scholarly journals About eigen sensitivity analysis of mechanical structures

2013 ◽  
Vol 40 (2) ◽  
pp. 263-275 ◽  
Author(s):  
Natasa Trisovic
Keyword(s):  
Order Approximation ◽  
Optimization Techniques ◽  
Design Parameters ◽  
Fe Model ◽  
Design Variables ◽  
Structural Reanalysis ◽  
First Order Approximation ◽  
Derivatives Of ◽  
Selection Of ◽  
Modal Method

Several methods for a calculation of derivatives of eigenvectors with respect to design parameters are described here. These are the finite-difference method, the modal method, a modified modal method, Nelson's method, an improved first-order approximation of eigenvalues and eigenvectors and an iterative method. By combining the other structural reanalysis techniques and one of these sensitivity methods, it is possible to enhance the efficiency and the accuracy of structural optimization techniques for determining the optimum condition of mechanical structure specified by an analyst. The sensitivity approach is based on the prior selection of updating parameters (design variables) in the initial FE model.

On the Nonlinear Dynamics of Pursuit Guidance for Marine Vehicles

1993 ◽  
Vol 37 (04) ◽  
pp. 342-353
Author(s):  
Fotis A. Papoulias
Keyword(s):  
Order Approximation ◽  
Design Parameters ◽  
Third Order ◽  
Marine Vehicles ◽  
Existence And Stability ◽  
Pure Pursuit ◽  
Fifth Order ◽  
Third Order Approximation ◽  
Dynamic Phenomena ◽  
Selection Of

A theoretical analysis of the nonlinear dynamic phenomena involved in pure pursuit guidance of marine vehicles is performed. Nomoto's model (Crane et al 1989) is used to provide the basis for the main vehicle turning lag. Results obtained in closed-form expressions demonstrate the existence of bifurcations to periodic solutions. The center manifold of the system is evaluated to within a third-order approximation. Third-and fifth-order expansions are utilized in order to provide information on limit cycle existence and stability. Recommendations regarding the appropriate selection of control design parameters are provided.

A Multi-Variable Approach to Determine the “Best” Gear Design

2000 ◽  
Author(s):  
Donald R. Houser ◽  
Jonny Harianto ◽  
B. Chandrasekaran ◽  
John Josephson ◽  
Naresh Iyer
Keyword(s):  
Objective Function ◽  
Optimization Techniques ◽  
Response Variable ◽  
Gear Design ◽  
Variable Approach ◽  
Design Variables ◽  
Simulation Based ◽  
To Come ◽  
Selection Of ◽  
Response Variables

Abstract Gear design requires the designer to compromise many design variables in order to determine the best performance of a gear set. Unfortunately the designer has a multiplicity of goals including keeping both bending and pitting stresses under an allowable value, minimizing scoring, achieving minimum efficiency and trying to minimize noise. This latter response variable is rarely considered in the initial gear design. In this work, noise is considered to be one of the more important design considerations. One approach to multi-variable gear design that has been tried is design optimization. Usually optimization techniques are limited in the number of variables that can be handled and with so many response variables, it is difficult to come up with an objective function that reflects the considerations of a real gear designer. In this paper we present a simulation-based approach to gear design that allows the designer to essentially “run all of the cases”. The simulation accounts for the true load distribution of the gears when computing response variables. Also, such factors as manufacturing tolerances may be included in the simulation so that truly robust designs may be obtained. Rather than using an objective function approach, designs are analyzed with a dominance filter that assesses each response variable in a manner that results in the “best” design. After these “best” designs are found, an interactive viewer allows the selection of those designs that best meet the designer’s goals with regard to all design variables. Several examples are presented in this paper. In each case, over 65,000 designs are evaluated and the dominance filter results in from 200 to 900 successful designs, depending on the tolerances that are applied. After sorting with the viewer the designer usually ends up with from 5 to 20 designs whose features may vary significantly, but have similar performances.

scholarly journals Optimization of the Curved Metal Damper to Improve Structural Energy Dissipation Capacity

Buildings ◽  
2022 ◽  
Vol 12 (1) ◽  
pp. 67
Author(s):  
Young-Chan Kim ◽  
Seyed Javad Mortazavi ◽  
Alireza Farzampour ◽  
Jong-Wan Hu ◽  
Iman Mansouri ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Shape Optimization ◽  
Specific Area ◽  
Material Model ◽  
Optimization Techniques ◽  
Hysteretic Behavior ◽  
Design Parameters ◽  
Fe Model ◽  
Constitutive Material Model ◽  
Energy Dissipation Capacity

