Modern additive manufacturing processes enable fabricating architected cellular materials of complex shape,which can be used for different purposes.Among them,lattice structures are increasingly used in applications r...Modern additive manufacturing processes enable fabricating architected cellular materials of complex shape,which can be used for different purposes.Among them,lattice structures are increasingly used in applications requiring a compromise among lightness and suited mechanical properties,like improved energy absorption capacity and specific stiffness-to-weight and strength-to-weight ratios.A dedicated modeling strategy to assess the energy absorption capacity of lattice structures under uni-axial compression loading is presented in this work.The numerical model is developed in a non-linear framework accounting for the strain rate effect on the mechanical responses of the lattice structure.Four geometries,i.e.,cubic body centered cell,octet cell,rhombic-dodecahedron and truncated cuboctahedron 2+,are investigated.Specifically,the influence of the relative density of the representative volume element of each geometry,the strain-rate dependency of the bulk material and of the presence of the manufacturing process-induced geometrical imperfections on the energy absorption capacity of the lattice structure is investigated.The main outcome of this study points out the importance of correctly integrating geometrical imperfections into the modeling strategy when shock absorption applications are aimed for.展开更多
As a new type of lightweight structure,metallic lattice structure has higher stiffness and strength to weight ratio.To freely obtain 316L lattice structures with designed cell structure and adjustable porosity,additiv...As a new type of lightweight structure,metallic lattice structure has higher stiffness and strength to weight ratio.To freely obtain 316L lattice structures with designed cell structure and adjustable porosity,additive manufacturing combined with investment casting was conducted to fabricate the 316L lattice structures with Kelvin cell.The compression simulation of 316L lattice structures with different porosities was carried out by using the finite element method.The numerical simulation results were verified by compression experiment,and the simulated results were consistent with the compression tests.The compressive mechanical properties of 316L lattice structures are directly related to porosity and independent of strut diameters.The 316L lattice structures with Kelvin cell have a smooth stress-strain curve and obvious plastic platform,and the hump stress-strain curves are avoided.展开更多
Bio-inspired porous metallic scaffolds have tremendous potential to be used as artificial bone substitutes.In this work,a radially graded lattice structure (RGLS),which mimics the structures of natural human bones,was...Bio-inspired porous metallic scaffolds have tremendous potential to be used as artificial bone substitutes.In this work,a radially graded lattice structure (RGLS),which mimics the structures of natural human bones,was designed and processed by laser powder bed fusion of martensitic Ti-rich TiNi powder.The asymmetric tension-compression behaviour,where the compressive strength is significantly higher than the tensile strength,is observed in this Ti-rich TiNi material,which echoes the mechanical behaviour of bones.The morphologies,mechanical properties,deformation behaviour,and biological compatibility of RGLS samples were characterised and compared with those in the uniform lattice structure.Both the uniform and RGLS samples achieve a relative density higher than 99%.The graded porosities and pore sizes in the RGLS range from 40%-80% and 330-805 µm,respectively,from the centre to the edge.The chemical etching has significantly removed the harmful partially-melted residual powder particles on the lattice struts.The compressive yield strength of RGLS is 71.5 MPa,much higher than that of the uniform sample (46.5 MPa),despite having a similar relative density of about 46%.The calculated Gibson-Ashby equation and the deformation behaviour simulation by finite element suggest that the dense outer regions with high load-bearing capability could sustain high applied stress,improving the overall strength of RGLS significantly.The cell proliferation study suggests better biological compatibility of the RGLS than the uniform structures.The findings highlight a novel strategy to improve the performance of additively manufactured artificial implants by bio-inspiration.展开更多
Lattice structures have drawn much attention in engineering applications due to their lightweight and multi-functional properties.In this work,a mathematical design approach for functionally graded(FG)and helicoidal l...Lattice structures have drawn much attention in engineering applications due to their lightweight and multi-functional properties.In this work,a mathematical design approach for functionally graded(FG)and helicoidal lattice structures with triply periodic minimal surfaces is proposed.Four types of lattice structures including uniform,helicoidal,FG,and combined FG and helicoidal are fabricated by the additive manufacturing technology.The deformation behaviors,mechanical properties,energy absorption,and acoustic properties of lattice samples are thoroughly investigated.The load-bearing capability of helicoidal lattice samples is gradually improved in the plateau stage,leading to the plateau stress and total energy absorption improved by over 26.9%and 21.2%compared to the uniform sample,respectively.This phenomenon was attributed to the helicoidal design reduces the gap in unit cells and enhances fracture resistance.For acoustic properties,the design of helicoidal reduces the resonance frequency and improves the peak of absorption coefficient,while the FG design mainly influences the peak of absorption coefficient.Across broad range of frequency from 1000 to 6300 Hz,the maximum value of absorption coefficient is improved by18.6%-30%,and the number of points higher than 0.6 increased by 55.2%-61.7%by combining the FG and helicoidal designs.This study provides a novel strategy to simultaneously improve energy absorption and sound absorption properties by controlling the internal architecture of lattice structures.展开更多
