23 Chapter 3 METHODOLOGY FOR FINITE ELEMENT ANALYSIS 3.1 INTRODUCTION Finite Element calculations more and more replace analytical methods especially if problems have to be solved which are adjusted to specific tasks. In many countries, a lot of efforts are carried out to get new code standards for the calculation of ultimate load capacity of single steel angles under eccentric loadings. All these calculation methods are based on linear descriptions of the material behavior. Concerning the non-linear and time dependent characteristics of materials, standard linear elastic finite element calculations in addition to code methods are often not suitable. Therefore, a new finite element model was developed to describe the real (elastic-plastic) behavior of the single steel angle under eccentric edge loads. Besides, an exact geometric modeling the description of the material behavior of all components is very important for the quality of performed analysis. This applies to analytical as well as to numerical methods. For components made of steel elastic or elastic-plastic material laws are able to simulate the real behavior of those parts in sufficient accuracy. The actual work regarding the finite element modeling of a single steel angle connected to end plates has been described in detail in this chapter. The representation of various physical elements with the FEM (Finite Element Modeling) elements, properties assigned to them, boundary conditions, material behavior and analysis types have also been discussed. The various obstacles faced during modeling, material behavior used and details of finite element meshing were also discussed in detail. 3.2 THE FINITE ELEMENT PACKAGES A large number of finite element analysis computer packages are available now. They vary in degree of complexity and versatility. The names of few such
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Chapter 3: Methodology for Finite Element Analysis 23
Chapter 3
METHODOLOGY FOR FINITE ELEMENT ANALYSIS
3.1 INTRODUCTION
Finite Element calculations more and more replace analytical methods
especially if problems have to be solved which are adjusted to specific tasks. In
many countries, a lot of efforts are carried out to get new code standards for the
calculation of ultimate load capacity of single steel angles under eccentric loadings.
All these calculation methods are based on linear descriptions of the material
behavior. Concerning the non-linear and time dependent characteristics of materials,
standard linear elastic finite element calculations in addition to code methods are
often not suitable.
Therefore, a new finite element model was developed to describe the real
(elastic-plastic) behavior of the single steel angle under eccentric edge loads.
Besides, an exact geometric modeling the description of the material behavior of all
components is very important for the quality of performed analysis. This applies to
analytical as well as to numerical methods. For components made of steel elastic or
elastic-plastic material laws are able to simulate the real behavior of those parts in
sufficient accuracy.
The actual work regarding the finite element modeling of a single steel angle
connected to end plates has been described in detail in this chapter. The
representation of various physical elements with the FEM (Finite Element
Modeling) elements, properties assigned to them, boundary conditions, material
behavior and analysis types have also been discussed. The various obstacles faced
during modeling, material behavior used and details of finite element meshing were
also discussed in detail.
3.2 THE FINITE ELEMENT PACKAGES
A large number of finite element analysis computer packages are available
now. They vary in degree of complexity and versatility. The names of few such
Chapter 3: Methodology for Finite Element Analysis 24
packages are:
- ANSYS (General purpose, PC and work stations)
- DYNA-3D (Crash / impact analysis)
- SDRC/I-DEAS (Complete CAD / CAM / CAE packages)
- NASTRAN (General purpose FEA on main frames)
- ABAQUS (Non-linear and dynamic analyses)
- COSMOS (General purpose FEA)
- ALGOR (PC and work stations)
- PATRAN (Pre / post processor)
- Hyper Mesh (Pre / post processor)
Of these packages ANSYS10.0 has been chosen for its versatility and
relative ease of use. ANSYS is capable of modeling and analyzing a vast range of
two- dimensional and three-dimensional practical problems. Buckling analysis of a
real structure (calculation of buckling loads and determination of the buckling mode
shape) can be performed quite satisfactorily by means of this software. . Both linear
(eigenvalue) buckling and nonlinear buckling analyses are possible
3.3 FINITE ELEMENT MODELING OF THE STRUCTURE
Figure 3.1: General sketch of a single steel angle with end plates at its both ends subjected to eccentric load.
End plate
Steel angle
Applied force
Chapter 3: Methodology for Finite Element Analysis 25
3.3.1 Modeling of Steel Angle and End Plates To facilitate the non-linear buckling analysis of the whole system, modeling
procedure has been simplified by eliminating bolts and considering end plates at the
two ends of the steel angle.
Since the whole modeling was performed in 3-dimension, the element used
here is 3-D in nature. For representing both the steel angle and the end plates,
SHELL-181(a 4 node structural shell element) has been used. Discussion about the
element is shown below in details:
SHELL181 Element Description
SHELL181 is suitable for analyzing thin to moderately-thick shell structures.
It is a 4-node element with six degrees of freedom at each node: translations in the x,
y, and z directions, and rotations about the x, y, and z-axes. (If the membrane option
is used, the element has translational degrees of freedom only). The degenerate
triangular option should only be used as filler elements in mesh generation.
SHELL181 is well-suited for linear, large rotation, and/or large strain
nonlinear applications. Change in shell thickness is accounted for in nonlinear
analyses. In the element domain, both full and reduced integration schemes are
supported. SHELL181 accounts for follower (load stiffness) effects of distributed
pressures.
Figure 3.2: SHELL181 Geometry
Chapter 3: Methodology for Finite Element Analysis 26
xo = Element x-axis if ESYS is not provided.
x = Element x-axis if ESYS is provided.
SHELL181 Input Data The geometry, node locations, and the coordinate system for this element are
shown in "SHELL181 ". The element is defined by four nodes: I, J, K, and L. The
element formulation is based on logarithmic strain and true stress measures. The
element kinematics allows for finite membrane strains (stretching).The thickness of
the shell may be defined at each of its nodes. The thickness is assumed to vary
smoothly over the area of the element. If the element has a constant thickness, only
TK(I) needs to be input. If the thickness is not constant, all four thicknesses must be
input.
A summary of the element input is given in below (Table 3.1).
Table 3.1: SHELL181 Input Summary
Element name SHELL181 Nodes
I, J, K, L
Degrees of Freedom
UX, UY, UZ, ROTX, ROTY, ROTZ if KEYOPT (1) = 0
UX, UY, UZ if KEYOPT (1) = 1
Real Constants TK(I), TK(J), TK(K), TK(L), THETA,
ADMSUA
E11, E22, E12, DRILL, MEMBRANE, BENDING
Material Properties
EX, EY, EZ, (PRXY, PRYZ, PRXZ, or NUXY, NUYZ, NUXZ),