Reduced Basis Technique for Evaluating Sensitivity Derivatives of the Nonlinear Response of the Space Shuttle Orbiter Nose-Gear Tire

1993 ◽  
Vol 21 (4) ◽  
pp. 232-259 ◽  
Author(s):  
A. K. Noor ◽  
J. A. Tanner ◽  
J. M. Peters
Keyword(s):  
Finite Element ◽  
Space Shuttle ◽  
Mixed Finite Element ◽  
Second Order ◽  
Algebraic Equations ◽  
Global Approximation ◽  
Reduced Basis ◽  
First Order ◽  
Sensitivity Coefficients ◽  
Design Variables

Abstract A study is made of the sensitivity of the nonlinear tire response to variations in the design variables. The tire is discretized by using three-field mixed finite element models. An efficient reduced basis technique is used for calculating the nonlinear tire response as well as the first-order and second-order sensitivity coefficients (derivatives with respect to design variables). In this technique the vector of structural response and its first-order and second-order sensitivity coefficients are each expressed as a linear combination of a small number of basis (or global approximation) vectors. The Bubnov-Galerkin technique is then used to approximate each of the finite element equations governing the response and the sensitivity coefficients by a small number of algebraic equations in the amplitudes of the vectors. Extensive numerical results are presented for the sensitivity coefficients of the Space Shuttle orbiter nose-gear tire, when subjected to uniform inflation pressure.

scholarly journals Some Second-Order σ Schemes Combined with an H1-Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 187
Author(s):  
Yaxin Hou ◽  
Cao Wen ◽  
Hong Li ◽  
Yang Liu ◽  
Zhichao Fang ◽  
...  
Keyword(s):  
Finite Element ◽  
Diffusion Equation ◽  
Mixed Finite Element ◽  
Second Order ◽  
Stability And Convergence ◽  
Numerical Examples ◽  
The Stability ◽  
High Order Time ◽  
Distributed Order ◽  
Convergence Of The Scheme

In this article, some high-order time discrete schemes with an H 1 -Galerkin mixed finite element (MFE) method are studied to numerically solve a nonlinear distributed-order sub-diffusion model. Among the considered techniques, the interpolation approximation combined with second-order σ schemes in time is used to approximate the distributed order derivative. The stability and convergence of the scheme are discussed. Some numerical examples are provided to indicate the feasibility and efficiency of our schemes.

scholarly journals A Dynamic Analysis of the Rotary Cutting System of King Grass Shredder

2020 ◽  
Vol 145 ◽  
pp. 02080
Author(s):  
Zunxiang Li ◽  
Ou Zhongqing ◽  
Jiao jing ◽  
Huang xiaohong ◽  
Du jihua
Keyword(s):  
Finite Element ◽  
Critical Speed ◽  
Great Influence ◽  
Second Order ◽  
Belt Drive ◽  
Finite Element Models ◽  
Rotating Shaft ◽  
First Order ◽  
Rotary Cutting ◽  
Cutting System

With the rotary cutting system of king grass shredder as the research object, this paper established finite element models for rotating shaft, rotating shaft-belt pulley, rotating shaft-rotary cutting part and rotary cutting system and analyzed the influences of belt pulley and rotary cutting part on the dynamic characteristics of rotary cutting system. The results showed that the belt pulley and rotary cutting part had a great influence on the second order critical speed of rotary cutting system, and the rotary cutting part had a greater influence on the critical speed of first order forward precession than the belt pulley. Meanwhile, the critical speed of rotary cutting system that conformed to facts was calculated. There was a big difference between its first order and second order critical speeds, but the critical speed of first order backward precession was lower. Finally, it was found after analysis that the natural frequency of rotary cutting system was lower than the vibration frequency induced by belt drive, so the shredder can run safely.

Computation of State Reachable Points of Second Order Linear Time-Invariant Descriptor Systems

2017 ◽  
Vol 32 ◽  
pp. 301-316
Author(s):  
Subashish Datta ◽  
V Mehrmann
Keyword(s):  
Linear Time ◽  
Second Order ◽  
Reachable Set ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Order System ◽  
State Variables ◽  
Algebraic Equations ◽  
Free System ◽  
First Order

This paper considers the problem of computing the state reachable points (from the origin) of a linear constant coefficient second order descriptor system. A new method is proposed to compute the reachable set in a numerically stable way. The original descriptor system is transformed into a strangeness-free system within the behavioral framework followed by a projection that separates the system into different order differential and algebraic equations while keeping the original state variables. This reformulation is followed by a first order formulation that avoids all unnecessary smoothness requirements. For the resulting first order system, it is shown that the computation of the image space of two matrices, associated with the projected system, is enough to numerically compute the reachable set. Moreover, a characterization is presented of all the inputs by which one can reach an arbitrary point in the reachable set. These results are used to compute two different types of reachable sets for second order systems. The new approach is demonstrated through a numerical example.

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