Probabilistic Optimal Design Using Second Moment Criteria

1988 ◽  
Vol 110 (3) ◽  
pp. 324-329 ◽  
Author(s):  
A. D. Belegundu
Keyword(s):  
Finite Element Method ◽  
Sensitivity Analysis ◽  
Optimal Design ◽  
Design Sensitivity ◽  
Design Criterion ◽  
Second Order ◽  
Design Parameters ◽  
The Finite Element Method ◽  
Programming Technique ◽  
Second Moment

Probability-based optimal design of structures is presented. The emphasis here is to develop a practical approach to optimal design given random design parameters. The method is applicable to structures which are modeled using the finite element method. The Hasofer-Lind (H-L) second-moment design criterion is used to formulate the general design problem. A method for calculating the sensitivity coefficients is presented, which involves second-order design sensitivity analysis. The importance of second order derivatives is established. A nonlinear programming technique is used to solve the problem. Numerical results are presented, where stiffness parameters are treated as random variables.

First- and Second-Order Design Sensitivity Analysis Scheme Based on Trefftz Method

1999 ◽  
Vol 121 (1) ◽  
pp. 84-91 ◽  
Author(s):  
E. Kita ◽  
Y. Kataoka ◽  
N. Kamiya
Keyword(s):  
Sensitivity Analysis ◽  
Design Sensitivity ◽  
Second Order ◽  
Design Sensitivity Analysis ◽  
Design Parameters ◽  
Trefftz Method ◽  
Analysis Scheme ◽  
Complete Functions ◽  
Approximate Expressions ◽  
Physical Quantities

This paper presents a new scheme for the first- and second-order design sensitivity analysis of the two-dimensional elastic problem by using Trefftz method. In the Trefftz method, the physical quantities are approximated by superposition of regular T-complete functions. Therefore, direct differentiation of the approximate expressions with respect to design parameters leads to the regular expressions of the sensitivities. The present schemes are applied to some examples in order to confirm the validity.

Vibration characteristics of steering columns with bellows

2001 ◽  
Vol 215 (2) ◽  
pp. 171-178
Author(s):  
K H Kim ◽  
G H Han ◽  
H K Kim
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optimal Design ◽  
Vibration Characteristics ◽  
Sensitivity Analyses ◽  
Design Parameters ◽  
The Finite Element Method ◽  
Negative Effects ◽  
Vibration Sensitivity ◽  
Element Method

Bellows can be used as collapse elements for automotive steering columns. The crash performance of the steering column can be significantly improved with the bellows. However, the bending flexibility of the bellows has negative effects on the vibration characteristics. An effort is made to improve the vibration characteristics of steering columns with bellows. To understand the effects of various design parameters on the collapse and vibration, sensitivity analyses are performed by the finite element method using Taguchi's scheme. It is shown that the structure of the upper mounting bracket is the most important parameter affecting the vibration characteristics. An optimal design is proposed for a lower tilt type steering column.

scholarly journals Simulative investigation of ring creep on a planetary bearing of a wind turbine gearbox

2021 ◽  
Author(s):  
Jonas Gnauert ◽  
Felix Schlüter ◽  
Georg Jacobs ◽  
Dennis Bosse ◽  
Stefan Witter
Keyword(s):  
Experimental Data ◽  
Finite Element Method ◽  
Sensitivity Analysis ◽  
Planetary Gear ◽  
The Finite Element Method ◽  
Relative Movement ◽  
Wind Turbine Gearbox ◽  
Interference Fit ◽  
Planetary Gears ◽  
Module Coefficient

AbstractWind turbines (WT) must be further optimized concerning availability and reliability. One of the major reasons of WT downtime is the failure of gearbox bearings. Some of these failures occur, due to the ring creep phenomenon, which is mostly detected in the planetary bearings. The ring creep phenomenon describes a relative movement of the outer ring to the planetary gear. In order to improve the understanding of ring creep, the finite element method (FEM) is used to simulate ring creep in planetary gears. First, a sensitivity analysis is carried out on a small bearing size (NU205), to characterize relevant influence parameters for ring creep—considered parameters are teeth module, coefficient of friction, interference fit and normal tooth forces. Secondly, a full-scale planetary bearing (SL185030) of a 1MW WT is simulated and verified with experimental data.

DESIGN FEATURES OF CARBIDE ASSEMBLY WORKING ELEMENTS OF DEFORMING BROACHES

2021 ◽  
pp. 134-142
Author(s):  
Я.Б. Немировский ◽  
И.В. Шепеленко ◽  
С.Е. Шейкин ◽  
Ю.А. Цеханов ◽  
Ф.Й. Златопольский ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Hard Alloy ◽  
Contact Surface ◽  
Design Parameters ◽  
The Finite Element Method ◽  
Design Features ◽  
Working Element ◽  
External Loads