Diamond tools with orderly arrangements of diamond grits have drawn considerable attention in the machining field owing to their outstanding advantages of high sharpness and long service life.This diamond super tool,a...Diamond tools with orderly arrangements of diamond grits have drawn considerable attention in the machining field owing to their outstanding advantages of high sharpness and long service life.This diamond super tool,as well as the manufacturing equipment,has been unavailable to Chinese enterprises for a long time due to patents.In this paper,a diamond blade segment with a 3D lattice of diamond grits was additively manufactured using a new type of cold pressing equipment(AME100).The equipment,designed with a rotary working platform and 16 molding stations,can be used to additively manufacture segments with diamond grits arranged in an orderly fashion,layer by layer;under this additive manufacturing process,at least 216000 pcs of diamond green segments with five orderly arranged grit layers can be produced per month.The microstructure of the segment was observed via SEM and the diamond blade fabricated using these segments was compared to other commercial cutting tools.The experimental results showed that the 3D lattice of diamond grits was formed in the green segment.The filling rate of diamond grits in the lattice could be guaranteed to be above 95%;this is much higher than the 90%filling rate of the automatic array system(ARIX).When used to cut stone,the cutting amount of the blade with segments made by AME100 is two times that of ordinary tools,with the same diamond concentration.When used to dry cut reinforced concrete,its cutting speed is 10%faster than that of ARIX.Under wet cutting conditions,its service life is twice that of ARIX.By applying the machine vision online inspection system and a special needle jig with a negative pressure system,this study developed a piece of additive manufacturing equipment for efficiently fabricating blade segments with a 3D lattice of diamond grits.展开更多
Based on the flow simulation in the condensing zone of compact spinning with lattice apron and a bead-elastic rod dynamic model of the flexible fiber,trajectories of fibers with different negative pressure are simulat...Based on the flow simulation in the condensing zone of compact spinning with lattice apron and a bead-elastic rod dynamic model of the flexible fiber,trajectories of fibers with different negative pressure are simulated by specially designed Matlab procedure.Then displacement components of fibers at YZ profile under different negative pressure conditions are extracted and compared.The results show that the fibers of different initial positions gradually converge,and are interlaced for position change in yarn cross-section,caused by the airflow in the condensing zone.Finally,compact-spun yarn with different negative pressure and conventional ring spun yarn are produced and their twists are tested.Both the results of simulation and experiments illustrate the existence of additional twists.Also the relationship between additional twists and negative pressure is verified.展开更多
Triangular lattice metamaterials composed of bi-layer curved rib elements (called the Lehman-Lakes lattice) possess unbounded thermal expansion, high stiffness and impossibility of thermal buckling, which are highly d...Triangular lattice metamaterials composed of bi-layer curved rib elements (called the Lehman-Lakes lattice) possess unbounded thermal expansion, high stiffness and impossibility of thermal buckling, which are highly desirable in many engineering structural applications subjected to large fluctuations in temperature. However, the requirement of such lattice metamaterial is that it must be a hinged joint in order to achieve the bending deformation upon heating freely, which directly leads to poor manufacturability, especially in small dimensions. In this study, a new design of dual-constituent triangular lattice metamaterial (DTLM) with good manufacturability is proposed to achieve the identical unbounded thermal expansion. In this lattice, a special bi-layer curved rib element where layer one is partially covered by layer two is presented, where the hinge joints are not necessary because the flexural rigidity in the single-layer part is much smaller than that in the bi-layer part, and the desirable thermal bending deformation can be achieved. A sample fabricated by additive manufacturing is given in order to show the good manufacturability;simultaneously, the multifunctional performance of the tailored DTLM with zero, large positive or negative coefficient of thermal expansion (CTE) can remain excellent, as well as the Lehman-Lakes lattice. Examples illustrate that the DTLM with zero CTE has about 34.2% improvement in stiffness and meanwhile has 17% reduction in weight compared with the Lehman-Lakes lattice. The stiffness of the DTLM has a moderate reduction when achieving the same large positive or negative CTE. In addition, the thermomechanical properties of the DTLM are given by the closed-form analytical solution and their effectiveness is verified by the detailed numerical simulation.展开更多
