Compliant assembly analysis including initial deviations and geometric nonlinearity—Part I: Beam structure

2018 ◽  
Vol 233 (12) ◽  
pp. 4233-4246
Author(s):  
Tao Liu ◽  
Zhi-Min Li ◽  
Sun Jin ◽  
Wei Chen
Keyword(s):  
Geometric Nonlinearity ◽  
Large Scale ◽  
Virtual Work ◽  
Flexible Beam ◽  
Beam Model ◽  
Analysis Method ◽  
Variation Analysis ◽  
Beam Structures ◽  
Compliant Assembly ◽  
Assembly Analysis

In the past decades, several compliant assembly analysis models have been developed to consider structural deformations during assembly progresses. Available methods address the influence of linear elastic deformations, whereas for the case of large-scale flexible structures with complex boundary conditions, the geometric nonlinearity will be a significant factor affecting the accuracy of assembly variation prediction. This paper introduces a refined mechanical model to develop a variation analysis method for beam structures. Based on the Timoshenko theory, governing equations of flexible beam are obtained by using the principle of virtual work with consideration of initial deviations and a von Kármán type of kinematic nonlinearity. Moreover, corresponding finite element formulas are presented, which also can be degenerated into non-initial deviation form or the linearized form. With the nonlinear beam model, an assembly variation analysis method is proposed for beam structures, which takes initial deviations, fixture errors, and matching deviations into account. Case studies of static loading analysis and slender beam assembly springback analysis are demonstrated to verify the feasibility and accuracy of the presented method.

Compliant assembly analysis including initial deviations and geometric nonlinearity, part II: Plate structure

2018 ◽  
Vol 233 (11) ◽  
pp. 3717-3732 ◽  
Author(s):  
Tao Liu ◽  
Zhi-min Li ◽  
Sun Jin ◽  
Wei Chen
Keyword(s):  
Geometric Nonlinearity ◽  
Mindlin Plate ◽  
Variation Analysis ◽  
Governing Equations ◽  
Plate Structures ◽  
Orthotropic Composite ◽  
Compliant Assembly ◽  
Variation Propagation ◽  
Springback Prediction ◽  
Assembly Analysis

Part I of this paper (Liu et al., “Compliant assembly analysis including initial deviations and geometric nonlinearity, part I: Beam structure”) has studied the variation propagation of beam structures with consideration of initial deviations and geometric nonlinearity. In practices, plate structures are more commonly used in manufacturing fields, and the attempt of this paper is to expand previous methodology for the assembly process of orthotropic composite plate structures. Similarly, initial deviations and von Kármán-type geometric nonlinearity are introduced into variation analysis model, with Mindlin plate theory accounting for shear effect. The analyzed plates are set as orthotropic composite materials, which also preserve the compatibility with isotropic metal materials. Governing equations and corresponding finite element expressions can be obtained by applying the principle of virtual work. Also, a linearized model or noninitial model can be regarded as a degradation of origin governing equations. A variation analysis approach for plate structures is proposed to make more refined assembly variation predictions with consideration of initial deviations, fixture errors, and matching deviations. The verification of the developed method is implemented with case studies on springback prediction of two composite plates assembly.

scholarly journals Application of the Generalized Nonlinear Constitutive Law in 2D Shear Flexible Beam Structures

2021 ◽  
Author(s):  
Damian Mrówczyński ◽  
Tomasz Gajewski ◽  
Tomasz Garbowski
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Reference Model ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Flexible Beam ◽  
Beam Model ◽  
Beam Structures ◽  
Nodal Displacements ◽  
Nonlinear Constitutive Law

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

Real-Time Structure Shape Estimation Using Distributed Fiber Bragg Grating Sensors

2009 ◽  
Author(s):  
Hong-Il Kim ◽  
Lae-Hyong Kang ◽  
Jae-Hung Han
Keyword(s):  
Real Time ◽  
High Speed ◽  
Estimation Method ◽  
Time Estimation ◽  
Flexible Beam ◽  
Beam Model ◽  
Shape Estimation ◽  
Rotating Beam ◽  
Structural Shape ◽  
Beam Structures

One of the emerging issues in lightweight aerospace structures is the real-time estimation of the structural shape changes. In order to reconstruct the structure shape based on the measured strain data at multiple points, the displacement-strain transformation (DST) method has been used. In this study, simulation for a 1-D beam model was performed to verify the DST method. Bending displacements for various excitation conditions were successfully estimated using the simulated strain signals. Strain sensor positions were optimized by the minimization of the condition number of the DST matrix for the 1-D beam. We further expanded the shape estimation method to rotating beams. A rotating flexible beam experimental model was constructed and a numerical simulation model was also prepared. Multiplexed four FBG sensors were fabricated and attached to the rotating beam structures to measure strains at four different locations. The experimental device has an optical rotary coupler, and the sensor signals are transmitted through the optical rotary coupler. Bending displacements were estimated based on the FBG signals and compared with directly measured displacement data using photographs taken by a high-speed camera. This shows the validity of the proposed shape estimation technique based on DST matrix for rotating beam structures.

