Problem 3B Solving using Finite Element Method
The taut elastic string was plotted in COMSOL in the 1D PDE Coefficient form
For the sub domain settings coefficients ea and c were taken to be 1 while the rest were
set at zero. This defined the PDE which must be satisfied by the solution.
The initial condition in this problem, u(x,0), is equal to a piecewise function this time
instead of a constant. In order to set the initial condition, this piecewise function must be
defined in COMSOL. It was defined using a table under the Other-Functions menu and
then applied as the initial condition. The table and its corresponding plot are shown
below.
Problem 3B Solving using Finite Element Method
Problem 3B Solving using Finite Element Method
The problem description stated that u(0,t)=0 and u(1,t)=0 therefore the boundary settings
for COMSOL were as follows:
The geometry was then meshed. Using time dependent solver parameters, the time
interval was changed to 0 to 2s with .05s time increments. The solution was animated for
the time frame and shows how when the string is held at both ends it rises upward
initially and then deflects downward. As seen at t=0, the solution is in the form of the
piecewise function and peaks at a value that appears to be close to .1 which was the
maximum deflection according to the problem description. The following graphs depict
the function u(x, t) behavior between 0s and 2s.
Problem 3B Solving using Finite Element Method
Problem 3B Solving using Finite Element Method
Problem 3B Solving using Finite Element Method
Problem 3B Solving using Finite Element Method