The document discusses two methods for mesh refinement - the p-method and h-method. The p-method increases the order of the polynomial used in the finite element model, allowing for more accurate results without changing the mesh. The h-method reduces the size of elements to create a finer mesh, better approximating the real solution in areas of high stress gradients. Both methods aim to improve the accuracy of finite element analysis results, with the p-method doing so without requiring changes to the mesh.

1. Y.BOOPATHI
MESH REFINEMENT

2. MESH REFINEMENT
 Elements with high strain energy identify the
region of the body where mesh should be
refined.
p-method
h-method

3. P-METHOD
 The p-method of mesh refinement increases
the order of polynomial in an element.
 The p-method obtains results such as
displacements, stresses, or strains to a user-
specified degree of accuracy
 To calculate these results, the p-method
manipulates the polynomial level (p-level) of
the finite element shape functions which are
used to approximate the real solution

4.  Starting from a mesh with linear elements at
first a p-refinement should be considered up
to the cubic polynomial degree of the shape
functions.
 This feature works by taking a finite element
mesh, solving it at a given p-level, increasing
the p-level selectively, and then solving the
mesh again

5.  After each iteration the results are compared
for convergence against a set of
convergence criteria. You can specify the
convergence criteria to include
displacement, rotation, stress or strain at a
point (or points) in the model, and global
strain energy. The higher the p-level, the
better the finite element approximation to the
real solution.

6.  The p-method can improve the results for
any mesh automatically
 The p-method is most efficient when meshes
are generated considering that p-elements
will be used, but this is not a requirement

7. BENEFITS OF USING THE P-METHOD
 The p-method solution option offers many
benefits for linear structural static analyses
that are not available with the more
traditional h-method
 The most convenient benefit is the ability to
obtain good results to a desired level of
accuracy without rigorous user-defined
meshing controls

8.  If you are new to finite element analysis or do
not have a solid background in mesh
design, you might prefer this method since it
relieves you of the task of manually designing
an accurate mesh.
 For example, if you need to obtain highly
accurate solutions at a point, such as for
fracture or fatigue assessments, the p-method
offers an excellent means of obtaining these
results to the required accuracy.

9. THE PROCEDURE FOR A P-METHOD STATIC ANALYSIS
CONSISTS OF FOUR MAIN STEPS:
 Select the p-method procedure.
 Build the model.
 Apply loads and obtain the solution.
 Review the results.

10. PROCEDURE
Select the p-Method
 The p-method solution procedure in two
ways: through the GUI or by defining a p-
element
Build the Model
 In order to build a model with p-elements, you
must follow the procedure listed below.
 Define the element types.
 Specify material properties and/or real
constants.
 Define the model geometry.
 Mesh the model into solid or shell elements.

11.  Define the Element Types
 2-D Quadrilateral
 2-D Triangle
 3-D Brick
 3-D Shell
 Note-H-elements and p-elements cannot be
active at the same time in your model.

12. Specify Material Properties and/or Real
Constants
 Material properties for p-elements may be either
constant or temperature-dependent, and
isotropic or orthotropic. As with other structural
analyses, if you plan to apply inertia loads (such
as gravity or rotational velocity), you must also
specify the density (DENS) that is required for
mass calculations. Young's modulus (EX) must
be defined for a static analysis, and if thermal
loads (temperatures) are to be applied, a
coefficient of thermal expansion (ALPX) must be
specified.

13.  Define the Model Geometry
 You can create your model using any of the
various techniques outlined in the ANSYS
Modeling and Meshing Guide, or you can
import it from a CAD system. If you are
generating your model from within
ANSYS, you can use either solid modeling or
direct generation techniques.
 Mesh the Model into Solid or Shell
Elements

14.  Apply Loads and Obtain the Solution
 Review the Results

15. H-METHOD
 The h-method of mesh refinement reduces the size of
element.
 The simplest type of element has a linear shape
function
 This means that the function for displacement across
the element is linear. With the h-method, the shape
function of the element will usually be linear. In an
actual part, it is quite uncommon for the displacement
to vary linearly. The h-method accounts for this by
increasing the number of elements. More accurate
information is obtained by increasing the number of
elements.

16.  The finite element method was originally
developed by the work of
mathematicians, particularly those who
worked in the area of numeric
integration. The variable h is used to specify
the step size in numeric integration. This
variable name carried over into finite element
analysis.

17.  Suppose that the actual stress across a part
varied by the function represented by the
curve
If the problem was analyzed using linear
shape functions, then the results for a course
mesh would be represented by the bars

19.  If a part is modeled with a very course
mesh, then the stress distribution across the
part will be very inaccurate. In order to more
accurately find the stress distribution across
the part, we will need to increase the number
of elements. If the number of elements are
doubled, then the stress distribution would be
represented by the bars

21.  The number of elements must only be
increased in areas where the stress is
changes quickly over a small distance. This
could be the area where a load is
applied, around a hole, or where geometry is
changing. In these areas the stress can
change dramatically over a very small
distance. It is up to the user to determine
where more elements will be required to
obtain an accurate solution.

22.  THANKING U