Week - 2 - Explicit and Implicit Analysis

Aim:

To explain about implicit and explicit analysis and also to show mathematical calcaulation.

In explisit analysis the system will neber try bto come to equilibrium state after the incrimentation of a force in the coming interval. It will results that the diffrence between internal force of a system and the external force will never become equal to zero.

But in implicit analysis the sysytem will try get an equilirium stage in each interval when we apply the external force. It will result that the difference between internal force and external force will be more closest to zero.

It finally conclude that explicit analysis will not be ore closes to the true solution where the implicit analysis will be more closes to the true sloution because it used the Newton raphson iteration to make the equilibrium between internal and external force.

Explicit calculation:

We know F= K*U

So U= F/K

We know here K is the function of U; AND U is =U^3+9U^2+4U

d/du= 3U^2+18U+4

step 1:

Where u=0, delta F=1, Delta u is = F/K, U1=u0+u1

From the above we got

u1=0.25

u2=0.365

u3=0.456

From this with the help of an equation f internal = u+u^3/3

We can find the difference of F external and internal

change in f	u1=0.25	U1=0.256	0.001
change in f	u2=0.365	U2=0.381	0.737
change in f	u3=0.456	U3=0.487	0.031

So from the above table we can understand that the external force and internal forece of the system is not in equilbrium.

Implicit analysis

In implicit analysis a newton raphson itreration is added before the additon of external force so in such a way the system will come to close to theequilbrium

The newton rphson iteration is = `delta`u^j+1=(k(u)^j)^-1*R^j

So based on the differnce internal and external force in every interval the above formula will be used to find the iteration value and these value will be added at the end of every step and will make the difference close too the zero.

The iterations will be added until we get the closest solution

From the plot diagram we can understand that the result of implicit is very more near to the true solution but not for explicit.

Conclusion:

Understand the difference between explicit and implicit analysis