Question

what is the difference between analytical solution and FEA??

Answer 1

Analytical solutions are the exact solution to a problem. It can be be used to get accurate solutions in simple systems.

The FE solutions are approximate because it relies on discrete points rather than continuum. It is applied when the system gets complex. Numerical methods are used to solve the equations in such problems.

For example:

1. Numerical methods: Analytical solution to tan(x) = x is not possible to find analytically. In this case we take help of computer to solve the problem. One way is to iterate through different values of x in the range [-2pi , 2pi] until tan(x) - x is negligible and show the value of x.

Another example is th find the integral of a function f(x) in the range [a,b]. If the function f(x) is hard to solve analytically, we might use trapezoidal method or simpsons method are used to find the solution.

In FEA problems, the solution to the differential equations are solved using such methods to find the solution of the problem.

2. Example of heat conduction:

One can solve this problem analytically using the conduction equation. It can also be solved using computers where boundary conditions are given and differential equations are solved and we find a solution. The advantage of FEA being that solutions to more complex problems can be found with good accuracy.