We sttidy the problem of scheduling n jobs on m parallel bounded batch machines to minimize the sum of squared machine loads. Each batch contains at most B jobs, and the processing time of a batch is equal to the long...We sttidy the problem of scheduling n jobs on m parallel bounded batch machines to minimize the sum of squared machine loads. Each batch contains at most B jobs, and the processing time of a batch is equal to the longest processing time of the jobs in this batch. We prove this problem to be NP-hard. Furthermore, we present a polynomial time approximation scheme （PTAS） and a fully polynomial time approximation scheme （FPTAS） for this problem.展开更多
Naturally deposited soils are always found in the complex three-dimensional stress state.Constitutive models developed for modeling the three-dimensional mechanical behavior of soils should obey the basic laws of ther...Naturally deposited soils are always found in the complex three-dimensional stress state.Constitutive models developed for modeling the three-dimensional mechanical behavior of soils should obey the basic laws of thermo-mechanical principles.Based on the incremental dissipation function,a new deviatoric shift stress is derived and then introduced into the existing constitutive models to describe the yield behavior in the deviatoric plane for geomaterials.By adopting the proposed shift stress,the relationship between dissipative stress tensors and true stress tensors can be established.Therefore,the threedimensional plastic strain can be calculated reasonably through the associated flow rule in the three-dimensional dissipative stress space.At the same time,three methods that are conventionally adopted for generalizing constitutive models to model the three-dimensional stress-strain relationships are examined under the thermo-mechanical framework.The TS(transformed stress)method is shown to obey the thermo-mechanical rules and the TS space adopted in TS method is actually a translational three-dimensional dissipative stress space.However,it is illustrated that the other two approaches,the method of using failure criterion directly and the method of using g()function,violate the basic rules of thermo-mechanical theories although they may bring convenience and simplicity to numerical analysis for geotechnical engineering.Comparison between model predictions and experimental data confirms the validity of the proposed three-dimensional dissipative stress space.展开更多
文摘We sttidy the problem of scheduling n jobs on m parallel bounded batch machines to minimize the sum of squared machine loads. Each batch contains at most B jobs, and the processing time of a batch is equal to the longest processing time of the jobs in this batch. We prove this problem to be NP-hard. Furthermore, we present a polynomial time approximation scheme （PTAS） and a fully polynomial time approximation scheme （FPTAS） for this problem.
基金supported by the National Natural Science Foundation of China (Grants Nos. 11072016,51179003,11272031,51209002)
文摘Naturally deposited soils are always found in the complex three-dimensional stress state.Constitutive models developed for modeling the three-dimensional mechanical behavior of soils should obey the basic laws of thermo-mechanical principles.Based on the incremental dissipation function,a new deviatoric shift stress is derived and then introduced into the existing constitutive models to describe the yield behavior in the deviatoric plane for geomaterials.By adopting the proposed shift stress,the relationship between dissipative stress tensors and true stress tensors can be established.Therefore,the threedimensional plastic strain can be calculated reasonably through the associated flow rule in the three-dimensional dissipative stress space.At the same time,three methods that are conventionally adopted for generalizing constitutive models to model the three-dimensional stress-strain relationships are examined under the thermo-mechanical framework.The TS(transformed stress)method is shown to obey the thermo-mechanical rules and the TS space adopted in TS method is actually a translational three-dimensional dissipative stress space.However,it is illustrated that the other two approaches,the method of using failure criterion directly and the method of using g()function,violate the basic rules of thermo-mechanical theories although they may bring convenience and simplicity to numerical analysis for geotechnical engineering.Comparison between model predictions and experimental data confirms the validity of the proposed three-dimensional dissipative stress space.