Laser additive manufacturing (AM) of lattice structures with light weight, excellent impact resistance, and energy absorption performance is receiving considerable attention in aerospace, transportation, and mechanica...Laser additive manufacturing (AM) of lattice structures with light weight, excellent impact resistance, and energy absorption performance is receiving considerable attention in aerospace, transportation, and mechanical equipment application fields. In this study, we designed four gradient lattice structures (GLSs) using the topology optimization method, including the unidirectional GLS, the bi-directional increasing GLS, the bi-directional decreasing GLS and the none-GLS. All GLSs were manufactureed by laser powder bed fusion (LPBF). The uniaxial compression tests and finite element analysis were conducted to investigate the influence of gradient distribution features on deformation modes and energy absorption performance of GLSs. The results showed that, compared with the 45° shear fracture characteristic of the none-GLS, the unidirectional GLS, the bi-directional increasing GLS and the bi-directional decreasing GLS had the characteristics of the layer-by-layer fracture, showing considerably improved energy absorption capacity. The bi-directional increasing GLS showed a unique combination of shear fracture and layer-by-layer fracture, having the optimal energy absorption performance with energy absorption and specific energy absorption of 235.6 J and 9.5 J g-1 at 0.5 strain, respectively. Combined with the shape memory effect of NiTi alloy, multiple compression-heat recovery experiments were carried out to verify the shape memory function of LPBF-processed NiTi GLSs. These findings have potential value for the future design of GLSs and the realization of shape memory function of NiTi components through laser AM.展开更多
Let (L, 〈, V, A) be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by V and A respectively...Let (L, 〈, V, A) be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by V and A respectively, is studied. We obtain: (i) the necessary and sufficient conditions for S(A,b)≠Ф; (ii) the necessary conditions for IS(A,b)| = 1. We also obtain the vector x ∈ Ln and prove that it is the largest element of S(A, b) if S(A, b)≠Ф.展开更多
In this article, we discuss several properties of the basic contact process on hexagonal lattice H, showing that it behaves quite similar to the process on d-dimensional lattice Zd in many aspects. Firstly, we constru...In this article, we discuss several properties of the basic contact process on hexagonal lattice H, showing that it behaves quite similar to the process on d-dimensional lattice Zd in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite space-time condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process.展开更多
Some characterizations of preregular operators between two Banach lattices are presented. Then several sufficient conditions for preregular operators being regular are given, and some related results are also obtained.
Sandwich structures possess a high bending stiffness compared to monolithic structures with a similar weight.This makes them very suitable for lightweight applications,where high stiffness to weight ratios are needed....Sandwich structures possess a high bending stiffness compared to monolithic structures with a similar weight.This makes them very suitable for lightweight applications,where high stiffness to weight ratios are needed.Most common manufacturing methods of sandwich structures involve adhesive bonding of the core material with the sheets.However,adhesive bonding is prone to delamination,a failure mode that is often difficult to detect.This paper presents the results of delamination testing of fully additive manufactured(AM)AlSi10Mg sandwich structures with pyramidal lattice truss core using Laser Powder Bed Fusion(LPBF).The faces and struts are 0.5 mm thick,while the core is 2 mm thick.The inclination of the struts is 45°.To characterise the bonding strength,climbing drum peel tests and out-of-plane tensile tests are performed.Analytical formulas are derived to predict the expected failure loads and modes.The analytics and tests are supported by finite element(FE)calculations.From the analytic approach,design guidelines to avoid delamination in AM sandwich structures are derived.The study presents a critical face sheet thickness to strut diameter ratio for which the structure can delaminate.This ratio is mainly influenced by the inclination of the struts.The peel tests resulted in face yielding,which can also be inferred from the analytics and numerics.The out-of-plane tensile tests didn’t damage the structure.展开更多
