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Structural Engineering and Mechanics
  Volume 14, Number 4, October 2002, pages 473-489

A matrix displacement formulation for minimum weight design of frames
Engin Orakdoen

     A static linear programming formulation for minimum weight design of frames that is based on a matrix displacement method is presented in this paper. According to elementary theory of plasticity, minimum weight design of frames can be carried out by using only the equilibrium equations, because the system is statically determinate when at an incipient collapse state. In the present formulation, a statically determinate released frame is defined by introducing hinges into the real frame and the bending moments in yield constraints are expressed in terms of unit hinge rotations and the external loads respectively, by utilizing the matrix displacement method. Conventional Simplex algorithm with some modifications is
utilized for the solution of linear programming problem. As the formulation is based on matrix displacement method, it may be easily adopted to the weight optimization of frames with displacement and deformation limitations. Four illustrative examples are also given for comparing the results to those obtained in previous studies.
Key Words
    minimum weight design; optimal plastic design; linear programming.
Faculty of Civil Engineering, Technical University of Istanbul, 80626, Maslak, Istanbul, Turkey

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