Study on the Stress-Stiffening Effect and Modal Synthesis Methods for the Dynamics of a Spatial Curved Beam

2016 ◽  
Vol 83 (8) ◽  
Author(s):  
Jianshu Zhang ◽  
Xiaoting Rui ◽  
Bo Li ◽  
Gangli Chen
Keyword(s):  
Small Deformation ◽  
Dynamics Simulation ◽  
Variation Principle ◽  
Synthesis Methods ◽  
Curved Beam ◽  
The Finite Element Method ◽  
High Rotational Speed ◽  
Modal Synthesis ◽  
Geometric Stiffening ◽  
Stiffening Effect

In this paper, based on the nonlinear strain–deformation relationship, the dynamics equation of a spatial curved beam undergoing large displacement and small deformation is deduced using the finite-element method of floating frame of reference (FEMFFR) and Hamiltonian variation principle. The stress-stiffening effect, which is also called geometric stiffening effect, is accounted for in the dynamics equation, which makes it possible for the dynamics simulation of the spatial curved beam with high rotational speed. A numerical example is carried out by using the deduced dynamics equation to analyze the stress-stiffening effect of the curved beam and then verified by abaqus software. Then, the modal synthesis methods, which result in much fewer numbers of coordinates, are employed to improve the computational efficiency.

Simulation of Flexible-Link Manipulators With Inertial and Geometric Nonlinearities

1995 ◽  
Vol 117 (1) ◽  
pp. 74-87 ◽  
Author(s):  
Chris Damaren ◽  
Inna Sharf
Keyword(s):  
Space Shuttle ◽  
Equations Of Motion ◽  
Theory Of Elasticity ◽  
Dynamics Simulation ◽  
The Finite Element Method ◽  
Flexible Link ◽  
Geometric Nonlinearities ◽  
Geometric Stiffening ◽  
Inertial Nonlinearities ◽  
Function Selection

Several important issues relevant to modeling of flexible-link robotic manipulators are addressed in this paper. First, we examine the question of which inertial nonlinearities should be included in the equations of motion for purposes of simulation. A complete model incorporating all inertial terms that couple rigid-body and elastic motions is presented along with a rational scheme for classifying them. Second, the issue of geometric nonlinearities is discussed. These are terms whose origin is the geometrically nonlinear theory of elasticity, as well as the terms arising from the interbody coupling due to the elastic deformation at the link tip. Accordingly, a general way of incorporating the well-known geometric stiffening effect is presented along with several schemes for treating the elastic kinematics at the joint interconnections. In addition, the question of basis function selection for spatial discretization of the elastic displacements is also addressed. The finite element method and an eigenfunction expansion techniques are presented and compared. All issues are examined numerically in the context of a simple beam example and the Space Shuttle Remote Manipulator System. Unlike a single-link system, the results for the latter show that all terms are required for accurate simulation of faster maneuvers. Hence, the conclusions of the paper are contrary to some of the previous findings on the validity of various models for dynamics simulation of flexible-body systems.

scholarly journals A Finite Element Approach to the Analysis of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft

1994 ◽  
Author(s):  
Wen Zhang ◽  
Wenliang Wang ◽  
Hao Wang ◽  
Jiong Tang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Equation Of Motion ◽  
Coupled Systems ◽  
The Finite Element Method ◽  
Bladed Disk ◽  
Modal Synthesis ◽  
Element Approach ◽  
Final Equation

A method for dynamic analysis of flexible bladed-disk/shaft coupled systems is presented in this paper. Being independant substructures first, the rigid-disk/shaft and each of the bladed-disk assemblies are analyzed separately in a centrifugal force field by means of the finite element method. Then through a modal synthesis approach the equation of motion for the integral system is derived. In the vibration analysis of the rotating bladed-disk substructure, the geometrically nonlinear deformation is taken into account and the rotationally periodic symmetry is utilized to condense the degrees of freedom into one sector. The final equation of motion for the coupled system involves the degrees of freedom of the shaft and those of only one sector of each of the bladed-disks, thereby reducing the computer storage. Some computational and experimental results are given.

A Survey of Modal Synthesis Methods

1971 ◽  
Author(s):  
Gary C. Hart ◽  
Walter C. Hurty ◽  
Jon D. Collins
Keyword(s):  
Synthesis Methods ◽  
Modal Synthesis

Alternating Stress Dynamics Analysis of Harmonic Gear Flexible Wheel

2012 ◽  
Vol 546-547 ◽  
pp. 102-109
Author(s):  
Xue Feng Han ◽  
Yang Bai ◽  
Ming Li ◽  
Hong Guang Jia
Keyword(s):  
Synthesis Method ◽  
Drive System ◽  
Dynamics Simulation ◽  
Theoretical Simulation ◽  
Gear Drive ◽  
Modal Synthesis ◽  
Change Trend ◽  
Simulation Results ◽  
To Come ◽  
Stress Simulation

This article is the study of alternating stress of flexible wheel in harmonic gear drive system. Firstly, according to elasticity theory to theoretically analyze flexible wheel stress; then, based on the basic principle of sub-structure modal synthesis method , use the software of UG、PATRAN and ADAMS to carry out co-simulation; Finally, based on the dynamics simulation, to analyze the alternating stress simulation results of flexible wheel and compare theoretical results and simulation results to come conclusion. The results show that: altering stress simulation results of flexible wheel are coincident with theoretical simulation results, have a deeper understand the stress change trend in the drive process of flexible wheel, lay a foundation for further carrying out dynamics simulation of harmonic gear drive system.

