On a class of optimization problems for framed structures

A unified treatment is presented for four types of problems on limit analysis of framed structures and related design problems. With the use of the lower bound theorem in plasticity these problems are formulated as standard linear programming problems. Two significant improvements are made. The new formulation of the design problems reduces the number of equations in the resulting linear program. An improved simplex algorithm for large and sparse linear programs is employed. The formulational and algorithmic improvements provide large capacity and high efficiency that are indispensable for computational analysis and design of large and complex structures.