In this paper,we develop an advanced computational framework for the topology optimization of orthotropic materials using meshless methods.The approximation function is established based on the improved moving least s...In this paper,we develop an advanced computational framework for the topology optimization of orthotropic materials using meshless methods.The approximation function is established based on the improved moving least squares(IMLS)method,which enhances the efficiency and stability of the numerical solution.The numerical solution formulas are derived using the improved element-free Galerkin(IEFG)method.We introduce the solid isotropic microstructures with penalization(SIMP)model to formulate a mathematical model for topology opti-mization,which effectively penalizes intermediate densities.The optimization problem is defined with the numerical solution formula and volume fraction as constraints.The objective function,which is the minimum value of flexibility,is optimized iteratively using the optimization criterion method to update the design variables efficiently and converge to an optimal solution.Sensitivity analysis is performed using the adjoint method,which provides accurate and efficient gradient information for the optimization algorithm.We validate the proposed framework through a series of numerical examples,including clamped beam,cantilever beam,and simply supported beam made of orthotropic materials.The convergence of the objective function is demonstrated by increasing the number of iterations.Additionally,the stability of the iterative process is analyzed by examining the fluctuation law of the volume fraction.By adjusting the parameters to an appropriate range,we achieve the final optimization results of the IEFG method without the checkerboard phenomenon.Comparative studies between the Element-Free Galerkin(EFG)and IEFG methods reveal that both methods yield consistent optimization results under identical parameter settings.However,the IEFG method significantly reduces computational time,highlighting its efficiency and suitability for orthotropic materials.展开更多
The influence of solid solution treatments on the dissolution of carbides precipitates,the grain size,and the hardness of high strength low expansion alloy were investigated through XRD analysis,microstructure observa...The influence of solid solution treatments on the dissolution of carbides precipitates,the grain size,and the hardness of high strength low expansion alloy were investigated through XRD analysis,microstructure observations,and theoretical computation.It was seen that most primary Mo2C type carbide band dissolved in a temperature range of 1 100-1 150 ℃.When the temperature was over 1 200 ℃,the grain size increased remarkably,which led to the reduction of hardness.展开更多
Solid-phase-sintered Si C-based composites with short carbon fibers（Csf/SSi C） in concentrations ranging from 0 to 10wt% were prepared by pressureless sintering at 2100°C. The phase composition, microstructure,...Solid-phase-sintered Si C-based composites with short carbon fibers（Csf/SSi C） in concentrations ranging from 0 to 10wt% were prepared by pressureless sintering at 2100°C. The phase composition, microstructure, density, and flexural strength of the composites with different Csf contents were investigated. SEM micrographs showed that the Csf distributed in the SSi C matrix homogeneously with some gaps at the fiber/matrix interfaces. The densities of the composites decreased with increasing Csf content. However, the bending strength first increased and then decreased with increasing Csf content, reaching a maximum value of 390 MPa at a Csf content of 5wt%, which was 60 MPa higher than that of SSi C because of the pull-out strengthening mechanism. Notably, Csf was graphitized and damaged during the sintering process because of the high temperature and reaction with boron derived from the sintering additive B4C; this graphitization degraded the fiber strengthening effect.展开更多
1. General Survey The Laboratory of Solid State Microstruc-tures (LSSMS) of Nanjing University islocated in the centre of the historic cityNanjing. It is one of the major labs establi-shed with the approval and specia...1. General Survey The Laboratory of Solid State Microstruc-tures (LSSMS) of Nanjing University islocated in the centre of the historic cityNanjing. It is one of the major labs establi-shed with the approval and special grantfrom the National Planning Commissionof China in 1984, based on the Instituteof Solid State Physics of Nanjing University. The research direction of LSSMS focuses展开更多
The amounts of rare earth in the solid solution in steel 16Mn were determined by means of inductive coupling plasma(ICP)spectroscopy.While the RE/S ratio was less than 1.9,the amounts of rare earth in solid solution w...The amounts of rare earth in the solid solution in steel 16Mn were determined by means of inductive coupling plasma(ICP)spectroscopy.While the RE/S ratio was less than 1.9,the amounts of rare earth in solid solution were not more than 8 ppm,which rised slightly with the increase of the rare earth content in the steel.While the RE/S was more than 1.9,MnS disappeared completely in the steel and the amounts of rare earth in solid solution increased rapidly with the increasing of the rare earth content.The solubility of cerium in steel 16 Mn(St 52)is less than 0.011 wt% at room temperature.The results also indicate that rare earth in solid solution can reduce the amount of pearlite and increase that of ferrite and its mierohardness.The rela- tionship between microhardness(Hv)and the amount of rare earth in solid solution can be expressed by the equation of Hv=117+7 RE(ppm).展开更多
