A new approach for the solution of truss shape and topology optimization problems under local and global stability constraints is proposed.By employing the cross sectional areas of each bar and some shape parameters a...A new approach for the solution of truss shape and topology optimization problems under local and global stability constraints is proposed.By employing the cross sectional areas of each bar and some shape parameters as topology design variables,the difficulty arising from the jumping of buckling length phenomenon can be easily overcome without the necessity of introduc- ing the overlapping bars into the initial ground structure.Therefore computational efforts can be saved for the solution of this kind of problem.By modifying the elements of the stiffness matrix using Sigmoid function,the continuity of the objective and constraint functions with respect to shape design parameters can be restored to some extent.Some numerical examples demonstrate the effectiveness of the proposed method.展开更多
In the present paper,a so-called epsilon-continuation approach is proposed for the solution of singular optimum in truss topology optimization problems.This approach is an improved version of the epsilon-relaxed appro...In the present paper,a so-called epsilon-continuation approach is proposed for the solution of singular optimum in truss topology optimization problems.This approach is an improved version of the epsilon-relaxed approach developed by the authors previously.In the proposed approach, we start the optimization process from a relaxation parameter with a relatively large value and obtain a solution by applying the epsilon-relaxed approach.Then we decrease the value of the relaxation parameter by a small amount and choose the optimal solution found from the previous optimization process as the initial design for the next optimization.This continuation process is continued until a small termination value of the relaxation parameter is reached.Convergence analysis of the proposed approach is also presented.Numerical examples show that this approach can alleviate the dependence of the final solution on the initial choice of the design variable and enhance the probability of finding the singular optimum from rather arbitrary initial designs.展开更多
We discuss semiconvergence of the extrapolated iterative methods for solving singular linear systems. We obtain the upper bounds and the optimum convergence factor of the extrapolation method as well as its associated...We discuss semiconvergence of the extrapolated iterative methods for solving singular linear systems. We obtain the upper bounds and the optimum convergence factor of the extrapolation method as well as its associated optimum extrapolation parameter. Numerical examples are given to illustrate the theoretical results.展开更多
This paper proposes a global topology optimization algorithm based on subset simulation for the singular optimum problem subject to stress constraints of trusses. The constraints are handled by a fitness function whic...This paper proposes a global topology optimization algorithm based on subset simulation for the singular optimum problem subject to stress constraints of trusses. The constraints are handled by a fitness function which reflects their degree of violation. The rational and global topology results are guaranteed by the judgment of the samples’ rationality and the Metropolis-Hasting algorithm. Three examples show that the established method can quickly reduce the searching region to the feasible region and converge to the global optimum precisely enough for the singular optimum problem.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos.200112023 and 10032030).
文摘A new approach for the solution of truss shape and topology optimization problems under local and global stability constraints is proposed.By employing the cross sectional areas of each bar and some shape parameters as topology design variables,the difficulty arising from the jumping of buckling length phenomenon can be easily overcome without the necessity of introduc- ing the overlapping bars into the initial ground structure.Therefore computational efforts can be saved for the solution of this kind of problem.By modifying the elements of the stiffness matrix using Sigmoid function,the continuity of the objective and constraint functions with respect to shape design parameters can be restored to some extent.Some numerical examples demonstrate the effectiveness of the proposed method.
基金The project supported by the National Natural Science Foundation of China (10102003,10032010 and 10032030)
文摘In the present paper,a so-called epsilon-continuation approach is proposed for the solution of singular optimum in truss topology optimization problems.This approach is an improved version of the epsilon-relaxed approach developed by the authors previously.In the proposed approach, we start the optimization process from a relaxation parameter with a relatively large value and obtain a solution by applying the epsilon-relaxed approach.Then we decrease the value of the relaxation parameter by a small amount and choose the optimal solution found from the previous optimization process as the initial design for the next optimization.This continuation process is continued until a small termination value of the relaxation parameter is reached.Convergence analysis of the proposed approach is also presented.Numerical examples show that this approach can alleviate the dependence of the final solution on the initial choice of the design variable and enhance the probability of finding the singular optimum from rather arbitrary initial designs.
基金supported by the National Natural Science Foundation of China under grant 10371056the Foundation for the Authors of the National Excellent Doctoral Thesis Award of China under grant 200720+1 种基金the Natural Science Foundation of Jiangsu Province under grant BK2006725the College Natural Science Foundation of Jiangsu Province under grant 05KJB110062
文摘We discuss semiconvergence of the extrapolated iterative methods for solving singular linear systems. We obtain the upper bounds and the optimum convergence factor of the extrapolation method as well as its associated optimum extrapolation parameter. Numerical examples are given to illustrate the theoretical results.
基金supported by the National Natural Science Foundation of China (Grant No. 50875213)
文摘This paper proposes a global topology optimization algorithm based on subset simulation for the singular optimum problem subject to stress constraints of trusses. The constraints are handled by a fitness function which reflects their degree of violation. The rational and global topology results are guaranteed by the judgment of the samples’ rationality and the Metropolis-Hasting algorithm. Three examples show that the established method can quickly reduce the searching region to the feasible region and converge to the global optimum precisely enough for the singular optimum problem.
