Topology Optimization of a MEMS Resonator Using Hybrid Fuzzy Techniques

2008 ◽  
Author(s):  
Mohamed S. Senousy ◽  
Hesham A. Hegazi ◽  
Sayed M. Metwalli
Keyword(s):  
Topology Optimization ◽  
Random Search ◽  
Minimum Weight ◽  
Geometry Optimization ◽  
Gradient Projection ◽  
Stress Constraint ◽  
Complex Method ◽  
Search Technique ◽  
Mems Resonator ◽  
Macro Scale

This paper introduces a new methodology for the design of structures by geometry and topology optimization accounting for loading and boundary conditions as well as material properties. The Fuzzy Heuristic Gradient Projection (FHGP) method is used as a direct search technique for the geometry optimization, while the Complex Method (CM) is used as a random search technique for the topology optimization. In the proposed method, elements are designed such that they all have the same amount of stresses using the Fuzzy Heuristic Gradient Projection method. On the other hand, the complex method is used for the topology optimization step satisfying any constraint other than the stress constraint. The developed hybrid fuzzy technique is applied for different applications ranging from micro-scale to macro-scale applications. The method is applied to a micro-mechanical resonator as a microelectro-mechanical system (MEMS). The resonator is solved for minimum weight and is subjected to an equality frequency constraint and an inequality stress constraint. The proposed method is compared with the Multi-objective Genetic Algorithms (MOGAs) on solving the MEMS resonator. Results showed that the proposed hybrid fuzzy technique converges to optimum solutions faster than (MOGAs). The time consumed is improved by a 77%.

scholarly journals Macro-scale topology optimization for controlling internal shear stress in a porous scaffold bioreactor

2012 ◽  
Vol 109 (7) ◽  
pp. 1844-1854 ◽  
Author(s):  
K. Youssef ◽  
J.J. Mack ◽  
M.L. Iruela-Arispe ◽  
L.-S. Bouchard
Keyword(s):  
Shear Stress ◽  
Topology Optimization ◽  
Porous Scaffold ◽  
Macro Scale

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.

Tendon Geometry Optimization Using Path Integrals

2020 ◽  
Vol 61 (4) ◽  
pp. 247-254
Author(s):  
Jack Lehrecke ◽  
Juan Pablo Osman-Letelier ◽  
Mike Schlaich
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Path Integral ◽  
Path Integrals ◽  
Geometry Optimization ◽  
Structural Behavior ◽  
Spatial Structures ◽  
Simply Supported ◽  
Mathematical Background ◽  
Doubly Curved

The implementation of post-tensioned elements in concrete structures offers a multitude of benefits with regards to the overall structural behavior, with the efficacy of the applied tendons depending heavily on their geometry. However, the derivation of an optimal tendon geometry for a given structure is nontrivial, requiring engineering experience or the use of complex and often computationally demanding methodologies, e.g.the use of topology optimization strategies. This paper aims to investigate the possibility for optimizing tendon geometries using a path integral based objective function developed at the TU Berlin. For this purpose, the mathematical background is first presented to illustrate the proposed concept. Beginning with a tendon geometry optimization of a simply supported beam and progressing to more complex systems, a generalized approach for doubly curved spatial structures will be presented.

Hybrid General Heuristic Gradient Projection for Frame Optimization of Micro and Macro Applications

2009 ◽  
Author(s):  
Mohmmad M. A. Hanafy ◽  
Sayed M. Metwalli
Keyword(s):  
Projection Method ◽  
Stress Constraints ◽  
Gradient Projection ◽  
Gradient Projection Method ◽  
Hybrid Technique ◽  
Bending Stress ◽  
Design And Optimization ◽  
Frame Design ◽  
Mems Resonator ◽  
Heuristic Technique

