Isogeometric Optimal Design of Compliant Mechanisms Using Finite Deformation Curved Beam Built-Up Structures

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Myung-Jin Choi ◽  
Seonho Cho
Keyword(s):  
Finite Deformation ◽  
Compliant Mechanisms ◽  
Optimization Method ◽  
Design Sensitivity ◽  
Continuity Condition ◽  
Cross Sectional ◽  
Design Variables ◽  
Strain Formulation ◽  
Nonconservative Loading ◽  
Total Lagrangian Formulation

Abstract This paper presents a configuration and sizing design optimization method for large deformation planar compliant mechanisms, using a continuum-based adjoint design sensitivity analysis (DSA) approach for built-up structures. Under the total Lagrangian formulation, the Jaumann strain formulation using the discretization of the global displacement field is employed to account for the finite deformation of arbitrarily curved Kirchhoff beams. In multipatch models, a rotational junction continuity condition is imposed using penalty and Lagrange multiplier methods. The developed adjoint DSA method can handle nonconservative loading conditions, which lead to asymmetry of tangent operator. Performance measures are displacements and rotation angles, and neutral axis configuration and cross-sectional thickness are considered as design variables. Also, analytical design sensitivity expressions for the rotation continuity condition are derived. Various compliant mechanisms including path-generators and an angular rotator are synthesized to demonstrate the applicability of the proposed method.

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 fast multiobjective optimization approach to S-duct scoop inlets design with both inflow and outflow

2018 ◽  
Vol 233 (9) ◽  
pp. 3381-3394
Author(s):  
Lifang Zeng ◽  
Dingyi Pan ◽  
Shangjun Ye ◽  
Xueming Shao
Keyword(s):  
Multiobjective Optimization ◽  
Total Pressure ◽  
Optimization Method ◽  
Navier Stokes ◽  
Integral Model ◽  
Optimization Approach ◽  
Navier Stokes Equation ◽  
Cross Sectional ◽  
Design Variables ◽  
Computational Fluid Dynamics Analysis

A fast multiobjective optimization method for S-duct scoop inlets considering both inflow and outflow is developed and validated. To reduce computation consumption of optimization, a simplified efficient model is proposed, in which only inflow region is simulated. Inlet pressure boundary condition of the efficient model is specified by solving an integral model with both inflow and outflow. An automated optimization system integrating the computational fluid dynamics analysis, nonuniform rational B-spline geometric representation technique, and nondominated sorting genetic algorithm II is developed to minimize the total pressure loss and distortion at the exit of diffuser. Flow field is numerically simulated by solving the Reynolds-averaged Navier–Stokes equation coupled with k–ω shear stress transport turbulence model, and results are validated to agree well with previous experiment. S-duct centreline shape and cross-sectional area distribution are parameterized as the design variables. By analyzing the results of a suggested optimal inlet chosen from the obtained Pareto front, total pressure recovery has increased from 97% to 97.4%, and total pressure distortion DC60 has decreased by 0.0477 (21.7% of the origin) at designed Mach number 0.7. The simplified efficient model has been validated to be reliable, and by which the time cost for the optimization project has been reduced by 70%.

Optimal design of nonlinear large-scale suspendome using cascade optimization

2017 ◽  
Vol 33 (1) ◽  
pp. 3-18 ◽  
Author(s):  
Ali Kaveh ◽  
Masoud Rezaei ◽  
MR Shiravand
Keyword(s):  
Optimal Design ◽  
Large Scale ◽  
Simple Procedure ◽  
Geometry Optimization ◽  
Steel Structures ◽  
Optimization Method ◽  
Scale Space ◽  
Cross Sectional ◽  
Colliding Bodies Optimization ◽  
Design Variables

