  This work aims to provide standard formulations for direct minimization
approaches on various types of static problems of continuum mechanics.
Particularly, form-finding problems of tension structures are discussed in the
first half and the large deformation problems of continuum bodies are discussed
in the last half. In the first half, as the standards of iterative direct
minimization strategies, two types of simple recursive methods are presented,
namely the two-term method and the three-term method. The dual estimate is also
introduced as a powerful means of involving equally constraint conditions into
minimization problems. As examples of direct minimization approaches on usual
engineering issues, some form finding problems of tension structures which can
be solved by the presented strategies are illustrated. Additionally, it is
pointed out that while the two-term method sometimes becomes useless, the
three-term method always provides remarkable rate of global convergence
efficiency. Then, to show the potential ability of the three-term method, in
the last part of this work, some principle of virtual works which usually
appear in the continuum mechanics are approximated and discretized in a common
manner, which are suitable to be solved by the three-term method. Finally, some
large deformation analyses of continuum bodies which can be solved by the
three-term method are presented.
