ME3602 FEA Lab Report 1 Applications of Finite Element Modelling in Stress Analysis Student Number: 1216434 1. Abstract The stress analysis carried out in this report was done using ANSYS Workbench on a thin plate consisting of double row of holes in it. The report demonstrates the study of localized stress or stress concentration around the holes using nominal stress and stress concentration factor. The analysis system used for this report was Static Structural Analysis which determined the total deformation, maximum equivalent stress and maximum principal stress of the plate when it was under an axial load in both positive and negative y-axis. The assumption made here is that load applied was constant and uniformly distributed on the horizontal edges of the plate, taking into account the effect of Poisson’s ratio. Using the Static Structural Analysis system the geometry creation, mesh generation and refinement, applying boundary conditions and solving were carried out. The results for maximum principal stress and number of elements were noted down in MS Excel and convergence plot of the results were obtained. The results showed convergence after the meshes were refined each time until no further refinement causes any variation. Both theoretical and actual stress concentration factors, Kt and K, were determined and similar pattern were obtained in the plot of K vs staggered angle between the rows of the holes. 2. Introduction to FEA Analysis Finite Element Modelling is an important numerical analysis technique in mechanical design where a physical model is converted into a discrete mathematical model which to carry out mesh generation and simulation for obtaining a certain set of results. Mechanical engineers use FEA software such as ANSYS Workbench to solve static, structural, dynamic, linear, nonlinear, and thermal problems. FEA analysis generally involves three stages: Pre-processor, Solver and Post- processor. For a given static or dynamic problem under investigation, Pre-processor stage is where the model creation and mesh generation can be carried out. The Solver stage takes over to assemble a stiffness matrix from the mesh and proceed to solve the structural field where displacement is first calculated and later other results such as stress, deformation and strains are obtained. Linear problems can be solved easily using Hooke’s Law whereas non-linear problems can be complicated to solve. The Post-processing stage is where the data for different set of results are generated and displayed in a contour plot. Advantages of FEA analysis are: irregular boundaries, general loads, different materials, boundary conditions, variable element size, easy modification etc. Disadvantages of FEA include: approximate solutions, element density affects the solution for a plate with a circular hole, poor shape quality of elements reduce accuracy of the solution, errors in input data. [1]
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ME3602 FEA Lab Report
1
Applications of Finite Element Modelling in Stress Analysis
Student Number: 1216434
1. Abstract
The stress analysis carried out in this report was done using ANSYS Workbench on a thin plate
consisting of double row of holes in it. The report demonstrates the study of localized stress or
stress concentration around the holes using nominal stress and stress concentration factor. The
analysis system used for this report was Static Structural Analysis which determined the total
deformation, maximum equivalent stress and maximum principal stress of the plate when it was
under an axial load in both positive and negative y-axis. The assumption made here is that load
applied was constant and uniformly distributed on the horizontal edges of the plate, taking into
account the effect of Poisson’s ratio. Using the Static Structural Analysis system the geometry
creation, mesh generation and refinement, applying boundary conditions and solving were carried
out. The results for maximum principal stress and number of elements were noted down in MS
Excel and convergence plot of the results were obtained. The results showed convergence after
the meshes were refined each time until no further refinement causes any variation. Both
theoretical and actual stress concentration factors, Kt and K, were determined and similar pattern
were obtained in the plot of K vs staggered angle between the rows of the holes.
2. Introduction to FEA Analysis Finite Element Modelling is an important numerical analysis technique in mechanical design where
a physical model is converted into a discrete mathematical model which to carry out mesh
generation and simulation for obtaining a certain set of results. Mechanical engineers use FEA
software such as ANSYS Workbench to solve static, structural, dynamic, linear, nonlinear, and
thermal problems. FEA analysis generally involves three stages: Pre-processor, Solver and Post-
processor. For a given static or dynamic problem under investigation, Pre-processor stage is
where the model creation and mesh generation can be carried out. The Solver stage takes over to
assemble a stiffness matrix from the mesh and proceed to solve the structural field where
displacement is first calculated and later other results such as stress, deformation and strains are
obtained. Linear problems can be solved easily using Hooke’s Law whereas non-linear problems
can be complicated to solve. The Post-processing stage is where the data for different set of
results are generated and displayed in a contour plot. Advantages of FEA analysis are: irregular
boundaries, general loads, different materials, boundary conditions, variable element size, easy
modification etc. Disadvantages of FEA include: approximate solutions, element density affects the
solution for a plate with a circular hole, poor shape quality of elements reduce accuracy of the
solution, errors in input data. [1]
ME3602 FEA Lab Report
2
3. Pre-Processing 3.1 3D-modelling of the plate
Diameter of
hole (a) /
mm
Spacing
between
holes (b) /
mm
Length of
the plate /
mm
Width of
the plate /
mm
Elastic
Modulus /
GPa
Poisson’s
ratio
Yield
Stress /
MPa
2 32 250 100 210 0.32 250
Table_1: Parameters given for the geometry.
Figure_1 shows the schematic of the semi-finite plate containing the double-row of staggered
holes subject to axial tension.
Figure_1: Plate geometry.
The distance between the rows of holes, c, was variable from 0 mm to 45 mm and also the
thickness of the plate, t, had values of 3, 5 and 7 mm. The staggered angle, 𝜃, was dependent on
the values of c and b. Stress was applied on the plate by means of an axial tensile load of 1200 N
in the y-axis. The main tasks were: to determine the peak stress around the hole, and hence using
nominal stress, to calculate the stress concentration factor, SCF for different staggered angle and
different thickness of the plate. Figure_2 shows the 3D model of the plate created, with symmetry
of axis.
Figure_2: Extruded plate with double-row of holes.
c
b
a θ
σ
σ
w
l
𝜽
c
ME3602 FEA Lab Report
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The symmetry of axis was created and used to reduce the plate total surface area, hence
increasing the mesh elements and nodes in the half-plate to get more accurate results for better
mesh refinement. Also it is less time consuming to obtain the results for half-plate than a full plate.
3.2 Addition of material properties of the plate
The properties given were the Elastic modulus, Poisons ratio and Tensile or Yield strength. The
materials inside the ‘Engineering Data’ of the Static Structural Analysis system did not have the
exact properties which were given therefore a new material called ‘FEA_Material’ was added to the
material library and given parameters were inserted manually and used for the plate model for
meshing and simulation to make sure that peak stress and SCF calculation are solely based on the
input parameters only.
3.3 Mesh Discretization and Mesh-refinement study
Once the 3D model of the geometry is created, mesh can be generated in terms of elements and
nodes, with choice of different types of meshes such as prism mesh, tetrahedron mesh,
hexahedron mesh, quadrilateral mesh etc. The results obtained were affected by the choice of
mesh type. Four types mesh were generated, amongst which one was an ‘Auto Mesh’. The other
three were Prism mesh, Hexahedron mesh and Quadrilateral mesh. The figures below show the