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.

Multiobjective Topology Extraction of the Compliant Mechanisms

2014 ◽  
Vol 971-973 ◽  
pp. 1941-1948
Author(s):  
Zhao Kun Li ◽  
Hua Mei Bian ◽  
Li Juan Shi ◽  
Xiao Tie Niu
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Threshold Value ◽  
Jump Discontinuity ◽  
Engineering Practice ◽  
Distribution Method ◽  
Black And White ◽  
Design Variables

Homogenization or material distribution method based topology optimization will create final topologies in grey level image and saw tooth jump discontinuity boundaries that are not suitable for direct engineering practice, so it is necessary to extract the topological diagram. And a new topology extraction method for compliant mechanisms is presented. In the fist stage, the grey image is transferred into the black-and white finite element topology optimization results. The threshold value meeting to objective function is obtained so that each element is either empty or solid; in the second stage, the density contour approach is used by redistributing nodal densities to generate the smooth boundaries; in the third stage, Smooth boundaries are represented by parameterized B-spline curves whose control points selected from the viewpoint of stiffness and flexibility constitute the parameters ready to undergo shape optimization; Then shape optimization is executed to improve stress-based local performance, The parameters that present the outer shape of the compliant mechanism are used as design variables; In the final stage, simulations of numerical examples are presented to show the validity of the proposed method.

Topology Optimization-Based Design of a Compliant Aircraft Wing for Morphing Leading and Trailing Edges

2010 ◽  
Author(s):  
Pakeeruraju Podugu ◽  
G. K. Ananthasuresh
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Flexible Structures ◽  
Least Square ◽  
Small Displacement ◽  
Aircraft Wing ◽  
Aircraft Wings ◽  
Shape Morphing ◽  
Geometric Moments ◽  
Trailing Edges

In this paper, we present a methodology for designing a compliant aircraft wing, which can morph from a given airfoil shape to another given shape under the actuation of internal forces and can offer sufficient stiffness in both configurations under the respective aerodynamic loads. The least square error in displacements, Fourier descriptors, geometric moments, and moment invariants are studied to compare candidate shapes and to pose the optimization problem. Their relative merits and demerits are discussed in this paper. The ‘frame finite element ground structure’ approach is used for topology optimization and the resulting solutions are converted to continuum solutions. The introduction of a notch-like feature is the key to the success of the design. It not only gives a good match for the target morphed shape for the leading and trailing edges but also minimizes the extension of the flexible skin that is to be put on the airfoil frame. Even though linear small-displacement elastic analysis is used in optimization, the obtained designs are analysed for large displacement behavior. The methodology developed here is not restricted to aircraft wings; it can be used to solve any shape-morphing requirement in flexible structures and compliant mechanisms.

Topology Optimization of Compliant Mechanisms With Strength Considerations

2001 ◽  
Author(s):  
Anupam Saxena ◽  
G. K. Ananthasuresh
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Local Stress ◽  
Stress Constraints ◽  
Topology Design ◽  
Optimal Balance ◽  
Conflicting Objectives ◽  
Local Stresses ◽  
Failure Conditions ◽  
Programming Algorithms

Abstract Multi-criteria formulations reported previously in topology design of compliant mechanisms address the flexibility and stiffness issues simultaneously and aim at attaining an optimal balance between these two conflicting attributes. Such techniques are successful in indirectly controlling the local stress levels by constraining the input displacement. Individual control on the conflicting objectives is often difficult to achieve with these flexible and stiff formulations. Resultant topologies may sometimes be overly stiff and there is no guarantee for design against failure as local stresses may exceed the permissible yield strength of the constituting material. In this paper, local failure conditions via stress constraints are incorporated in topology optimization algorithms to obtain compliant and strong designs. Quality functions are employed to impose stress constraints on retained material ignoring non-existing regions in the design domain. Stress constraints are further relaxed to regularize the design space to help the KKT conditions-based mathematical programming algorithms yield improved solutions. Examples are solved to corroborate the solutions for failure-free compliant topologies that are much improved than those obtained using flexible and stiff multi-criteria objectives.

Piezoelectric Actuator Performance Metrics and Relation to Compliant Mechanism Design

2001 ◽  
Author(s):  
Hima Maddisetty ◽  
Mary Frecker
Keyword(s):  
Topology Optimization ◽  
Performance Metrics ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mechanical Efficiency ◽  
High Energy ◽  
High Energy Density ◽  
High Bandwidth ◽  
Compliant Mechanism Design ◽  
Actuator Performance

Abstract Piezoceramic actuators have gained widespread use due to their desirable qualities of high force, high bandwidth, and high energy density. Compliant mechanisms can be designed for maximum stroke amplification of piezoceramic actuators using topology optimization. In this paper, the mechanical efficiency and other performance metrics of such compliant mechanism/actuator systems are studied. Various definitions of efficiency and other performance metrics of actuators with amplification mechanisms from the literature are reviewed. These metrics are then applied to two compliant mechanism example problems and the effect of the stiffness of the external load is investigated.