In this paper, a generalization is suggested for the Heuristic Gradient Projection method. The previous Heuristic Gradient Projection method (HGP) has been developed for 3D-frame design and optimization. It mainly employed bending stress relations in order to simplify the process of iterations for stress constrained optimization. The General Heuristic Gradient Projection (GHGP) is used in a more general form to satisfy the stress constraints. Another direct search method is hybridized to satisfy other constraints on deflection. Two examples are solved using the new method. The proposed method is compared with the Hybrid Fuzzy Heuristic technique (FHGP) when solving a MEMS resonator. Results showed that the proposed hybrid technique with (GHGP) converges to the optimum solutions faster by an 8%. The MEMS weight is also decreased by 23.7%. For a macro level, the GHGP improved the solution time by 33.3%. The hybrid technique with (GHGP) improved the stresses in the members of the optimum ten-member cantilever.

An examination of the adaptive random search technique

AIChE Journal ◽  
1976 ◽  
Vol 22 (4) ◽  
pp. 744-750 ◽  
Author(s):  
M. W. Heuckroth ◽  
J. L. Gaddy ◽  
L. D. Gaines
Keyword(s):  
Random Search ◽  
Search Technique ◽  
Adaptive Random Search

Multiscale Topology Optimization for Additively Manufactured Objects

2018 ◽  
Vol 18 (3) ◽  
Author(s):  
John C. Steuben ◽  
Athanasios P. Iliopoulos ◽  
John G. Michopoulos
Keyword(s):  
Topology Optimization ◽  
Energy Deposition ◽  
Multiple Scales ◽  
Precise Control ◽  
Hand Tool ◽  
Macro Scale ◽  
Performance Specifications ◽  
Future Work ◽  
Am Processes ◽  
Meso Scale

The precise control of mass and energy deposition associated with additive manufacturing (AM) processes enables the topological specification and realization of how space can be filled by material in multiple scales. Consequently, AM can be pursued in a manner that is optimized such that fabricated objects can best realize performance specifications. In the present work, we propose a computational multiscale method that utilizes the unique meso-scale structuring capabilities of implicit slicers for AM, in conjunction with existing topology optimization (TO) tools for the macro-scale, in order to generate structurally optimized components. The use of this method is demonstrated on two example objects including a load bearing bracket and a hand tool. This paper also includes discussion concerning the applications of this methodology, its current limitations, a recasting of the AM digital thread, and the future work required to enable its widespread use.

A Generalization of the Heuristic Gradient Projection for 2D and 3D Frame Optimization

2017 ◽  
Author(s):  
Mahmoud S. Abd El-Rahman ◽  
Khalid M. Abd El-Aziz ◽  
Sayed M. Metwalli
Keyword(s):  
Recursive Formula ◽  
Stress Constraints ◽  
Gradient Projection ◽  
Stress Constraint ◽  
Combined Loads ◽  
Topology And Shape Optimization ◽  
Bending Loads ◽  
Optimum Solution ◽  
2D And 3D ◽  
Loading Type

This paper introduces a generalization of the heuristic gradient projection (HGP) method for solving 2D and 3D frames. The main objective is to minimize the frame weight by means of size, topology and shape optimization considering stress constraint activation. HGP can give a specific iterative equation for each element cross section and loading type and consequently reach the optimum solution in a relatively smaller number of iterations compared to general heuristic recursive equations. However, the solution of frames with combined loads applied on the elements might converge slowly or oscillate around the constrained optimum value. Many approaches were investigated for the generalization of the HGP. However, the emphasis was always directed towards axial and bending loads. Although other types of loads may have an effect on the problem, like shear and torsion stresses in shafts or 3D frames. These types of loads are introduced into the optimization problem with more general algorithm. Weighting factors are utilized to give a weight to each stress type applied on each element. This factor is used to change the power of the HGP iterative formula for each element in the frame, which changes the power of the recursive formula according to the contribution of each loading type applied on the element. The proposed technique shows more accurate results in activating the stress constraints than previously developed HGP when dealing with combined loads, and keeps the advantage of the HGP in finding the optimum solution in a relatively small number of structural analyses. In the case studies several sample applications were solved to highlight the robustness of the proposed method.

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