subsearches making the procedure computationally expensive. Here, a modified algorithm is presented wherein the number of masks is adaptively varied within a single search, in addition to their positions and sizes, thereby generating material voids, both efficiently and effectively. A stochastic, mutation-only search with different mutation strategies is employed. The honeycomb parameterization naturally eliminates all subregion connectivity anomalies without requiring additional suppression methods. Boundary smoothening as a new preprocessing step further facilitates accurate evaluations of intermediate and final designs with moderated notches. Thus, both material and contour boundary interpretation steps, that can alter the synthesized solutions, are avoided during postprocessing. Various features, e.g., (i) effective use of the negative masks, (ii) convergence, (iii) mesh dependency, (iv) solution dependence on the reaction force, and (v) parallel search are investigated through the synthesis of small deformation fully compliant mechanisms that are designed to be robust under the specified loads. The proposed topology search algorithm shows promise for design of single-material large deformation continua as well.

An Optimality Criteria Approach for the Topology Synthesis of Compliant Mechanisms

1998 ◽  
Author(s):  
A. Saxena ◽  
G. K. Ananthasuresh
Keyword(s):  
Energy Density ◽  
Mathematical Programming ◽  
Objective Function ◽  
Compliant Mechanisms ◽  
Optimality Criteria ◽  
Optimality Criteria Method ◽  
New Energy ◽  
Method Of Solution ◽  
Design Parameterization ◽  
The Continuum

Abstract The physical insight used in formulating a multi-criteria optimization problem for the synthesis of compliant mechanisms, is quickly lost if mathematical programming techniques (SLP, SQP etc.) are used to determine the optimal solution. As opposed to the previous works that relied upon mathematical programming search techniques to find the optimum solution, in this paper we present an alternative method of solution called the optimality criteria method. Optimality criteria methods have proven to be effective in structural optimization problems with a large number of variables, and very few constraints as is the case in the topology synthesis of compliant mechanisms. The important new results of this paper include: (i) the derivation of a physically insightful optimal property of compliant mechanisms which states that the ratio of the mutual potential energy density and the strain energy density is uniform throughout the continuum (ii) the development of the optimality criteria method of solution in the form of a simple update formula for the design variables by using the above property (iii) design parameterization using the frame finite-element based ground-structure that appropriately accounts for the requisite bending behavior in the continuum, and (iv) numerical implementation of previously reported density based design parameterization using bilinear plane-stress elements. In addition, a new energy based multi-criteria objective function is presented to maximize the useful output energy (which is equivalent to maximizing the mechanical advantage) while meeting the kinematic requirements. Several examples are included to demonstrate the validity of the optimal property, the optimality-criteria method of solution, and the improvements made possible by the new energy based objective function.

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