Разработан алгоритм и проведена оценка прочности сборных твердосплавных элементов со сплошной и дискретной рабочими поверхностями. Получены зависимости, позволяющие установить связь между конструктивными параметрами сборных деформирующих инструментов и их прочностью. Выполнены прочностные расчеты деформирующего инструмента для обработки отверстий значительного диаметра со сплошной и дискретной рабочими поверхностями. Численным моделированием, методом конечных элементов получены распределения эквивалентных напряжений в элементах инструмента и контактных напряжений по поверхности контакта твердосплавная вставка-корпус, что позволило проанализировать прочность инструмента под нагрузкой. Определены конструктивные параметры инструмента и приведены алгоритмы последовательности расчета сборных деформирующих элементов (ДЭ). Разработан алгоритм последовательности расчета сборного ДЭ для дискретного протягивания. Предложенная конструкция сборного рабочего элемента позволяет не только улучшить обрабатываемость изделия резания, но и уменьшить расход остродефицитного твердого сплава по сравнению с твердосплавным ДЭ аналогичных размеров на 6 кг. Полученные результаты можно использовать в инженерных расчетах при проектировании сборного инструмента для дискретного деформирования, а также для оценки прочности сборных инструментов, например, фрез, зенкеров, разверток при уточнении внешних нагрузок We developed an algorithm and assessed the strength of prefabricated carbide elements with solid and discrete working surfaces. We obtained dependencies that make it possible to establish a relationship between the design parameters of prefabricated deforming tools and their strength. We performed strength calculations of the deforming tool for machining holes of significant diameter with solid and discrete working surfaces. We obtained the distributions of equivalent stresses in the elements of the tool and contact stresses over the contact surface of the hard-alloy insert - body by numerical modeling, by the finite element method, which made it possible to analyze the strength of the tool under load. We determined the design parameters of the tool and here we give algorithms for the sequence of calculation of prefabricated deforming elements (DE). We developed an algorithm for the sequence of calculating the prefabricated DE for discrete broaching. The proposed design of the prefabricated working element allows not only to improve the machinability of the cutting product but also to reduce the consumption of an acutely deficient hard alloy in comparison with a hard alloy DE of similar dimensions by 6 kg. The results obtained can be used in engineering calculations when designing a prefabricated tool for discrete deformation, as well as for assessing the strength of prefabricated tools, for example, cutters, countersinks, reamers when specifying external loads

Design Sensitivity Analysis of Nonlinear Multidisciplinary Multibody Systems in the MIXEDMODELS Platform

2007 ◽  
Author(s):  
Shilpa A. Vaze ◽  
Prakash Krishnaswami ◽  
James DeVault
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
The State ◽  
Design Sensitivity Analysis ◽  
Design Parameters ◽  
State Variables ◽  
Sensitivity Coefficients ◽  
Design Variables

Most state-of-the-art multibody systems are multidisciplinary and encompass a wide range of components from various domains such as electrical, mechanical, hydraulic, pneumatic, etc. The design considerations and design parameters of the system can come from any of these domains or from a combination of these domains. In order to perform analytical design sensitivity analysis on a multidisciplinary system (MDS), we first need a uniform modeling approach for this class of systems to obtain a unified mathematical model of the system. Based on this model, we can derive a unified formulation for design sensitivity analysis. In this paper, we present a modeling and design sensitivity formulation for MDS that has been successfully implemented in the MIXEDMODELS (Multidisciplinary Integrated eXtensible Engine for Driving Metamodeling, Optimization and DEsign of Large-scale Systems) platform. MIXEDMODELS is a unified analysis and design tool for MDS that is based on a procedural, symbolic-numeric architecture. This architecture allows any engineer to add components in his/her domain of expertise to the platform in a modular fashion. The symbolic engine in the MIXEDMODELS platform synthesizes the system governing equations as a unified set of non-linear differential-algebraic equations (DAE’s). These equations can then be differentiated with respect to design to obtain an additional set of DAE’s in the sensitivity coefficients of the system state variables with respect to the system’s design variables. This combined set of DAE’s can be solved numerically to obtain the solution for the state variables and state sensitivity coefficients of the system. Finally, knowing the system performance functions, we can calculate the design sensitivity coefficients of these performance functions by using the values of the state variables and state sensitivity coefficients obtained from the DAE’s. In this work we use the direct differentiation approach for sensitivity analysis, as opposed to the adjoint variable approach, for ease in error control and software implementation. The capabilities and performance of the proposed design sensitivity analysis formulation are demonstrated through a numerical example consisting of an AC rectified DC power supply driving a slider crank mechanism. In this case, the performance functions and design variables come from both electrical and mechanical domains. The results obtained were verified by perturbation analysis, and the method was shown to be very accurate and computationally viable.

Design sensitivity analysis for optimal design of geometrically nonlinear lattice structures

2018 ◽  
Vol 168 ◽  
pp. 915-928 ◽  
Author(s):  
Ji-Yang Fu ◽  
Ben-Gang Wu ◽  
Jiu-Rong Wu ◽  
Ting Deng ◽  
Yong-Lin Pi ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Design ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Geometrically Nonlinear ◽  
Lattice Structures ◽  
Nonlinear Lattice
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