In order to solve the problem of substantial computational resources of lattice structure during optimization, a local relative density mapping(LRDM) method is proposed. The proposed method uses solid isotropic micros...In order to solve the problem of substantial computational resources of lattice structure during optimization, a local relative density mapping(LRDM) method is proposed. The proposed method uses solid isotropic microstructures with penalization to optimize a model at the macroscopic scale. The local relative density information is obtained from the topology optimization result. The contour lines of an optimized model are extracted using a density contour approach, and the triangular mesh is generated using a mesh generator. A local mapping relationship between the elements’ relative density and the struts’ relative cross?sectional area is established to automatically determine the diameter of each individual strut in the lattice structures. The proposed LRDM method can be applied to local finite element meshes and local density elements, but it is also suitable for global ones. In addition, some cases are con?sidered in order to test the e ectiveness of the LRDM method. The results show that the solution time of the LRDM is lower than the RDM method by approximately 50%. The proposed method provides instructions for the design of more complex lattice structures.展开更多
The paper considers the lattice of fully invariant subgroups of the cotorsion hull ?when a separable primary group T?is an arbitrary direct sum of torsion-complete groups.The investigation of this problem in the case ...The paper considers the lattice of fully invariant subgroups of the cotorsion hull ?when a separable primary group T?is an arbitrary direct sum of torsion-complete groups.The investigation of this problem in the case of a cotorsion hull is important because endomorphisms in this class of groups are completely defined by their action on the torsion part and for mixed groups the ring of endomorphisms is isomorphic to the ring of endomorphisms of the torsion part if and only if the group is a fully invariant subgroup of the cotorsion hull of its torsion part. In the considered case, the cotorsion hull is not fully transitive and hence it is necessary to introduce a new function which differs from an indicator and assigns an infinite matrix to each element of the cotorsion hull. The relation ?difined on the set ?of these matrices is different from the relation proposed by the autor in the countable case and better discribes the lower semilattice. The use of the relation ?essentially simplifies the verification of the required properties. It is proved that the lattice of fully invariant subgroups of the group is isomorphic to the lattice of filters of the lower semilattice.展开更多
We present some convergence and boundedness theorems with respect to filter convergence for lattice group-valued measures. We give a direct proof, based on the sliding hump argument. Furthermore we pose some open prob...We present some convergence and boundedness theorems with respect to filter convergence for lattice group-valued measures. We give a direct proof, based on the sliding hump argument. Furthermore we pose some open problems.展开更多
文摘Modern additive manufacturing processes enable fabricating architected cellular materials of complex shape,which can be used for different purposes.Among them,lattice structures are increasingly used in applications requiring a compromise among lightness and suited mechanical properties,like improved energy absorption capacity and specific stiffness-to-weight and strength-to-weight ratios.A dedicated modeling strategy to assess the energy absorption capacity of lattice structures under uni-axial compression loading is presented in this work.The numerical model is developed in a non-linear framework accounting for the strain rate effect on the mechanical responses of the lattice structure.Four geometries,i.e.,cubic body centered cell,octet cell,rhombic-dodecahedron and truncated cuboctahedron 2+,are investigated.Specifically,the influence of the relative density of the representative volume element of each geometry,the strain-rate dependency of the bulk material and of the presence of the manufacturing process-induced geometrical imperfections on the energy absorption capacity of the lattice structure is investigated.The main outcome of this study points out the importance of correctly integrating geometrical imperfections into the modeling strategy when shock absorption applications are aimed for.
基金supported by the Technology Development Fund of the China Academy of Machinery Science and Technology(No.170221ZY01).
文摘As a new type of lightweight structure,metallic lattice structure has higher stiffness and strength to weight ratio.To freely obtain 316L lattice structures with designed cell structure and adjustable porosity,additive manufacturing combined with investment casting was conducted to fabricate the 316L lattice structures with Kelvin cell.The compression simulation of 316L lattice structures with different porosities was carried out by using the finite element method.The numerical simulation results were verified by compression experiment,and the simulated results were consistent with the compression tests.The compressive mechanical properties of 316L lattice structures are directly related to porosity and independent of strut diameters.The 316L lattice structures with Kelvin cell have a smooth stress-strain curve and obvious plastic platform,and the hump stress-strain curves are avoided.
基金financially supported by the National Natural Science Foundation of China(52005189)Guangdong Basic and Applied Basic Research Foundation(2019A1515110542 and 2020A1515110699)+1 种基金Guangzhou Foreign Cooperation Projects(2020B1212060049 and 201704030067)Guangdong Academy of Sciences and the University of Birmingham(Contract 17-0551).
