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### Fem

1. 1. Y.BOOPATHI MESH REFINEMENT
2. 2. MESH REFINEMENT  Elements with high strain energy identify the region of the body where mesh should be refined. p-method h-method
3. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 14.  Apply Loads and Obtain the Solution  Review the Results
15. 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. 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. 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
18. 18.  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
19. 19.  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.
20. 20.  THANKING U