In this thesis, mechanical design problem in which shape of two-dimensional truss structures play the role of design variables are formulated, analyzed, and solved numerically. A prototype problem with stress constraint in the structure is formulated in a variational form to illustrate important factor in problem formulation. The material derivative idea from continuum mechanics is imployed for calculation of the first order variation of a functional defined of a domain. This technique enables one to evaluate the first order variation of the functional over a fixed domain or its boundary. The first order variation of the functional obtained by this technic contains variation of the state variable of the problem, which is not explicitly known and, hence, not calculable. The adjoint variable technique of design sensitivity analysis is used to eliminate this state variable dependency of the first order variation of the functional. As a result, one obtains a computable expression for the effect of boundary shape variation of the functional. These results can be used to adapt generalized optimization algorithms for interactive shape optimal design. Two two-dimensional truss structures are presented to illustrate use of the method.