The present paper deals with results of stability/instability of solitary waves with nonzero asymptotic value for a microstructure PDE. By the exact solitary wave solutions and detailed computations, we set up the exp...The present paper deals with results of stability/instability of solitary waves with nonzero asymptotic value for a microstructure PDE. By the exact solitary wave solutions and detailed computations, we set up the explicit expression for the discrimination d′′（c）. Finally, a complete study of orbital stablity/instablity for the explicit exact solutions is given.展开更多
Morphology evolution of prior β grains of laser solid forming （LSF） Ti-xAl-yV （x 11,y 20） alloys from blended elemental powders is investigated. The formation mechanism of grain morphology is revealed by incorpor...Morphology evolution of prior β grains of laser solid forming （LSF） Ti-xAl-yV （x 11,y 20） alloys from blended elemental powders is investigated. The formation mechanism of grain morphology is revealed by incorporating columnar to equiaxed transition （CET） mechanism during solidification. The morphology of prior β grains of LSF Ti-6Al-yV changes from columnar to equiaxed grains with increasing element V content from 4 to 20 wt.-%. This agrees well with CET theoretical prediction. Likewise, the grain morphology of LSF Ti-xAl-2V from blended elemental powders changes from large columnar to small equiaxed with increasing Al content from 2 to 11 wt.-%. The macro-morphologies of LSF Ti-8Al-2V and Ti-11Al-2V from blended elemental powders do not agree with CET predictions. This is caused by the increased disturbance effects of mixing enthalpy with increasing Al content, generated in the alloying process of Ti, Al, and V in the molten pool.展开更多
This study proposes a non-probabilistic reliability-based topology optimization(NRBTO)method based on isogeometric analysis(IGA),considering the structural stiffness performance.In this study,a geometric model was con...This study proposes a non-probabilistic reliability-based topology optimization(NRBTO)method based on isogeometric analysis(IGA),considering the structural stiffness performance.In this study,a geometric model was constructed using non-uniform rational B-splines(NURBS),and the NURBS basis function was used as the shape function of the analytical model.In topology optimization,the classic finite element method(FEM)was replaced by a mesh-independent IGA method.The formulation of isogeometric topology optimization(ITO)based on the solid isotropic microstructures with penalization(SIMP)interpolation model was derived,and a sensitivity analysis was performed using the adjoint method.Considering the uncertainties of material properties and loads,the parameter uncertainty is quantified by interval theory,the propagation analysis is conducted using the interval parametric vertex method,the optimization feature distance is selected as the nonprobabilistic reliability-based index,and a sensitivity analysis is performed on the reliability index to establish a reliability-based topology optimization method based on isogeometric analysis.The method of moving asymptotes(MMA)is used to solve the optimization problem.Several numerical examples were used to verify the method’s effectiveness in practical applications.展开更多
基金supported by the Graduate Student Scientific Research Innovation Project through Research Innovation Fund for Graduate Students in Shanxi Province(Project No.2024KY648).
文摘In this paper,we develop an advanced computational framework for the topology optimization of orthotropic materials using meshless methods.The approximation function is established based on the improved moving least squares(IMLS)method,which enhances the efficiency and stability of the numerical solution.The numerical solution formulas are derived using the improved element-free Galerkin(IEFG)method.We introduce the solid isotropic microstructures with penalization(SIMP)model to formulate a mathematical model for topology opti-mization,which effectively penalizes intermediate densities.The optimization problem is defined with the numerical solution formula and volume fraction as constraints.The objective function,which is the minimum value of flexibility,is optimized iteratively using the optimization criterion method to update the design variables efficiently and converge to an optimal solution.Sensitivity analysis is performed using the adjoint method,which provides accurate and efficient gradient information for the optimization algorithm.We validate the proposed framework through a series of numerical examples,including clamped beam,cantilever beam,and simply supported beam made of orthotropic materials.The convergence of the objective function is demonstrated by increasing the number of iterations.Additionally,the stability of the iterative process is analyzed by examining the fluctuation law of the volume fraction.By adjusting the parameters to an appropriate range,we achieve the final optimization results of the IEFG method without the checkerboard phenomenon.Comparative studies between the Element-Free Galerkin(EFG)and IEFG methods reveal that both methods yield consistent optimization results under identical parameter settings.However,the IEFG method significantly reduces computational time,highlighting its efficiency and suitability for orthotropic materials.
文摘The influence of solid solution treatments on the dissolution of carbides precipitates,the grain size,and the hardness of high strength low expansion alloy were investigated through XRD analysis,microstructure observations,and theoretical computation.It was seen that most primary Mo2C type carbide band dissolved in a temperature range of 1 100-1 150 ℃.When the temperature was over 1 200 ℃,the grain size increased remarkably,which led to the reduction of hardness.
