Design of linkage mechanisms of partially rigid frames using limit analysis with quadratic yield functions

A method is presented for generating linkage mechanisms consisting of frame members. A quadratic programming problem is solved to obtain an infinitesimal mechanism allowing a hinge rotating about an axis in arbitrarily inclined direction. The problem is equivalent to a plastic limit analysis problem with quadratic yield functions with respect to member-end moments and axial force. The directions of hinges are obtained from the ratios of member-end moments along the local axes. A finite mechanism is generated by carrying out geometrically nonlinear analysis and adding hinges, if necessary. Effectiveness of the proposed method is demonstrated through examples of 3-dimensional mechanisms.