Structural curved metal dampers are implemented in various applications to mitigate the damages at a specific area efficiently. A stable and saturated hysteretic behavior for the in-plane direction is dependent on the shape of a curved-shaped damper. However, it has been experimentally shown that the hysteretic behavior in the conventional curved-shaped damper is unstable, mainly as a result of bi-directional deformations. Therefore, it is necessary to conduct shape optimization for curved dampers to enhance their hysteretic behavior and energy dissipation capability. In this study, the finite element (FE) model built in ABAQUS, is utilized to obtain optimal shape for the curved-shaped damper. The effectiveness of the model is checked by comparisons of the FE model and experimental results. The parameters for the optimization include the curved length and shape of the damper, and the improved approach is conducted by investigating the curved sections. In addition, the design parameters are represented by B-spline curves (to ensure enhanced system performance), regression analysis is implemented to derive optimization formulations considering energy dissipation, constitutive material model, and cumulative plastic strain. Results determine that the energy dissipation capacity of the curved steel damper could be improved by 32% using shape optimization techniques compared to the conventional dampers. Ultimately, the study proposes simple optimal shapes for further implementations in practical designs.

scholarly journals Automotive Occupant Dynamics Optimization

1995 ◽  
Vol 2 (6) ◽  
pp. 471-479 ◽  
Author(s):  
J.A. Bennett ◽  
G.J. Park
Keyword(s):  
Order Approximation ◽  
Problem Formulation ◽  
Second Order ◽  
Parameter Analysis ◽  
Step Size ◽  
Design Variables ◽  
Lumped Parameter ◽  
Highly Nonlinear ◽  
Response Measures ◽  
First Order Approximation

One of the more difficult optimal design tasks occurs when the data describing the system to be optimized is either highly nonlinear or noisy or both. This situation arises when trying to design restraint systems for automotive crashworthiness using the traditional lumped parameter analysis methods. The nonlinearities in the response can come from either abrupt changes in the occupants interaction with the interior or from relatively minor fluctuation in the response due to the interactions of two restraint systems such as belts and airbags. In addition the calculated response measures are usually highly nonlinear functions of the accelerations. Two approaches using an approximate problem formulation strategy are proposed. One approach uses a first-order approximation based on finite difference derivatives with a nonlocal step size. The second and more effective approach uses a second-order curve fitting strategy. Successful example problems of up to 16 design variables are demonstrated. A conservative design strategy using a derivative-based constraint padding is also discussed. The approach proves effective because analytical expressions are available for the second-order terms.

Integrated Structural and Control Optimization

2004 ◽  
Vol 10 (10) ◽  
pp. 1377-1391 ◽  
Author(s):  
Ijar M. Fonseca ◽  
Peter M. Bainum
Keyword(s):  
Analytical Approach ◽  
Minimum Weight ◽  
Space Structure ◽  
Design Parameters ◽  
Gravity Gradient ◽  
Control Optimization ◽  
Design Variables ◽  
Analytical Derivatives ◽  
And Control ◽  
Derivatives Of

This paper focuses on the integrated structural/control optimization of a large space structure with a robot arm subject to the gravity-gradient torque through a semi-analytical approach. It is well known that the computer effort to compute numerically derivatives of the constraints with respect to design variables makes the process expensive and time-consuming. In this sense, a semi-analytical approach may represent a good alternative when optimizing systems that require sensitivity calculations with respect to design parameters. In this study, constraints from the structure and control disciplines are imposed on the optimization process with the aim of obtaining the structure’s minimum weight and the optimum control performance. In the process optimization, the sensitivity of the constraints is computed by a semi-analytical approach. This approach combines the use of analytical derivatives of the mass and stiffness matrices with the numerical solution of the eigenvalue problem to obtain the eigenvalue derivative with respect to the design variables. The analytical derivatives are easy to obtain since our space structure is a long one-dimensional beam-like spacecraft.

Automotive Occupant Dynamics Optimization

1991 ◽  
Author(s):  
J. A. Bennett ◽  
G. J. Park
Keyword(s):  
Order Approximation ◽  
Problem Formulation ◽  
Second Order ◽  
Parameter Analysis ◽  
Step Size ◽  
Design Variables ◽  
Lumped Parameter ◽  
Highly Nonlinear ◽  
Response Measures ◽  
First Order Approximation

Abstract One of the more difficult optimal design tasks occurs when the data describing the system to be optimized is either highly nonlinear or noisy or both. This situation arises when trying to design restraint systems for automotive crashworthiness using the traditional lumped parameter analysis methods. The nonlinearities in the response can come from either abrupt changes in the occupants interaction with the interior or from relatively minor fluctuation in the response due to the interactions of two restraint systems such as belts and airbags. In addition the calculated response measures are usually highly nonlinear functions of the accelerations. Two approaches using an approximate problem formulation strategy are proposed. One approach uses a first order approximation based on finite difference derivatives with a non local step size. The second and more effective approach uses the second order curve fitting strategy as proposed by Vanderplaats. Successful example problems of up to 16 design variables are demonstrated. A conservative design strategy using a derivative based constraint padding is also discussed. The approach proves effective because analytical expressions are available for the second order terms.

