The guide-weight method is introduced to solve two kinds of topology optimization problems with multiple loads in this paper.The guide-weight method and its Lagrange multipliers' solution methods are presented fir...The guide-weight method is introduced to solve two kinds of topology optimization problems with multiple loads in this paper.The guide-weight method and its Lagrange multipliers' solution methods are presented first,and the Lagrange multipliers' soution method of problems with multiple constraints is improved by the dual method.Then the iterative formulas of the guide-weight method for topology optimization problems of minimum compliance and minimum weight are derived and coresponding numerical examples are calculated.The results of the examples exhibits that when the guide-weight method is used to solve topology optimization problems with multiple loads,it works very well with simple iterative formulas,and has fast convergence and good solution.After comparison with the results calculated by the SCP method in Ansys,one can conclude that the guide-weight method is an effective method and it provides a new way for solving topology optimization problems.展开更多
The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem tu- △u=au-b（x）up in Ω×R＋,u（0）=u0,u（t ）｜ Ω=0, as p→ ＋∞, where Ω is a bounded domain, and b（x...The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem tu- △u=au-b（x）up in Ω×R＋,u（0）=u0,u（t ）｜ Ω=0, as p→ ＋∞, where Ω is a bounded domain, and b（x） is a nonnegative function. The authors deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards fully describe its long time behavior.展开更多
基金supported in part by the National Natural Science Founda-tion of China (Grant No 51075222)the Fund of State Key Laboratory of Tribology (Grant No SKLT10C02)the National Key Scientific and Technological Project (Grant No 2010ZX04004-116)
文摘The guide-weight method is introduced to solve two kinds of topology optimization problems with multiple loads in this paper.The guide-weight method and its Lagrange multipliers' solution methods are presented first,and the Lagrange multipliers' soution method of problems with multiple constraints is improved by the dual method.Then the iterative formulas of the guide-weight method for topology optimization problems of minimum compliance and minimum weight are derived and coresponding numerical examples are calculated.The results of the examples exhibits that when the guide-weight method is used to solve topology optimization problems with multiple loads,it works very well with simple iterative formulas,and has fast convergence and good solution.After comparison with the results calculated by the SCP method in Ansys,one can conclude that the guide-weight method is an effective method and it provides a new way for solving topology optimization problems.
基金Project supported by Fundaco para a Ciência e a Tecnologia (FCT) (No. PEst OE/MAT/UI0209/2011)supported by an FCT grant (No. SFRH/BPD/69314/201)
文摘The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem tu- △u=au-b（x）up in Ω×R＋,u（0）=u0,u（t ）｜ Ω=0, as p→ ＋∞, where Ω is a bounded domain, and b（x） is a nonnegative function. The authors deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards fully describe its long time behavior.