Variation modeling and analysis with interval approach for the assembly of compliant aeronautical structures

2018 ◽  
Vol 233 (3) ◽  
pp. 948-959 ◽  
Author(s):  
Biao Mei ◽  
Weidong Zhu ◽  
Pengyu Zheng ◽  
Yinglin Ke
Keyword(s):  
Interval Arithmetic ◽  
Assembly Systems ◽  
Influence Coefficient ◽  
Production Volume ◽  
Analysis Method ◽  
Variation Analysis ◽  
Modeling And Analysis ◽  
Aircraft Manufacturing ◽  
Compliant Assembly ◽  
Interval Approach

Due to small production volume in aircraft industry, the available information of variation sources is often not enough to make assumptions on their probabilistic characteristics, especially in the stage of prototype manufacturing. To deal with the problem, an assembly variation modeling and analysis method based on the elasticity mechanics and interval approach is proposed for aircraft assembly. First, variation sources are modeled as bounded convex sets, which are defined as interval structural parameters in interval arithmetic. Then, variation modeling and analysis are successively implemented using the method of influence coefficient and interval arithmetic. After that, a uniform-splitting method is applied to achieve the refinement of the interval extension in variation analysis. To reduce the complexity of the finite element analysis and assembly variation computation, part deformation forms including warpage and torsion are concisely characterized with angle instead of the deviations of isolated key points on the part. The comparison of the assembly variations estimated with the proposed variation analysis method and actual experiment results verifies the effectiveness of the constructed assembly variation model and the proposed method. The interval approach–based assembly variation analysis method is a good complement to traditional probabilistic approach–based methods for compliant assembly systems, which is suited for linear and linearized nonlinear assembly systems. The proposed method provides an improved understanding of the application of compliant assembly variation analysis methods in aircraft manufacturing.

scholarly journals GaLactic and Extragalactic All-sky Murchison Widefield Array (GLEAM) survey III: South Galactic Pole data release

2021 ◽  
Vol 38 ◽  
Author(s):  
T. M. O. Franzen ◽  
N. Hurley-Walker ◽  
S. V. White ◽  
P. J. Hancock ◽  
N. Seymour ◽  
...  
Keyword(s):  
Large Scale ◽  
Angular Resolution ◽  
Beam Model ◽  
Spectral Variability ◽  
Extragalactic Source ◽  
Automated Algorithm ◽  
Data Release ◽  
Murchison Widefield Array ◽  
Source Populations ◽  
One Year

Abstract We present the South Galactic Pole (SGP) data release from the GaLactic and Extragalactic All-sky Murchison Widefield Array (GLEAM) survey. These data combine both years of GLEAM observations at 72–231 MHz conducted with the Murchison Widefield Array (MWA) and cover an area of 5 113 $\mathrm{deg}^{2}$ centred on the SGP at $20^{\mathrm{h}} 40^{\mathrm{m}} < \mathrm{RA} < 05^{\mathrm{h}} 04^{\mathrm{m}}$ and $-48^{\circ} < \mathrm{Dec} < -2^{\circ} $ . At 216 MHz, the typical rms noise is ${\approx}5$ mJy beam–1 and the angular resolution ${\approx}2$ arcmin. The source catalogue contains a total of 108 851 components above $5\sigma$ , of which 77% have measured spectral indices between 72 and 231 MHz. Improvements to the data reduction in this release include the use of the GLEAM Extragalactic catalogue as a sky model to calibrate the data, a more efficient and automated algorithm to deconvolve the snapshot images, and a more accurate primary beam model to correct the flux scale. This data release enables more sensitive large-scale studies of extragalactic source populations as well as spectral variability studies on a one-year timescale.

Flexibility Effects in a Single Link Robotic Manipulator

1993 ◽  
Author(s):  
C. Nataraj
Keyword(s):  
Large Scale ◽  
Robotic Manipulator ◽  
Flexible Beam ◽  
Rotating Speed ◽  
Weighted Residuals ◽  
Individual Interaction ◽  
Single Link ◽  
Rigid Mass ◽  
The Individual ◽  
Future Work

Abstract A single link robotic manipulator is modeled as a rotating flexible beam with a rigid mass at the tip and accurate energy expressions are derived. The resulting partial differential equations are solved using an approximate method of weighted residuals. From the solutions, coupling between axial and flexural deformations and the interactions with rigid body motions are rigorously analyzed. The emphasis in the current paper is not on an exhaustive analysis of existing systems but it is rather intended to compare and highlight the various flexibility effects in a relatively simple system. Hence, a nondimensional parametric analysis is performed to determine the effect of several parameters (including the rotating speed) on the errors and the individual interaction effects are discussed. Comparison with previous work in the field shows important phenomena often ignored or buried in large scale numerical analyses. Future work including application to multi-link robots is outlined.

Variation Analysis for Compliant Assembly

2000 ◽  
Author(s):  
S. Jack Hu ◽  
Yufeng Long ◽  
Jaime Camelio
Keyword(s):  
Sheet Metal ◽  
Assembly Line ◽  
Assembly Process ◽  
Variation Analysis ◽  
Assembly Lines ◽  
Compliant Assembly ◽  
Single Station ◽  
Dimensional Variation ◽  
Sheet Metal Assembly

Abstract Assembly processes for compliant non-rigid parts are widely used in manufacturing automobiles, furniture, and electronic appliances. One of the major issues in the sheet metal assembly process is to control the dimensional variation of assemblies throughout the assembly line. This paper provides an overview of the recent development in variation analysis for compliant assembly. First, the unique characteristics of compliant assemblies are discussed. Then, various approaches to variation modeling for compliant assemblies are presented for single station and multi-station assembly lines. Finally, examples are given to demonstrate the applications of compliant assembly variation models.

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