A New Approach to the Theory of Thin, Slightly Cambered Profiles

1957 ◽  
Vol 24 (2) ◽  
pp. 177-182
Author(s):  
F. S. Weinig
Keyword(s):  
Complex Variable ◽  
Complex Potential ◽  
Imaginary Axis ◽  
Velocity Potential ◽  
Order Approximation ◽  
New Approach ◽  
The Real ◽  
First Order ◽  
First Order Approximation ◽  
Derivatives Of

Abstract If real and imaginary parts of a function of a complex variable are interpreted as velocity potential and stream function, then real and imaginary parts of the kth derivatives are the (k–1) st derivatives of the velocity components in the direction of the real and negative imaginary axis. For slightly cambered profiles that deviate little from the real axis and have the shape of a polynomial of nth order, the imaginary part of the nth derivative of the complex potential is constant in first-order approximation. It is easy to establish such functions of the complex variable in the case of single as well as cascade profiles. Integration then yields the intended results. While there is no continuing need for such a method for single profiles, it is needed for cascades of profiles.

Optimization of orthotropic girders in cable supported bridges by parametric studies

2019 ◽  
Author(s):  
Mads Baandrup ◽  
Peter Noe Poulsen ◽  
John Forbes Olesen ◽  
Henrik Polk
Keyword(s):  
Boundary Conditions ◽  
Suspension Bridge ◽  
Design Parameters ◽  
Fe Model ◽  
Design Variables ◽  
Gradient Based ◽  
Parametric Studies ◽  
Bridge Girder ◽  
Support Conditions ◽  
Material Utilization

<p>For the last six decades closed-box orthotropic steel girders have been widely used in cable supported bridges due to their simple but useful structural concepts. Several numerical parametric studies were previously carried out in order to investigate inherent fatigue stress problems and in general, to improve the bridge girder designs. However, often such studies have been carried out with over-simplified finite element models, especially where boundary conditions have been challenging. In the present work, an advanced multi-scale FE model of a suspension bridge is established with sophisticated boundary conditions applied to a local parametric sub-model of a bridge girder. Thus, the model accommodates realistic support conditions. With this sub-model, a parametric study of the usual design parameters is carried out with focus on fatigue and a Eurocode stiffness requirement. The study reveals trends and correlations for the varying design parameters. Finally, the parametric sub-model is utilized in an automatic gradient-based optimization of multiple design variables simultaneously with the goal of minimizing weight. The methods allow bridge engineers to push material utilization to its limits by giving new insight into the effect of changing design parameters.</p>

A General Design Program Based on Genetic Algorithms With Applications

1995 ◽  
Author(s):  
Cornelia M. Kalker ◽  
Marcel F. Offermans
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Optimal Solution ◽  
Problem Definition ◽  
Design Parameters ◽  
Interactive Program ◽  
Design Variables ◽  
Design Program ◽  
Standard Values ◽  
Selection Of

Abstract When designing constructions, a number of decisions must be made as to types of constructions, values of geometric or other design variables, choices of materials and selection of standard values. These decisions are often based on conflicting requirements. In the present paper, a genetic algorithm is proposed for finding an optimal solution for those problems. The genetic algorithm has been implemented in an interactive program. The problem is formulated in terms of design parameters and relations (equalities, inequalities or procedures) between them. This information is parsed by a preprocessor and results in a problem definition that can be optimized with the genetic algorithm. During the optimization, the process can be followed and controlled by the designer. The values of all design parameters can be monitored, search intervals can be changed and parameters of the algorithm modified. All this speeds up the algorithm and improves the designer’s insight in the problem. As an example the design of navigation locks is treated.

Optimization of Catenary Risers

1999 ◽  
Vol 121 (2) ◽  
pp. 90-94 ◽  
Author(s):  
C. M. Larsen ◽  
T. Hanson
Keyword(s):  
Water Depth ◽  
Equivalent Stress ◽  
Nonlinear Function ◽  
Design Parameters ◽  
Design Variables ◽  
Function Design ◽  
General Constraints ◽  
Riser Design ◽  
Selection Of

This paper describes how the design of a catenary riser can be formulated as an optimization problem by using riser costs as the criteria function, design requirements in terms of maximum allowable stress and buckling capacity as constraints, and riser dimensions as free variables. The theory has been implemented in a computer program that can generate an optimized riser design for given design parameters such as water depth, diameter, pressure, and platform excursions. The developed software consists of a conventional program for two-dimensional riser analysis and a set of standard routines to minimize a nonlinear function subjected to general constraints. A case study where design parameters and requirements have been varied is also presented. The importance of buckling versus allowable equivalent stress as the most critical constraint has been investigated for varying water depth. The Conclusion of this work is that optimization is a useful tool for riser design, and that the proposed strategy for selection of design variables and constraints will enable an engineer to identify designs with minimum costs in an efficient way.

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