文摘Bio-inspired porous metallic scaffolds have tremendous potential to be used as artificial bone substitutes.In this work,a radially graded lattice structure (RGLS),which mimics the structures of natural human bones,was designed and processed by laser powder bed fusion of martensitic Ti-rich TiNi powder.The asymmetric tension-compression behaviour,where the compressive strength is significantly higher than the tensile strength,is observed in this Ti-rich TiNi material,which echoes the mechanical behaviour of bones.The morphologies,mechanical properties,deformation behaviour,and biological compatibility of RGLS samples were characterised and compared with those in the uniform lattice structure.Both the uniform and RGLS samples achieve a relative density higher than 99%.The graded porosities and pore sizes in the RGLS range from 40%-80% and 330-805 µm,respectively,from the centre to the edge.The chemical etching has significantly removed the harmful partially-melted residual powder particles on the lattice struts.The compressive yield strength of RGLS is 71.5 MPa,much higher than that of the uniform sample (46.5 MPa),despite having a similar relative density of about 46%.The calculated Gibson-Ashby equation and the deformation behaviour simulation by finite element suggest that the dense outer regions with high load-bearing capability could sustain high applied stress,improving the overall strength of RGLS significantly.The cell proliferation study suggests better biological compatibility of the RGLS than the uniform structures.The findings highlight a novel strategy to improve the performance of additively manufactured artificial implants by bio-inspiration.
基金supported by the NUS R&G Postdoc Fellowship Program (No.A-0000065-76-00)the China Scholarship Council (No.202006050088)。
文摘Lattice structures have drawn much attention in engineering applications due to their lightweight and multi-functional properties.In this work,a mathematical design approach for functionally graded(FG)and helicoidal lattice structures with triply periodic minimal surfaces is proposed.Four types of lattice structures including uniform,helicoidal,FG,and combined FG and helicoidal are fabricated by the additive manufacturing technology.The deformation behaviors,mechanical properties,energy absorption,and acoustic properties of lattice samples are thoroughly investigated.The load-bearing capability of helicoidal lattice samples is gradually improved in the plateau stage,leading to the plateau stress and total energy absorption improved by over 26.9%and 21.2%compared to the uniform sample,respectively.This phenomenon was attributed to the helicoidal design reduces the gap in unit cells and enhances fracture resistance.For acoustic properties,the design of helicoidal reduces the resonance frequency and improves the peak of absorption coefficient,while the FG design mainly influences the peak of absorption coefficient.Across broad range of frequency from 1000 to 6300 Hz,the maximum value of absorption coefficient is improved by18.6%-30%,and the number of points higher than 0.6 increased by 55.2%-61.7%by combining the FG and helicoidal designs.This study provides a novel strategy to simultaneously improve energy absorption and sound absorption properties by controlling the internal architecture of lattice structures.
基金Supported by Scientific Research Funds of Guangdong Province of China(Grant No.2017B090922008)the Scientific Project of Chaozhou of China(Grant No.2018ZD10).
文摘Diamond tools with orderly arrangements of diamond grits have drawn considerable attention in the machining field owing to their outstanding advantages of high sharpness and long service life.This diamond super tool,as well as the manufacturing equipment,has been unavailable to Chinese enterprises for a long time due to patents.In this paper,a diamond blade segment with a 3D lattice of diamond grits was additively manufactured using a new type of cold pressing equipment(AME100).The equipment,designed with a rotary working platform and 16 molding stations,can be used to additively manufacture segments with diamond grits arranged in an orderly fashion,layer by layer;under this additive manufacturing process,at least 216000 pcs of diamond green segments with five orderly arranged grit layers can be produced per month.The microstructure of the segment was observed via SEM and the diamond blade fabricated using these segments was compared to other commercial cutting tools.The experimental results showed that the 3D lattice of diamond grits was formed in the green segment.The filling rate of diamond grits in the lattice could be guaranteed to be above 95%;this is much higher than the 90%filling rate of the automatic array system(ARIX).When used to cut stone,the cutting amount of the blade with segments made by AME100 is two times that of ordinary tools,with the same diamond concentration.When used to dry cut reinforced concrete,its cutting speed is 10%faster than that of ARIX.Under wet cutting conditions,its service life is twice that of ARIX.By applying the machine vision online inspection system and a special needle jig with a negative pressure system,this study developed a piece of additive manufacturing equipment for efficiently fabricating blade segments with a 3D lattice of diamond grits.