Large-scale suspendomes are elegant architectural structures which cover a vast area with no interrupting columns in the middle. These domes have attractive shapes which are also economical. Domes are built in a wide variety of forms. In this article, an algorithm is developed for optimum design of domes considering the topology, geometry, and size of member section using the cascade-enhanced colliding bodies optimization method. In large-scale space steel structures, a large number of design variables are involved. The idea of cascade optimization allows a single optimization problem to be tackled in a number of successive autonomous optimization stages. The variables are the optimum height of crown and tubular sections of these domes, the initial strain, the length of the struts, and the cross-sectional areas of the cables in the tensegrity system of domes. The number of joints in each ring and the number of rings are considered for topology optimization of ribbed and Schwedler domes. Weight of the dome is taken as the objective function for minimization. A simple procedure is defined to determine the configuration of the domes. The design constraints are considered according to the provisions of Load and Resistance Factor Design–American Institute of Steel Constitution. In order to investigate the efficiency of the presented method, a large-scale suspendome with more than 2266 members is investigated. Numerical results show that the utilized method is an efficient tool for optimal design of large-scale domes. Additionally, in this article, a topology and geometry optimization for two common ribbed and Schwedler domes are performed to find their optimum graphs considering various spans.

The Modified Quadrilateral Discretization Model for the Topology Optimization of Compliant Mechanisms

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Hong Zhou ◽  
Pranjal P. Killekar
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Local Stress ◽  
Optimization Method ◽  
Stress Constraint ◽  
Cell Problem ◽  
Design Variables ◽  
Design Cell

The modified quadrilateral discretization model for the topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. There is a certain location shift between two neighboring rows of quadrilateral design cells. This modified quadrilateral discretization model allows any two contiguous design cells to share an edge whether they are in the horizontal, vertical, or diagonal direction. Point connection is completely eliminated. In the proposed topology optimization method, design variables are all binary, and every design cell is either solid or void to prevent gray cell problem that is usually caused by intermediate material states. Local stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum. No postprocessing is required for topology uncertainty caused by either point connection or gray cell. The presented modified quadrilateral discretization model and the proposed topology optimization procedure are demonstrated by two synthesis examples of compliant mechanisms.

Implementation of Design Sensitivity Analysis with Existing Finite Element Codes

1987 ◽  
Vol 109 (3) ◽  
pp. 385-391 ◽  
Author(s):  
K. K. Choi ◽  
J. L. T. Santos ◽  
M. C. Frederick
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Cross Sectional ◽  
Design Variables ◽  
Accurate Design ◽  
Analysis Theory ◽  
Problem Design ◽  
Selection Of

A numerical method is presented to implement structural design sensitivity analysis theory, using the versatility and convenience of existing finite element structural analysis programs. Design variables such as thickness and cross-sectional areas of components of individual members and built-up structures are considered. Structural performance functionals considered include displacement and stress. The method is also applicable for eigenvalue problem design sensitivity analysis. It is shown that calculations can be carried out outside existing finite element codes, using postprocessing data only. Thus design sensitivity analysis software does not have to be imbedded in an existing finite element code. Feasibility of the method is shown through analysis of several problems, including a built-up structure. Accurate design sensitivity results are obtained without the uncertainty of numerical accuracy associated with selection of finite difference perturbations.

The Modified Quadrilateral Discretization Model for the Topology Optimization of Compliant Mechanisms

2011 ◽  
Author(s):  
Hong Zhou ◽  
Pranjal P. Killekar
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Local Stress ◽  
Optimization Method ◽  
Initial Guess ◽  
Stress Constraint ◽  
Design Variables ◽  
Conduct Sensitivity Analysis

The modified quadrilateral discretization model for the topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. There is a certain location shift between two neighboring rows of quadrilateral design cells. This modified quadrilateral discretization model allows any two contiguous design cells to share an edge whether they are in the horizontal, vertical or diagonal direction. Point connection is completely eliminated. In the proposed topology optimization method, design variables are all binary and every design cell is either solid or void to prevent grey cell problem that is usually caused by intermediate material states. Local 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 avoid the need to select the initial guess solution and conduct sensitivity analysis. No postprocessing is needed for topology uncertainty caused by point connection or grey cell. The presented modified quadrilateral discretization model and the proposed topology optimization procedure are demonstrated by two synthesis examples of compliant mechanisms.

