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This assignment solution was submitted to Amar Sharma for Finite Element Method course at Aligarh Muslim University. It includes: Interpolation, Model, Propose, Field, Variable, Six-ode, Rectangular, Element, Considerations
Typology: Exercises
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Q.No.1. What kind of interpolation model would you propose for the field variable for the six-node rectangular element shown in Figure 3.13. Discuss how the various considerations given in Section 3.5 are satisfied?
Solution:
Given:
The six-node rectangular element
Find:
Schematic:
FINITE ELEMENT METHODS
PAGE | 1
Analysis:
1. Proposed model Proposed model for six-node two dimensional rectangular element is 2. Satisfaction of various considerations While choosing the order of the polynomial in a polynomial-type interpolation function, the following considerations have been satisfied. a) The interpolation polynomial satisfies, as far as possible, the convergence requirements stated below. i. The field variable is continuous within the elements. This requirement is easily satisfied by choosing continuous functions as interpolation models. Since polynomials are inherently continuous, the polynomial type of interpolation model discussed satisfies this requirement. ii. All uniform states of the field variable and its partial derivatives up to the highest order appearing in the functional have representation in the interpolation polynomial when in the limit the element size reduces to zero.