Stiffness Model of the Armature Assembly in a Jet Pipe Pressure Servo Valve

2020 ◽  
Author(s):  
Yaobao Yin ◽  
Chengpeng He ◽  
Jing Li
Keyword(s):  
Finite Element ◽  
Complex Structure ◽  
Small Deformation ◽  
Element Model ◽  
Continuity Condition ◽  
The Finite Element Method ◽  
Servo Valve ◽  
Linear Elastic ◽  
Stiffness Model ◽  
Static Performance

Abstract The armature assembly of the jet pipe pressure servo valve plays an important role in connecting the torque motor and the jet pipe amplifier. A stiffness model of its complex structure is very necessary for analyzing the dynamic/static performance of the jet pipe pressure servo valve. At the present work, the component parts in the armature assembly are simplified into linear elastic beams. The simplified armature assembly is a fourfold statically indeterminate structure under the premise of small deformation. The unknown forces and moments are solved by using the section continuity condition as the additional supplement equation, and the functional relationship between the electromagnetic torque produced from the torque motor and the armature rotation angle /the nozzle displacement is derived based on the Castigliano's Theorem. The finite element model of the armature assembly is also established to calculate the deformation under different loads and different spring tube lengths. The simulated displacements with the finite element method are consistent with the theoretical results. The experimental results of the recovery pressure of the jet pipe valve verified the theoretical model. The proposed stiffness calculation method can be used as a reference for designing and optimizing the armature assembly in the jet pipe pressure servo valve.

CONSISTENT APPROXIMATION FOR THE STRAIN ENERGY OF A 3D ELASTIC BODY ADEQUATE FOR THE STRESS STIFFENING EFFECT

2004 ◽  
Vol 04 (02) ◽  
pp. 279-292 ◽  
Author(s):  
YU. VETYUKOV
Keyword(s):  
Elastic Body ◽  
Strain Energy ◽  
Conventional Approach ◽  
Deformation Model ◽  
Geometrically Nonlinear ◽  
Consistent Approximation ◽  
New Strategy ◽  
Geometric Stiffening ◽  
Angular Velocities ◽  
Stiffening Effect

Starting from the fully geometrically nonlinear deformation model of a 3D elastic body, a consistent approximation for the strain energy in the vicinity of a pre-deformed state is obtained. This allows for the stress (geometric) stiffening effect to be taken into account. Additional terms arise in the strain energy approximation in comparison to the conventional approach, in which stiffening is incorporated in the form of a so-called geometric stiffness matrix. Computational costs of the new model are of the same order as that of the conventional approach. When compared to the fully geometrically nonlinear theory, the numerical analysis shows the suggested model to describe the dynamics of an elastic rotating structure better than the conventional approach. A new strategy is suggested to treat the non-constant pre-deformation, which is important for the flexible multibody simulations when angular velocities and interaction forces vary in time.

Stress Concentration Factor Calculation for the Hooks in Lifting Appliance of Spent Fuel Well Cover

2014 ◽  
Author(s):  
Xiang Liu ◽  
Yue Li ◽  
Jinhua Wang ◽  
Bin Wu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Spent Nuclear Fuel ◽  
Curved Beam ◽  
Spent Fuel ◽  
The Finite Element Method ◽  
High Temperature Reactor

The spent nuclear fuel of HTR-PM (High Temperature Reactor–Pebblebed Modules) will be dry stored in wells. In the mouth of each well, there is a cover weighing 11 tons. A lifting appliance with three hooks is used to open and close the covers. The hooks are L-shaped with fillet at the inside corner. The stress concentration at the corner has a significant impact on the strength and fatigue life of hooks. For optimizing the structure of the hook, the stress concentration factor related to the radius of fillet is calculated by both theoretical and numerical methods. The theoretical calculation is based on the Saint-Venant’s Principle and the analytical solution of a curved beam. The result is consistent with the numerical calculation performed by the finite element method.

Dynamic Substructuring Based on a Double Modal Analysis

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
S. Besset ◽  
L. Jézéquel
Keyword(s):  
Finite Element Method ◽  
Forthcoming Paper ◽  
Synthesis Methods ◽  
Generalized Coordinates ◽  
Multimodal Analysis ◽  
Modal Synthesis ◽  
Dynamic Substructuring ◽  
Primal And Dual ◽  
Modal Truncation ◽  
Continuous Formulation

Modal synthesis methods have long been studied because the use of generalized coordinates makes it possible to reduce calculation costs. Our approach uses modes to describe each part of the assembly of several substructures. This method, called “Double Modal Synthesis,” is presented through primal and dual formulations. As modal truncation usually introduces a lack of precision, we will use an ω2 development if necessary. These formulations will first be explained using a continuous formulation. A finite element method will then be proposed. Another aim of the paper is to introduce formulations needed to understand the multimodal analysis methods that will be presented in a forthcoming paper.

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