The purpose of this paper is to investigate the application of topology description function （TDF） in material design. Using TDF to describe the topology of the microstructure, the formulation and the solving techni...The purpose of this paper is to investigate the application of topology description function （TDF） in material design. Using TDF to describe the topology of the microstructure, the formulation and the solving technique of the design problem of materials with prescribed mechanical properties are presented. By presenting the TDF as the sum of a series of basis functions determined by parameters, the topology optimization of material microstructure is formulated as a size optimization problem whose design variables are parameters of TDF basis functions and independent of the mesh of the design domain. By this method, high quality topologies for describing the distribution of constituent material in design domain can be obtained and checkerboard problem often met in the variable density method is avoided. Compared with the conventional level set method, the optimization problem can be solved simply by existing optimization techniques without the process to solve the ＇Hamilton-Jacobi-type＇ equation by the difference method. The method proposed is illustrated with two 2D examples. One gives the unit cell with positive Poisson＇s ratio, the other with negative Poisson＇s ratio. The examples show the method based on TDF is effective for material design.展开更多
This paper presents a functional language for the unambiguous description of digital circuits,a me- thod and algorithms to obtain a standard-cell layout,and a comparative evaluation of the developed func- tional stand...This paper presents a functional language for the unambiguous description of digital circuits,a me- thod and algorithms to obtain a standard-cell layout,and a comparative evaluation of the developed func- tional standard-cell placement technique.The presented placement scheme is different from traditional methods because the complete layout geometry is specified and constructed automatically from a function- al description.The construction relies on a translation that combines the simplicity of standard-cells with the elegance of functional programming.An evaluation of the method introduced shows that the quality of the resulting placement is close to the results achieved with simulated annealing while the computation time is significantly less.Furthermore,the evaluation suggests to employ the functional placement me- thod in conjunction with low-temperature simulated annealing for running-time reduction and improved- results.展开更多
The purpose of this paper is to generalize the (classical) Bochner theorem to the case where Radon probability measures are defined on the weak dual spaces of locally convex spaces. We also compare our result with oth...The purpose of this paper is to generalize the (classical) Bochner theorem to the case where Radon probability measures are defined on the weak dual spaces of locally convex spaces. We also compare our result with other topological descriptions of characteristic functionals of probability measures on other infinite dimensional spaces.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10332010) the Innovative Research Team Program (No. 10421202) the National Basic Research Program of China (No. 2006CB601205) and the Program for New Century Excellent Talents in Universities of China (2004).
文摘The purpose of this paper is to investigate the application of topology description function （TDF） in material design. Using TDF to describe the topology of the microstructure, the formulation and the solving technique of the design problem of materials with prescribed mechanical properties are presented. By presenting the TDF as the sum of a series of basis functions determined by parameters, the topology optimization of material microstructure is formulated as a size optimization problem whose design variables are parameters of TDF basis functions and independent of the mesh of the design domain. By this method, high quality topologies for describing the distribution of constituent material in design domain can be obtained and checkerboard problem often met in the variable density method is avoided. Compared with the conventional level set method, the optimization problem can be solved simply by existing optimization techniques without the process to solve the ＇Hamilton-Jacobi-type＇ equation by the difference method. The method proposed is illustrated with two 2D examples. One gives the unit cell with positive Poisson＇s ratio, the other with negative Poisson＇s ratio. The examples show the method based on TDF is effective for material design.
文摘This paper presents a functional language for the unambiguous description of digital circuits,a me- thod and algorithms to obtain a standard-cell layout,and a comparative evaluation of the developed func- tional standard-cell placement technique.The presented placement scheme is different from traditional methods because the complete layout geometry is specified and constructed automatically from a function- al description.The construction relies on a translation that combines the simplicity of standard-cells with the elegance of functional programming.An evaluation of the method introduced shows that the quality of the resulting placement is close to the results achieved with simulated annealing while the computation time is significantly less.Furthermore,the evaluation suggests to employ the functional placement me- thod in conjunction with low-temperature simulated annealing for running-time reduction and improved- results.
文摘The purpose of this paper is to generalize the (classical) Bochner theorem to the case where Radon probability measures are defined on the weak dual spaces of locally convex spaces. We also compare our result with other topological descriptions of characteristic functionals of probability measures on other infinite dimensional spaces.