Multifunctional Topology Design of Cellular Material Structures

2006 ◽  
Author(s):  
Carolyn Conner Seepersad ◽  
Janet K. Allen ◽  
David L. McDowell ◽  
Farrokh Mistree
Keyword(s):  
Heat Transfer ◽  
Topology Optimization ◽  
Cell Walls ◽  
Cellular Structure ◽  
Optimization Methods ◽  
Cellular Materials ◽  
Design Methods ◽  
Topology Design ◽  
Cellular Topology ◽  
Multifunctional Properties

Prismatic cellular or honeycomb materials exhibit favorable properties for multifunctional applications such as ultra-light load bearing combined with active cooling. Since these properties are strongly dependent on the underlying cellular structure, design methods are needed for tailoring cellular topologies with customized multifunctional properties that may be unattainable with standard cell designs. Topology optimization methods are available for synthesizing the form of a cellular structure—including the size, shape, and connectivity of cell walls and the number, shape, and arrangement of cell openings—rather than specifying these features a priori. To date, the application of these methods for cellular materials design has been limited primarily to elastic and thermo-elastic properties, however, and limitations of standard topology optimization methods prevent direct application to many other phenomena such as conjugate heat transfer with internal convection. In this paper, we introduce a practical, two-stage, flexibility-based, multifunctional topology design approach for applications that require customized multifunctional properties. As part of the approach, robust topology design methods are used to design flexible cellular topology with customized structural properties. Dimensional and topological flexibility is embodied in the form of robust ranges of cell wall dimensions and robust permutations of a nominal cellular topology. The flexibility is used to improve the heat transfer characteristics of the design via addition/removal of cell walls and adjustment of cellular dimensions, respectively, without degrading structural performance. We apply the method to design stiff, actively cooled prismatic cellular materials for the combustor liners of next-generation gas turbine engines.

Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Hong Zhou
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Diagonal Element ◽  
Initial Guess ◽  
Stress Constraint ◽  
Design Variables ◽  
Hybrid Discretization

The hybrid discretization model for topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. Each design cell is further subdivided into triangular analysis cells. This hybrid discretization model allows any two contiguous design cells to be connected by four triangular analysis cells whether they are in the horizontal, vertical, or diagonal direction. Topological anomalies such as checkerboard patterns, diagonal element chains, and de facto hinges are completely eliminated. In the proposed topology optimization method, design variables are all binary, and every analysis cell is either solid or void to prevent the gray cell problem that is usually caused by intermediate material states. Stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum and to avoid the need to choose the initial guess solution and conduct sensitivity analysis. The obtained topology solutions have no point connection, unsmooth boundary, and zigzag member. No post-processing is needed for topology uncertainty caused by point connection or a gray cell. The introduced hybrid discretization model and the proposed topology optimization procedure are illustrated by two classical synthesis examples of compliant mechanisms.

A Comparative Study of the Formulations for Topology Optimization of Compliant Mechanisms

2008 ◽  
Author(s):  
Sangamesh R. Deepak ◽  
M. Dinesh ◽  
Deepak Sahu ◽  
Salil Jalan ◽  
G. K. Ananthasuresh
Keyword(s):  
Topology Optimization ◽  
Comparative Study ◽  
Compliant Mechanisms ◽  
Computation Time ◽  
Initial Guess ◽  
Benchmark Problems ◽  
Topology Optimization Problem ◽  
Linear Elastic ◽  
Frame Element ◽  
Force Direction

The topology optimization problem for the synthesis of compliant mechanisms has been formulated in many different ways in the last 15 years, but there is not yet a definitive formulation that is universally accepted. Furthermore, there are two unresolved issues in this problem. In this paper, we present a comparative study of five distinctly different formulations that are reported in the literature. Three benchmark examples are solved with these formulations using the same input and output specifications and the same numerical optimization algorithm. A total of 35 different synthesis examples are implemented. The examples are limited to desired instantaneous output direction for prescribed input force direction. Hence, this study is limited to linear elastic modeling with small deformations. Two design parameterizations, namely, the frame element based ground structure and the density approach using continuum elements, are used. The obtained designs are evaluated with all other objective functions and are compared with each other. The checkerboard patterns, point flexures, the ability to converge from an unbiased uniform initial guess, and the computation time are analyzed. Some observations are noted based on the extensive implementation done in this study. Complete details of the benchmark problems and the results are included. The computer codes related to this study are made available on the internet for ready access.

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