0
Research Papers

Finite Element Modeling of Structures With L-Shaped Beams and Bolted Joints

[+] Author and Article Information
K. He

Department of Mechanical Engineering, University of Maryland, Baltimore County, Baltimore, MD 21250hekun1@umbc.edu

W. D. Zhu1

Department of Mechanical Engineering, University of Maryland, Baltimore County, Baltimore, MD 21250wzhu@umbc.edu

1

Corresponding author.

J. Vib. Acoust 133(1), 011011 (Jan 26, 2011) (13 pages) doi:10.1115/1.4001840 History: Received March 31, 2009; Revised April 13, 2010; Published January 26, 2011; Online January 26, 2011

Due to bending-torsion coupled vibrations of the L-shaped beams and numerous uncertainties associated with the bolted joints, modeling structures with L-shaped beams and bolted joints is a challenging task. With the recent development of the modeling techniques for L-shaped beams by the authors (He and Zhu, 2009, “Modeling of Fillets in Thin-Walled Beams Using Shell/Plate and Beam Finite Elements,” ASME J. Vibr. Acoust., 131(5), p. 051002), this work focuses on developing new finite element (FE) models for bolted joints in these structures. While the complicated behavior of a single bolted connection can be analyzed using commercial FE software, it is computationally expensive and inefficient to directly simulate the global dynamic response of an assembled structure with bolted joints, and it is necessary to develop relatively simple and accurate models for bolted joints. Three new approaches, two model updating approaches and a predictive modeling approach, are developed in this work to capture the stiffness and mass effects of bolted joints on the global dynamic response of assembled structures. The unknown parameters of the models in the model updating approaches are determined by comparing the calculated and measured natural frequencies. In the predictive modeling approach, the effective area of a bolted connection is determined using contact FE models and an analytical beam model; its associated stiffnesses can also be determined. The models developed for the bolted joints have relatively small sizes and can be easily embedded into a FE model of an assembled structure. For the structures studied, including a three-bay space frame structure with L-shaped beams and bolted joints, and some of its components, the errors between the calculated and measured natural frequencies are within 2% for at least the first 13 elastic modes, and the associated modal assurance criterion values are all over 94%.

Copyright © 2011 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 5

The measured FRFs with the excitation and measurement points at points 11 and 39 shown in Fig. 3, respectively, and the excitation and measurement points reversed

Grahic Jump Location
Figure 6

(a) Dimensions of an L-shaped beam and (b) its solid element model with 67,321 tetrahedron solid elements, generated with ABAQUS 6.7. The thickness of the flange is 0.006317 m.

Grahic Jump Location
Figure 7

(a) Two views of a bolted joint connecting two L-shaped beams and (b) the corresponding solid element model. The measurement points are the same as those in Fig. 3.

Grahic Jump Location
Figure 8

(a) A structure with three L-shaped beams and two bolted joints and (b) its solid element model

Grahic Jump Location
Figure 9

(a) A structure with two L-shaped beams and a bolted joint, where there are two rectangular beams connected to the joint, and (b) its solid element model. The numbers of elements used for each L-shaped beam and the bracket are the same as those for the model in Fig. 7.

Grahic Jump Location
Figure 10

(a) The structure in Fig. 9 with the right rectangular beam removed and (b) its solid element model

Grahic Jump Location
Figure 16

The rigid-link constraints used to restrict the relative translational motion between A and B and to prevent the penetration between the clamped components

Grahic Jump Location
Figure 17

The calculated (left) and measured (right) mode shapes of the (a) 5th, (b) 8th, (c) 9th, and (d) 14th elastic modes of the structure in Fig. 3

Grahic Jump Location
Figure 18

(a) Unextruded and (b) extruded solid cylinders used to model the bolted connections

Grahic Jump Location
Figure 2

A three-bay space frame structure on an air-bed

Grahic Jump Location
Figure 3

(a) A structure with two L-shaped beams and a bolted joint with the measurement points marked in (b) and some of its dimensions shown in (c)

Grahic Jump Location
Figure 4

(a) The magnitudes of the Fourier transforms of the excitation forces and (b) the corresponding measured FRFs of the structure in Fig. 3

Grahic Jump Location
Figure 11

The shell and beam element model of an L-shaped beam (1)

Grahic Jump Location
Figure 12

The (a) normal and (b) shear motions of a bolted connection

Grahic Jump Location
Figure 13

A bolted connection and its FE model with shell and solid elements

Grahic Jump Location
Figure 14

Sensitivities of the least-squares relative errors between the calculated and measured natural frequencies of the first nine elastic modes of the structure in Fig. 3 to changes in the nondimensional effective area radius, the nondimensional elastic modulus of the cylinders, or the nondimensional shear modulus of the cylinders’ three critical parameters associated with each bolted connection

Grahic Jump Location
Figure 15

The cross-sectional view of the bolted joint in Fig. 3. Points A and B correspond to the intersections of the center planes of the L-shaped beam and bracket, respectively.

Grahic Jump Location
Figure 19

The FE model of two aluminum circular plates clamped together by a pair of distributed forces: (a) the exaggerated deformations of the two plates and (b) the pressure distribution on the contact interface

Grahic Jump Location
Figure 20

Pressure distributions at the contact interface of a bolted connection with different interface properties; the data points for the frictionless and friction cases are virtually indistinguishable

Grahic Jump Location
Figure 21

Contact pressure distributions for the clamped components with different material properties and clamping forces; the data points for the aluminum and steel plates with a clamping force of 109 N/m2 are virtually indistinguishable. The radius of the contact area for the steel case with a clamping force of 108 N/m2 is 0.0005 m smaller than the other three cases (0.0126 m).

Grahic Jump Location
Figure 22

The pressure distribution in the two aluminum clamped plates calculated from the 2D contact model; a finer mesh than that in the 3D model in Fig. 1 is used here

Grahic Jump Location
Figure 23

A beam model for a bolted connection; M is the bending moment exerted by the neighboring material on the beam at x=a

Grahic Jump Location
Figure 24

(a) A bolted connection and (b) its parallel spring model

Grahic Jump Location
Figure 25

The pressure distribution in the two clamped components, whose thicknesses and material properties are the same as those for a bolted connection in Fig. 7, subjected to a clamping force of 109 N/m2, approximately forms four pressure cones in series, with apex angles α11=α22=28.30 deg and α21=α12=12.99 deg

Grahic Jump Location
Figure 26

The (a) measured and (b) calculated mode shapes of the 12th elastic mode of the frame structure in Fig. 2. There are 64 measurement points, as marked in (a).

Grahic Jump Location
Figure 27

(a) A structure with three L-shaped beams, two bolted joints, and two rectangular beams at the lower joint and (b) its FE model; 74 DOFs associated with 50 measurement points shown in (c) were measured to obtain the mode shapes and natural frequencies

Grahic Jump Location
Figure 1

Part of a tower at the Hoover Dam, consisting of L-shaped beams and a bolted joint with multiple bolted connections

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In