Civil Engineering Reference
In-Depth Information
Fig. 15.10
Finite element
model of bolted connection
RBE 2
Beam
element
Spring
element
Joint
I
Joint
II
Joint
III
Fig. 15.11
First three modes
of the structure from finite
element analysis
Mode 1: 11.442Hz
Mode 2: 31.321Hz
Mode 3: 58.335Hz
15.4.1 Finite Element Model
Midsurface shell elements are used to build the finite element model of the beam-like structure with four steel parts. For each
steel part, the midsurface shell elements locate in different planes when the thickness of the part varies. Therefore, the RBE2
from Multi-Point Constraint (MPC) is used to connect those elements in same steel part, but in different planes, as shown in
Fig.
15.10
. For the connection locations, the beam element is set up to simulate the bolt. The cross-section, material and
properties of the beam element are set based on those of the bolts used in the modal testing. Spring elements in two orthogonal
directions are used to simulate the interaction between different steel parts, such as extrusion and friction, as shown in Fig.
15.10
.
Firstly, the first three modes of the beam-like structure are obtained without considering the stiffness of spring elements,
which means the stiffness of spring elements is set to zero and different steel parts are connected with each other through beam
elements only. The first three natural frequencies and the corresponding mode shapes are depicted in Fig.
15.11
. Compared
with the data of modal testing in Group A, the finite element model without spring elements has the similar natural frequencies
with the structure, whose bolt preload is 2.0 Nm for all the joints. In order to obtain a proper finite element model of the beam-
like structure with larger bolt preload, the stiffness of spring elements must be considered. Model updating is adopted to set up
the proper finite element model of the bolted connection, and related theories can be found in reference [
9
,
10
].
15.4.2 Optimization Model
Modal parameters of the finite element model are influenced by the stiffness of spring elements, and different spring stiffness
can be used to simulate different bolt preloads. It is necessary to select the appropriate stiffness values for these spring
elements to obtain the reasonable finite element model of the bolted connection. Here, the optimization method based on
