The FEM is the most powerful tool for solving constitutive equations over complicated systems

1. Non-linear
structural
analysis

2. Introduction
• The FEM is the most powerful tool for solving constitutive equations over
complicated systems
• An advantage of the FEM based modeling is that it enables the consideration of
complex geometries and may attribute different material properties to various
components of a system
• since the 1970s, many commercial finite element software companies have
evolved: ANSYS, ABAQUS, COMSOL, ADINA, LS-DYNA, and MARC
• The Definition of material model is any product will deform when exposed to a
load
• The presentation is composed of seven main parts

3. Part 1 Difference between liner and non-liner analysis
Liner analysis
• linear relationship between the applied loads and the
response of the system.
• This means that in a linear analysis the flexibility of
the structure need only be calculated once (by
assembling the stiffness matrix and inverting it).
• This principle of superposition of load cases
assumes that the same boundary conditions are used
for all the load cases.
Nonlinear analysis
• the structure's stiffness changes as it deforms.
• a nonlinear relation holds between applied forces
and displacements
• All physical structures exhibit nonlinear behavior
• Nonlinear effects can originate from geometrical
nonlinearity’s
• Modern analysis software makes it possible to
obtain solutions to nonlinear problems.
The difference between linear and non-linear analyses applied on a structure depends on
several parameters, such as:
- Mechanical behavior of the structure (it depends on the construction material);
- Displacements of the structure.
- Boundary conditions.

4. Part 2 MATLAB-based two bar truss analysis to trace the full equilibrium path
Aim
 trace the full equilibrium path
• Steps
only modified the code in which adding the spring so that expresses the stiffness
of the bar truss
• Results
Height (h) half-width (w) Stiffness (EA)
Truss 0.1m 1m 1

5. Part 3 MATLAB-based simplified push-over analysis
Aim
• predict the non-linear behavior of a structure under incremental loads
• Estimate the limit state of a structure
Jacket information
Steps
 Define points coordinates in Data Truss file and Topology matrix
 Define loud applied on jacket and boundary condition
 Define number of coordinates of point need to be plotted in load -displacement curve
Results
 these results isn’t accurate because it’s neglected
the region when the elongation doesn’t increase as
much as it before the reason for that because we
cannot trace the curve in nonlinear region
U. Deck length Max length Deck height Number of points
jacket 4m 10m 3m 11m

6. Part 4 Reverse engineering simulations using a tensile experiment
Aim
build appropriate material models in the finite element analysis and then applied tension load to show the material
behavior under this load
Specimen information
Width thickness
Specimen 24mm 4mm
steps
We have force elongation curve from experimental data.
1) Transform force elongation to engineering stress strain curve
Stress=force/area
Strain=elongation / original length
2) Calculate True stress strain curve
𝜎𝑡 = 𝜎𝑒 1 + 𝜀𝑒
𝜀𝑡 = 𝑙𝑛 1 + 𝜀𝑒
3) Using the power low method to define the points after ultimate strength
point because the True stress strain valid only until ultimate point
𝜎𝑡 = 𝑘𝜀𝑡
𝑢
4) Applied General steps to make finite element analysis in LS-Dyna
5) Define effective plastic strain and Corresponding yield stress value after
ultimate point in LS-Dyna until using power low method
First step: Define Material
Second step: Define Section
Third step: Define Part
Fourth step: Define Set
Fifth step: Define Boundary
Seventh step: Run the analysis

7. Results
Comparison between experimental and LS-Dyna simulation
 two curves are identical in elastic
region
 after that its different due to in material modeling
by LS-Dyna we are using true stress strain and power
low method to obtain force elongation curve.

8. part 5 Buckling analysis of a stiffened panel using the material model from
previous task
Aim Stiffened panel information
Estimate the failure mode of stiffened panel and shown
the deflection behavior under compressive load using the
material model that’s obtained from previous part
Steps
Apply General steps to make finite element analysis in LS-Dyna
Results
 The results of nonlinear buckling Shown in fig due to the
complex shape of stiffened panel
 In simulation shown the failure happened in stiffener first
so, we need to taker about stiffener dimension and its material
length Width shell thick Stiff thick
panel 3m 1.5m 6 mm 5 mm

9. Part 6 Ultimate strength analysis of a simplified hull structure using the material model from part 4
Aim
Obtained the moment curvature curve to define
the maximum bending capacity of the hull girder
Steps
1) General steps to make finite element analysis in LS-Dyna are applied on cross-section
2) Apply tension force on the cross-section representing sagging condition.
3) Extract load-end shortening curves
Results

10. Part 7 Smith method-based calculation of the ultimate strength of the simplified hull
structure from f incl. the numerical simulation of the load-end shortening curves
Aim
using two methods to obtain the ultimate strength,
first one by using finite element method and other
one by using smith method
Steps
1) Divided the cross section into smaller elements
2) Derive the load -end shortening curves for each element using LS-DYNA
3) Calculate the maximum curvature Kf
4)Obtain the smith strain 𝜀 = 𝑑𝐾𝑓 𝑍𝑖 − 𝑍𝑛𝑎 and corresponding smith stress
5) Obtained the moment curvature curve.

11. Results
there are different between two method this difference due to:
1) The size of element in smith method takes small element but in LS-Dyna
simulation take large element size.
2) The change in natural axis was neglected due to large size of element.
3) The materiel modeling using not accurate due to mesh size effect neglected.

12. Thanks