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Objective functions for nonlinear structural analysis
An objective function that is suitable for both stable and
unstable equilibrium states since it is guaranteed to assume a
relative minimum at any equilibrium state is presented. The
objective function, which is the inner product of the equations
of equilibrium (algorithm 2), is compared with another objective
function which, for a static problem, is the total potential energy
(algorithm 3). The method of formulating the mathematical model
for algorithm 2 is presented in detail.
Algorithm 2 is found to be less efficient than algorithm 3.
However, it is d~10nstrated that algorithm 2 is able to solve for
equilibrium states on either the fundamental path or a bifurcation
path. Hence algorithm 2 is a powerful tool for nonlinear structural
analysis since it is able to predict the existence of limit and
bifurcation points and to determine post-buckled equilibrium states.
Also addressed are the methods of formulating mathematical
models for nonlinear structural analysis. A comparison of the
methods of integrating the equations of motion for nonlinear
dynamics problems and the selection of an appropriate time step
for the time integration schemes are presented.