scholarly journals Shape optimization and sensitivity of compliant beams for prescribed load-displacement response

2016 ◽  
Vol 7 (2) ◽  
pp. 219-232 ◽  
Author(s):  
Giuseppe Radaelli ◽  
Just L. Herder
Keyword(s):  
Shape Optimization ◽  
Isogeometric Analysis ◽  
Nonlinear Boundary ◽  
Optimization Procedure ◽  
Analysis Framework ◽  
State Equations ◽  
Beam Shape ◽  
Constraint Equations ◽  
Analytical Sensitivities ◽  
Nonlinear State

Abstract. This paper presents the shape optimization of a compliant beam for prescribed load-displacements response. The analysis of the design is based on the isogeometric analysis framework for an enhanced fidelity between designed and analysed shape. The sensitivities used for an improved optimization procedure are derived analytically, including terms due to the use of nonlinear state equations and nonlinear boundary constraint equations. A design example is illustrated where a beam shape is found that statically balances a pendulum over a range of 180° with good balancing quality. The analytical sensitivities are verified by comparison with finite difference sensitivities.

Derivement of Constraint Equations of Driving Motor for Rotary Crane Systems

2003 ◽  
Vol 17 (08n09) ◽  
pp. 1976-1982
Author(s):  
Jong Gyu Lee ◽  
Kazuhiko Terashima ◽  
Sang Ryong Lee
Keyword(s):  
Transfer Function ◽  
Lyapunov Function ◽  
Nonlinear Equations ◽  
Integral Method ◽  
Equations Of Motion ◽  
State Equations ◽  
Constraint Equations ◽  
Rotary Crane ◽  
Nonlinear Equations Of Motion ◽  
Nonlinear State

In this paper, the dynamical model of rotary crane systems becomes nonlinear state equations. These equations are obtained by nonlinear equations of motion which are derived from transfer function of driving motors and equations of motion for a load. From these state equations, Lyapunov function of rotary crane systems is derived from integral method. This function secures stability of autonomous rotary crane systems. Also Constraint equations of rotation motor, boom motor, and hoist motor are derived from this function.

Structural Shape Optimization Wth Error Control

1994 ◽  
Author(s):  
Pierre Duysinx ◽  
WeiHong Zhang ◽  
HaiGuang Zhong ◽  
Pierre Beckers ◽  
Claude Fleury
Keyword(s):  
Shape Optimization ◽  
Computer Aided Design ◽  
Adaptive Mesh Refinement ◽  
Error Control ◽  
Optimization Procedure ◽  
Adaptive Mesh ◽  
Structural Shape ◽  
Structural Shape Optimization ◽  
Design Variables ◽  
Recent Developments

Abstract A robust and automatic shape optimization procedure is presented in this paper, which incorporates recent developments in the field of computer-aided design (CAD) of mechanical structures, such as geometric modelling, automatic selection of independent design variables, sensitivity analysis using reliable mesh perturbation schemes, error estimation and adaptive mesh refinement. A numerical example is given to show the efficiency of the procedure.

Robust Shape Optimization of Uncertain Dense Gas Flows Through a Plane Turbine Cascade

2011 ◽  
Author(s):  
Samuel J. Hercus ◽  
Paola Cinnella
Keyword(s):  
Robust Optimization ◽  
Shape Optimization ◽  
Flow Behavior ◽  
Computational Cost ◽  
Optimization Procedure ◽  
System Stability ◽  
Dense Gas ◽  
Turbine Cascade ◽  
The Mean ◽  
Inlet Conditions

A robust shape optimization procedure based on a multi-objective genetic algorithm coupled to a non-intrusive uncertainty quantification analysis was applied to a transonic inviscid flow of a dense gas over a plane turbine cascade. The goal was to simultaneously improve the mean turbine performance and the system stability under fluctuating thermodynamic inlet conditions. Despite an elevated computational cost, the optimization procedure was capable of generating a Pareto front of turbine geometries which improved the mean isentropic turbine efficiency μ(ηs) over the baseline profile, while limiting the solution variability in terms of the coefficient of variation of the power output CV(P2D). In addition to demonstrating an excellent parallel scalability over 1600 processors, the robust optimization revealed that variability of CV(P2D) depends more on the variation of inlet conditions than turbine geometry. A posteriori stochastic analyses on selected optimized turbine geometries allowed an investigation of flow behavior variability, as well as propositions for the improved selection of robust optimization cost criteria in future simulations.

Model order reduction of nonlinear eddy-current field using parameterized CLN

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Miwa Tobita ◽  
Hamed Eskandari ◽  
Tetsuji Matsuo
Keyword(s):  
Model Order Reduction ◽  
Dynamical Behavior ◽  
Order Reduction ◽  
Parameter Variation ◽  
Computational Time ◽  
State Equations ◽  
Model Order ◽  
Content Type ◽  
Parameter Variations ◽  
Nonlinear State

Purpose The authors derive a nonlinear MOR based on the Cauer ladder network (CLN) representation, which serves as an application of the parameterized MOR. Two parametrized CLN representations were developed to handle the nonlinear magnetic field. Simulations using the parameterized CLN were also conducted using an iron-cored inductor model under the first-order approximation. Design/methodology/approach This work studies the effect of parameter variations on reduced systems and aims at developing a general formulation for parametrized model order reduction (MOR) methods with the dynamical transition of parameterized state. Findings Terms including time derivatives of basis vectors appear in nonlinear state equations, in addition to the linear network equations of the CLN method. The terms are newly derived by an exact formulation of the parameterized CLN and are named parameter variation terms in this study. According to the simulation results, the parameter variation terms play a significant role in the nonlinear state equations when reluctivity is used, while they can be neglected when differential reluctivity is used. Practical implications The computational time of nonlinear transient analyses can be greatly reduced by applying the parameterized CLN when the number of time steps is large. Originality/value The authors introduced a general representation for the dynamical behavior of the reduced system with time-varying parameters, which has not been theoretically discussed in previous studies. The effect of the parameter variations is numerically given as a form of parameter variation terms by the exact derivation of the nonlinear state equations. The influence of parameter variation terms was confirmed by simulation.

Design and Optimization of Stamping Process to Improve Manufacturing Feasibility

2000 ◽  
Author(s):  
H. Naceur ◽  
Y. Q. Guo ◽  
J. L. Batoz
Keyword(s):  
Numerical Procedure ◽  
Optimization Procedure ◽  
Forming Limit Diagram ◽  
Forming Limit ◽  
Programming Technique ◽  
Design And Optimization ◽  
Stamping Process ◽  
Design Variables ◽  
Risk Of Rupture ◽  
Analytical Sensitivities

Abstract In this paper, we present a numerical procedure combining a finite element inverse approach (I.A.) [10, 14–18] for the simplified analysis of the stamping process with a mathematical programming technique (BFGS method) to optimize some process parameters. Our objective is to optimize the quality of the final workpiece, by minimizing the risk of rupture and wrinkles. The design variables of the present problem are the drawbead restraining forces in relation with the Forming Limit Diagram (FLD). The optimization procedure associated to the analytical sensitivities analysis technique based on the adjoint method is applied for the square cup of Numisheet’93 and the Twingo dashpot cup proposed by RENAULT [32]. The satisfactory results demonstrate the usefulness of this automatic optimization procedure in the preliminary design of deep-drawing process.

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