Design optimization for truss structures under elasto-plastic loading condition
In this paper, a method for the design optimization of elasto-plastic truss structures is proposed based on parametric variational principles (PVPs). The optimization aims to find the minimum weight/volume solution under the constraints of allowable node displacements. The design optimization is a formulation of mathematical programming with equilibrium constraints (MPECs). To overcome the numerical difficulties of the complementary constraints in optimization, an iteration process, comprising a quadratic programming (QP) and an updating process, is employed as the optimization method. Furthermore, the elasto-plastic buckling of truss members is considered as a constraint in design optimization. A combinational optimization strategy is proposed for the displacement constraints and the buckling constraint, which comprises the method mentioned above and an optimal criterion. Three numerical examples are presented to show the validity of the methods proposed.
Key wordsparametric variational principles elasto-plasticity truss structure optimization elasto-plasticity buckling
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- Chan, S.L. and Chui, P.P.T., Non-linear Static and Cyclic Analysis of Steel Frames with Semi-rigid Connections, Amsterdam, Lausanne: Elsevier, 2000.Google Scholar
- Toklu, Y.C., On the solution of a minimum weight elastoplastic problem involving displacement and complementarity constraints, Computers methods in applied mechanics and engineering, Vol.174, 1999, 107–120.Google Scholar
- Zhong, W.X., Zhang, H.W. and Wu, C.W., Parametric Variational Principles and Their Engineering Application, Beijing: Science Press, 1997 (in Chinese).Google Scholar
- Zhong, W.X. and Zhang, H.W., Mixed Energy method for solution of quadratic programming problems and elastic-plastic analysis of truss structures, Acta Mechanica Solida Sinica, Vol.23, No.2, 2002, 125–132 (in Chinese).Google Scholar
- Fletcher, R., Leyffer, S., Scholtes, S. and Ralph, D., Local convergence of SQP methods for mathematical programming problems with equilibrium constraints, Dundee Numerical Analysis Report NA/209, 2002.Google Scholar
- Fletcher, R. and Leyffer, S., Numerical experience with solving MPECs as NLPs, University of Dundee Report NA/210, 2002.Google Scholar