文摘Based on the flow simulation in the condensing zone of compact spinning with lattice apron and a bead-elastic rod dynamic model of the flexible fiber,trajectories of fibers with different negative pressure are simulated by specially designed Matlab procedure.Then displacement components of fibers at YZ profile under different negative pressure conditions are extracted and compared.The results show that the fibers of different initial positions gradually converge,and are interlaced for position change in yarn cross-section,caused by the airflow in the condensing zone.Finally,compact-spun yarn with different negative pressure and conventional ring spun yarn are produced and their twists are tested.Both the results of simulation and experiments illustrate the existence of additional twists.Also the relationship between additional twists and negative pressure is verified.
基金the National Natural Science Foundation of China (Grants 11332004 and 11572071)111 Project (Grant B 14013)+1 种基金CATIC Industrial Production Projects (Grant CX Y2013DLLG32)the Fundamental Research Funds for the Central Universities (Grant DUT18ZD103).
文摘Triangular lattice metamaterials composed of bi-layer curved rib elements (called the Lehman-Lakes lattice) possess unbounded thermal expansion, high stiffness and impossibility of thermal buckling, which are highly desirable in many engineering structural applications subjected to large fluctuations in temperature. However, the requirement of such lattice metamaterial is that it must be a hinged joint in order to achieve the bending deformation upon heating freely, which directly leads to poor manufacturability, especially in small dimensions. In this study, a new design of dual-constituent triangular lattice metamaterial (DTLM) with good manufacturability is proposed to achieve the identical unbounded thermal expansion. In this lattice, a special bi-layer curved rib element where layer one is partially covered by layer two is presented, where the hinge joints are not necessary because the flexural rigidity in the single-layer part is much smaller than that in the bi-layer part, and the desirable thermal bending deformation can be achieved. A sample fabricated by additive manufacturing is given in order to show the good manufacturability;simultaneously, the multifunctional performance of the tailored DTLM with zero, large positive or negative coefficient of thermal expansion (CTE) can remain excellent, as well as the Lehman-Lakes lattice. Examples illustrate that the DTLM with zero CTE has about 34.2% improvement in stiffness and meanwhile has 17% reduction in weight compared with the Lehman-Lakes lattice. The stiffness of the DTLM has a moderate reduction when achieving the same large positive or negative CTE. In addition, the thermomechanical properties of the DTLM are given by the closed-form analytical solution and their effectiveness is verified by the detailed numerical simulation.
基金supported by the financial support from the National Natural Science Foundation of China(Nos.51735005 and U1930207)the Basic Strengthening Program(No.2019-JCJQ-JJ-331)+1 种基金National Natural Science Founda-tion of China for Creative Research Groups(No.51921003)the 15th Batch of‘Six Talents Peaks’Innovative Talents Team Program(No.TD-GDZB-001).
文摘Laser additive manufacturing (AM) of lattice structures with light weight, excellent impact resistance, and energy absorption performance is receiving considerable attention in aerospace, transportation, and mechanical equipment application fields. In this study, we designed four gradient lattice structures (GLSs) using the topology optimization method, including the unidirectional GLS, the bi-directional increasing GLS, the bi-directional decreasing GLS and the none-GLS. All GLSs were manufactureed by laser powder bed fusion (LPBF). The uniaxial compression tests and finite element analysis were conducted to investigate the influence of gradient distribution features on deformation modes and energy absorption performance of GLSs. The results showed that, compared with the 45° shear fracture characteristic of the none-GLS, the unidirectional GLS, the bi-directional increasing GLS and the bi-directional decreasing GLS had the characteristics of the layer-by-layer fracture, showing considerably improved energy absorption capacity. The bi-directional increasing GLS showed a unique combination of shear fracture and layer-by-layer fracture, having the optimal energy absorption performance with energy absorption and specific energy absorption of 235.6 J and 9.5 J g-1 at 0.5 strain, respectively. Combined with the shape memory effect of NiTi alloy, multiple compression-heat recovery experiments were carried out to verify the shape memory function of LPBF-processed NiTi GLSs. These findings have potential value for the future design of GLSs and the realization of shape memory function of NiTi components through laser AM.
