Thanks for your valuable hints. The matrix is symmetric.
Please run the atached code and follow the steps (if you have atleast 10 minutes!):
- Number of the elements = 3
- Number of the nodes = 4
- Elements have the same modulus of elasticity (modulus of elasticity for all elements is 1)
- Elements have the same cross sectional area (cross sectional area for all elements is 1)
- Elements have the same moment of inertia (moment of inertia for all elements is 1)
X and Y coordinates for nodes are as follows:
node 1 = (0,0)
node 2 = (0,1)
node 3 = (3,4)
node 4 = (4,4)
Node number for begining and end of elements:
element 1 = begining 1 end 2
element 2 = begining 2 end 3
element 3 = begining 3 end 4
number of conditional nodes: 2
conditional node number (for 1 from 2) = 1
select x and y
conditional node number (for 2 from 2) = 4
select x, y, theta
I found the answer with trial and error. In general, how it is possible to get the minimum positive real root without calculating parametric determinant?
For example assume that we use Newton iterative method. The determinant will be calculated at a certain point very fast. But the main problem is that the derivative of the determinant must be calculated at that point symbolically, which is a very time consuming procedure. If it is possible, please propose a way to calculate this part of Newton iterative method (the derivative of determinant at certain value of P in each step) numerically rather than symbolic computing of the determinant derivative.