5003 Lectures - Faculty of Engineering and Applied Science

E5003 - Ship Structures I 157
© C.G. Daley
Gaussian elimination is one common method. We
can assume that if we have N equations in N
unknowns that we can solve it.
To solve these in Maple (see 3bar_frame.pdf or
3bar_frame.mw), we would just expand the matrix
expression into a set of 12 simultaneous equations;
Maple will solve these equations in either
numerical or algebraic form, giving expressions for
all results in terms of the variable. For example,
for this problem, Maple will give;
Q1: With the above solution for force and
deflections at the nodes (the dofs), how would we
find the stresses in each member?
A1: To find the stresses we have to return to the
individual beams. We use the global stiffness
matrix of a single member. For example, for the
cross beam in the previous example (beam 2), we
find the member forces as follows;