基金supported by the NNSF (10471035,10771056) of China
文摘Let (L, 〈, V, A) be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by V and A respectively, is studied. We obtain: (i) the necessary and sufficient conditions for S(A,b)≠Ф; (ii) the necessary conditions for IS(A,b)| = 1. We also obtain the vector x ∈ Ln and prove that it is the largest element of S(A, b) if S(A, b)≠Ф.
基金Supported in part by the NNSF of China (10531070,10625101)the National Basic Research Program of China (2006CB805900)
文摘In this article, we discuss several properties of the basic contact process on hexagonal lattice H, showing that it behaves quite similar to the process on d-dimensional lattice Zd in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite space-time condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process.
文摘Some characterizations of preregular operators between two Banach lattices are presented. Then several sufficient conditions for preregular operators being regular are given, and some related results are also obtained.
基金Part of this work was supported by the German Federal Ministry for Economic Affairs and Energy(BMWi)(Grant No.20E1713B).
文摘Sandwich structures possess a high bending stiffness compared to monolithic structures with a similar weight.This makes them very suitable for lightweight applications,where high stiffness to weight ratios are needed.Most common manufacturing methods of sandwich structures involve adhesive bonding of the core material with the sheets.However,adhesive bonding is prone to delamination,a failure mode that is often difficult to detect.This paper presents the results of delamination testing of fully additive manufactured(AM)AlSi10Mg sandwich structures with pyramidal lattice truss core using Laser Powder Bed Fusion(LPBF).The faces and struts are 0.5 mm thick,while the core is 2 mm thick.The inclination of the struts is 45°.To characterise the bonding strength,climbing drum peel tests and out-of-plane tensile tests are performed.Analytical formulas are derived to predict the expected failure loads and modes.The analytics and tests are supported by finite element(FE)calculations.From the analytic approach,design guidelines to avoid delamination in AM sandwich structures are derived.The study presents a critical face sheet thickness to strut diameter ratio for which the structure can delaminate.This ratio is mainly influenced by the inclination of the struts.The peel tests resulted in face yielding,which can also be inferred from the analytics and numerics.The out-of-plane tensile tests didn’t damage the structure.
基金National Hi-tech Research and Development Program of China(863 Program,Grant No.2015BAF04B00)China Aerospace Science and Technology Corporation Program of China(CASIC Program,Grant No.461717)
文摘In order to solve the problem of substantial computational resources of lattice structure during optimization, a local relative density mapping(LRDM) method is proposed. The proposed method uses solid isotropic microstructures with penalization to optimize a model at the macroscopic scale. The local relative density information is obtained from the topology optimization result. The contour lines of an optimized model are extracted using a density contour approach, and the triangular mesh is generated using a mesh generator. A local mapping relationship between the elements’ relative density and the struts’ relative cross?sectional area is established to automatically determine the diameter of each individual strut in the lattice structures. The proposed LRDM method can be applied to local finite element meshes and local density elements, but it is also suitable for global ones. In addition, some cases are con?sidered in order to test the e ectiveness of the LRDM method. The results show that the solution time of the LRDM is lower than the RDM method by approximately 50%. The proposed method provides instructions for the design of more complex lattice structures.
文摘The paper considers the lattice of fully invariant subgroups of the cotorsion hull ?when a separable primary group T?is an arbitrary direct sum of torsion-complete groups.The investigation of this problem in the case of a cotorsion hull is important because endomorphisms in this class of groups are completely defined by their action on the torsion part and for mixed groups the ring of endomorphisms is isomorphic to the ring of endomorphisms of the torsion part if and only if the group is a fully invariant subgroup of the cotorsion hull of its torsion part. In the considered case, the cotorsion hull is not fully transitive and hence it is necessary to introduce a new function which differs from an indicator and assigns an infinite matrix to each element of the cotorsion hull. The relation ?difined on the set ?of these matrices is different from the relation proposed by the autor in the countable case and better discribes the lower semilattice. The use of the relation ?essentially simplifies the verification of the required properties. It is proved that the lattice of fully invariant subgroups of the group is isomorphic to the lattice of filters of the lower semilattice.
文摘We present some convergence and boundedness theorems with respect to filter convergence for lattice group-valued measures. We give a direct proof, based on the sliding hump argument. Furthermore we pose some open problems.
基金supported by Graduate Scientific Research and Innovation Foundation of Chongqing,China (No. CYB21005)the National Natural Science Foundation of China (No. 51875062)China Postdoctoral Science Foundation (No. 2021M700567)。