基金financially supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20110006110025)the National Natural Science Foundation of China(No.U1134102)
文摘Solid-phase-sintered Si C-based composites with short carbon fibers（Csf/SSi C） in concentrations ranging from 0 to 10wt% were prepared by pressureless sintering at 2100°C. The phase composition, microstructure, density, and flexural strength of the composites with different Csf contents were investigated. SEM micrographs showed that the Csf distributed in the SSi C matrix homogeneously with some gaps at the fiber/matrix interfaces. The densities of the composites decreased with increasing Csf content. However, the bending strength first increased and then decreased with increasing Csf content, reaching a maximum value of 390 MPa at a Csf content of 5wt%, which was 60 MPa higher than that of SSi C because of the pull-out strengthening mechanism. Notably, Csf was graphitized and damaged during the sintering process because of the high temperature and reaction with boron derived from the sintering additive B4C; this graphitization degraded the fiber strengthening effect.
文摘1. General Survey The Laboratory of Solid State Microstruc-tures (LSSMS) of Nanjing University islocated in the centre of the historic cityNanjing. It is one of the major labs establi-shed with the approval and special grantfrom the National Planning Commissionof China in 1984, based on the Instituteof Solid State Physics of Nanjing University. The research direction of LSSMS focuses
文摘The amounts of rare earth in the solid solution in steel 16Mn were determined by means of inductive coupling plasma(ICP)spectroscopy.While the RE/S ratio was less than 1.9,the amounts of rare earth in solid solution were not more than 8 ppm,which rised slightly with the increase of the rare earth content in the steel.While the RE/S was more than 1.9,MnS disappeared completely in the steel and the amounts of rare earth in solid solution increased rapidly with the increasing of the rare earth content.The solubility of cerium in steel 16 Mn(St 52)is less than 0.011 wt% at room temperature.The results also indicate that rare earth in solid solution can reduce the amount of pearlite and increase that of ferrite and its mierohardness.The rela- tionship between microhardness(Hv)and the amount of rare earth in solid solution can be expressed by the equation of Hv=117+7 RE(ppm).
基金Research is supported by Science Foundation of the Education Commission of Beijing(No.KM201210017008)National Natural Science Foundation of China under Grants(No.61403034)Youth Foundation of Beijing Institute of Petrolchemical Technology(No.N10-04)
文摘The present paper deals with results of stability/instability of solitary waves with nonzero asymptotic value for a microstructure PDE. By the exact solitary wave solutions and detailed computations, we set up the explicit expression for the discrimination d′′（c）. Finally, a complete study of orbital stablity/instablity for the explicit exact solutions is given.
基金supported by the State Key Laboratory of Solidification Processing in NWPU (Nos.SKLSP201102 and 06-BZ-2010)Lthe China Postdoc-toral Science Foundation (No.20100470040)the National Natural Science Foundation of China (No.50871089)
文摘Morphology evolution of prior β grains of laser solid forming （LSF） Ti-xAl-yV （x 11,y 20） alloys from blended elemental powders is investigated. The formation mechanism of grain morphology is revealed by incorporating columnar to equiaxed transition （CET） mechanism during solidification. The morphology of prior β grains of LSF Ti-6Al-yV changes from columnar to equiaxed grains with increasing element V content from 4 to 20 wt.-%. This agrees well with CET theoretical prediction. Likewise, the grain morphology of LSF Ti-xAl-2V from blended elemental powders changes from large columnar to small equiaxed with increasing Al content from 2 to 11 wt.-%. The macro-morphologies of LSF Ti-8Al-2V and Ti-11Al-2V from blended elemental powders do not agree with CET predictions. This is caused by the increased disturbance effects of mixing enthalpy with increasing Al content, generated in the alloying process of Ti, Al, and V in the molten pool.
基金supported by the National Natural Science Foundation of China(Grant Nos.12472114,12132001,52192632)the Defense Industrial Technology Development Program(Grant No.JCKY2023204A005)the Aeronautical Science Foundation of China(Grant No.20240029051001).
文摘This study proposes a non-probabilistic reliability-based topology optimization(NRBTO)method based on isogeometric analysis(IGA),considering the structural stiffness performance.In this study,a geometric model was constructed using non-uniform rational B-splines(NURBS),and the NURBS basis function was used as the shape function of the analytical model.In topology optimization,the classic finite element method(FEM)was replaced by a mesh-independent IGA method.The formulation of isogeometric topology optimization(ITO)based on the solid isotropic microstructures with penalization(SIMP)interpolation model was derived,and a sensitivity analysis was performed using the adjoint method.Considering the uncertainties of material properties and loads,the parameter uncertainty is quantified by interval theory,the propagation analysis is conducted using the interval parametric vertex method,the optimization feature distance is selected as the nonprobabilistic reliability-based index,and a sensitivity analysis is performed on the reliability index to establish a reliability-based topology optimization method based on isogeometric analysis.The method of moving asymptotes(MMA)is used to solve the optimization problem.Several numerical examples were used to verify the method’s effectiveness in practical applications.