scholarly journals Structural Optimization of Variable Section Slender Manipulator Based on Sensitivity Analysis Method

2011 ◽  
Vol 2-3 ◽  
pp. 291-295
Author(s):  
Zhong Luo ◽  
Le Liang ◽  
Yan Yan Chen ◽  
Fei Wang
Keyword(s):  
Sensitivity Analysis ◽  
Structural Optimization ◽  
Optimization Method ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Analysis Method ◽  
Design Variables ◽  
Variable Section ◽  
Sensitivity Analysis Method ◽  
In The Beginning

A parameter optimization method based on sensitivity analysis is presented for the structural optimization of variable section slender manipulator. Structure mechanism of a polishing robot is introduced firstly, and its stiffness model is established. Then, a design sensitivity analysis method and a sequential liner programming (SLP) strategy are proposed. In the beginning of the optimization, the design sensitivity analysis method can be used to select the sensitive design variables which can make the optimized results more efficient and accurate. And then, it can be used to improve the convergence during the process of the optimization. The design sensitivities are calculated using the finite difference method. The search for the final optimal structure is performed using the SLP method. Simulation results show that the structure optimization method is effective to enhance the stiffness of the manipulator, no matter when the manipulator suffers constant force or variable force. This work lays a theoretical foundation for the structural optimization for such manipulators.

Structural Synthesis by Method of Centers in Force Formulation under Size and Stress Constraints

2010 ◽  
Vol 26 (4) ◽  
pp. 513-524
Author(s):  
B. Farshi ◽  
A. Alinia-ziazi
Keyword(s):  
Minimum Weight ◽  
Load Condition ◽  
Optimization Method ◽  
Stress Constraints ◽  
Cross Sectional ◽  
Method Of Centers ◽  
Novel Approach ◽  
Design Variables ◽  
Weight Design ◽  
Optimization Routine

ABSTRACTThis paper studies a novel approach to optimize trusses and truss-like structures for minimum weight design. It is based on the force method of analysis which is incorporated inside the optimization routine. The design variables in force formulation are the member cross sectional areas and the redundant forces in each load condition. The optimization method used is the method of center points using the inscribed hyperspheres to the feasible-usable design space. By incorporating the analysis step as part of the optimization problem, a separate structural solution phase, which is necessary in all other methods, is avoided resulting in large computational savings. In this article the simplest form of structures i.e. trusses are treated to illustrate the efficacy of the method. Stress limits on the members as well as limitations on their sizes, and linking among them, under several load conditions have been considered. Combination of the method of center points and force formulation results in a viable routine for structural optimization. Comparison of the example results with those obtained by others clearly shows the effectiveness and novelty of the proposed method.

scholarly journals Structural Optimization of Slender Robot Arm Based on Sensitivity Analysis

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Zhong Luo ◽  
Xueyan Zhao ◽  
Le Liang ◽  
Fei Wang
Keyword(s):  
Sensitivity Analysis ◽  
Structural Optimization ◽  
Optimization Method ◽  
Design Sensitivity ◽  
Robot Arm ◽  
Analysis Method ◽  
Design Variables ◽  
Stiffness Model ◽  
Variable Section ◽  
Sensitivity Analysis Method

An effective structural optimization method based on a sensitivity analysis is proposed to optimize the variable section of a slender robot arm. The structure mechanism and the operating principle of a polishing robot are introduced firstly, and its stiffness model is established. Then, a design of sensitivity analysis method and a sequential linear programming (SLP) strategy are developed. At the beginning of the optimization, the design sensitivity analysis method is applied to select the sensitive design variables which can make the optimized results more efficient and accurate. In addition, it can also be used to determine the scale of moving step which will improve the convergency during the optimization process. The design sensitivities are calculated using the finite difference method. The search for the final optimal structure is performed using the SLP method. Simulation results show that the proposed structure optimization method is effective in enhancing the stiffness of the robot arm regardless of the robot arm suffering either a constant force or variable forces.

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