Learn Linear Shape Functions

To learn the graphs of linear shape functions be used to resolve problems during restricted element analysis.In Lagrange functions Hermite cubic polynomials each function is unity at its individual node and zero at the further nodes. Moreover, the Lagrange shape functions summation to unity everywhere. For the Hermite polynomials H1 and H3 sum to unity.The shape functions be use to find the field variable U since recognized values at extra locations. The formula is U  = N1 U1 + N2 U2 + ...,Wherever Ni be the shape functions and Ui are identified values.

Sample problem for learn linear shape functions


The Hermite shape functions are used for beam analysis wherever together the deflection and slope of adjacent elements be required to be the similar at every node. H1 and H2 are the deflection while H2 and H4 are the slope.

D = H1 D1 + H2 S1 + H3 D2 + H4 S2
Wherever D be the deflection and Si be the slope.

In the formulas below,

L be the length
S be X - X1
r be S / L





Example problems for learn linear shape functions


Example 1:

Solving the domain of  learn linear shape function f
f (x) = sqrt (5x - 25)

Solution:
The expression function f includes a square root. The expression below the radical have to assure the condition
5x - 25 >= 0    for the function to obtain real values.
solve the linear inequality
x >= 25/5
x=5
The domain, within interval notation, is  (5 , +infinity)

Example 2:

Solving the domain of  learn linear shape function f
f (x) = sqrt (9x - 36)

Solution:
The expression function f includes a square root. The expression below the radical have to assure the condition
9x - 36 >= 0    for the function to obtain real values.
solve the linear inequality
x >= 36/9
x=4
The domain, within interval notation, is  (4 , +infinity)

Example 3:

Solving the domain of  learn linear shape function f

f (x) = sqrt (-x +9)

Solution:
The expression function f include a square root. The expression below the radical have to assure the condition
-x +9 >= 0    for the function to obtain real values.
solve the linear inequality
x >= 9/-1
x=-9
The domain, within interval notation, is (-infinity, 8).