For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic de...For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.展开更多
Let G be a group and A and B be subgroups of G.If G=AB,then G is said to be factorized by A and B.Let p be a prime number.The factorization numbers of a 2-generators abelian p-group and a modular p-group have been det...Let G be a group and A and B be subgroups of G.If G=AB,then G is said to be factorized by A and B.Let p be a prime number.The factorization numbers of a 2-generators abelian p-group and a modular p-group have been determined.Further,suppose that G is a finite p-group as follows G=<a,b|a^(p)^(n)=b^(p)^(m)=1,a^(b)=a^(p^(n-1)+1)>,where n≥2,m≥1.In this paper,the factorization number of G is computed completely,which is a generalization of the result of Saeedi and Farrokhi.展开更多
Let p be a prime number and f_2(G) be the number of factorizations G = AB of the group G, where A, B are subgroups of G. Let G be a class of finite p-groups as follows,G = a, b | a^(p^n)= b^(p^m)= 1, a^b= a^(p^(n-1)+1...Let p be a prime number and f_2(G) be the number of factorizations G = AB of the group G, where A, B are subgroups of G. Let G be a class of finite p-groups as follows,G = a, b | a^(p^n)= b^(p^m)= 1, a^b= a^(p^(n-1)+1), where n > m ≥ 1. In this article, the factorization number f_2(G) of G is computed, improving the results of Saeedi and Farrokhi in [5].展开更多
A p-group G is called a JC-group if the normal closure HG of every cyclic subgroup H satisfies｜G：HG｜≤p or｜HG：H｜≤p.In this paper, we classify the non-Dedekindian JC-groups for p 〉 2.
Assume that G is a finite non-abelian p-group.If G has an abelian maximal subgroup whose number of Generators is at least n,then G is called an M_(n)-group.For p=2,M_(2)-groups have been classified.For odd prime p,thi...Assume that G is a finite non-abelian p-group.If G has an abelian maximal subgroup whose number of Generators is at least n,then G is called an M_(n)-group.For p=2,M_(2)-groups have been classified.For odd prime p,this paper provides the isomorphism classification of M_(2)-groups,thereby achieving a complete classification of M_(2)-groups.展开更多
Suppose that G is a finite p-group.If all subgroups of index p^(t)of G are abelian and at least one subgroup of index p^(t−1)of G is not abelian,then G is called an A_(t)-group.We useA0-group to denote an abelian grou...Suppose that G is a finite p-group.If all subgroups of index p^(t)of G are abelian and at least one subgroup of index p^(t−1)of G is not abelian,then G is called an A_(t)-group.We useA0-group to denote an abelian group.From the definition,we know every finite non-abelian p-group can be regarded as an A_(t)-group for some positive integer t.A_(1)-groups and A_(2)-groups have been classified.Classifying A_(3)-groups is an old problem.In this paper,some general properties about A_(t)-groups are given.A_(3)-groups are completely classified up to isomorphism.Moreover,we determine the Frattini subgroup,the derived subgroup and the center of every A_(3)-group,and give the number of A_(1)-subgroups and the triple(μ_(0),μ_(1),μ_(2))of every A_(3)-group,whereμi denotes the number of A_(i)-subgroups of index p of A_(3)-groups.展开更多
Suppose that G is a finite p-group. If G is not a Dedekind group, then G has a non-normal subgroup. We use p^M（G） and p^m（G） to denote the maximum and minimum of the orders of the non-normal subgroups of G, respec...Suppose that G is a finite p-group. If G is not a Dedekind group, then G has a non-normal subgroup. We use p^M（G） and p^m（G） to denote the maximum and minimum of the orders of the non-normal subgroups of G, respectively. In this paper, we classify groups G such that M（G） 〈 2m（G） ^- 1. As a by-product, we also classify p-groups whose orders of non-normal subgroups are p^k and p^k＋1.展开更多
Assume G is a finite group and H a subgroup of G. If there exists a subgroup K of G such that G = HK and H ∩ K = 1, then K is said to be a complement to H in G. A finite p-group G is called an NC-group if all its pro...Assume G is a finite group and H a subgroup of G. If there exists a subgroup K of G such that G = HK and H ∩ K = 1, then K is said to be a complement to H in G. A finite p-group G is called an NC-group if all its proper normal subgroups not contained in de（G） have complements. In this paper, some properties of NC-groups are investigated and some classes of NC-groups are classified. Keywords Finite p-groups, normal subgroups, subgroup complement展开更多
A subgroup of index p^k of a finite p-group G is called a k-maximal subgroup of G.Denote by d(G) the number of elements in a minimal generator-system of G and by δ_k(G) the number of k-maximal subgroups which do not ...A subgroup of index p^k of a finite p-group G is called a k-maximal subgroup of G.Denote by d(G) the number of elements in a minimal generator-system of G and by δ_k(G) the number of k-maximal subgroups which do not contain the Frattini subgroup of G.In this paper,the authors classify the finite p-groups with δ_(d(G))(G) ≤ p^2 and δ_(d(G)-1)(G) = 0,respectively.展开更多
Let G be a group and G＇ be its commutator subgroup. An automorphism α of a group G is called an IA-automorphism if x^-1α（x） ∈G＇ for each x∈G. The set of all IA-automorphisms of G is denoted by IA（G）. A group...Let G be a group and G＇ be its commutator subgroup. An automorphism α of a group G is called an IA-automorphism if x^-1α（x） ∈G＇ for each x∈G. The set of all IA-automorphisms of G is denoted by IA（G）. A group G is called semicomplete if and only if IA（G） = Inn（G）, where Inn（G） is the inner automorphism group of G. In this paper we completely characterize semicomplete finite p-groups of class 2; we also classify all semicomplete finite p-groups of order p^n （n≤5）, where p is an odd prime. This completes our work in 2011.展开更多
In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided int...In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided into,by the work of Amiot[Bull.Soc.Math.France,2007,135(3):435-474](see also[Adv.Math.,2008,217(6):2443-2484]and[J.Algebra,2016,446:426-449]),three classes:type A,type D and type E.展开更多
This paper presents a nonlinear micropolar nonclassical continuum theory (MPNCCT) for finite deformation, finite strain deformation physics of thermosviscoelastic solid medium with memory (polymeric micropolar solids)...This paper presents a nonlinear micropolar nonclassical continuum theory (MPNCCT) for finite deformation, finite strain deformation physics of thermosviscoelastic solid medium with memory (polymeric micropolar solids) based on classical rotations cΘand their rates. Contravariant second Piola-Kirchhoff stress and moment tensors, in conjunction with finite deformation measures derived by the authors in recent paper, are utilized in deriving the conservation and balance laws and the constitutive theories based on conjugate pairs in entropy inequality and the representation theorem. This nonlinear MPNCCT for TVES with rheology: 1) incorporates nonlinear ordered rate dissipation mechanism based on Green’s strain rates up to order n;2) also incorporates an additional ordered rate dissipation mechanism due to microconstituents, the viscosity of the medium and the rates of the symmetric part of the rotation gradient (of cΘ) tensor up to order n, referred to as micropolar dissipation or micropolar viscous dissipation mechanism;3) incorporates the primary mechanism of memory or rheology due to long chain molecules of the polymer and the viscosity of the medium by using the contravaraint second Piola-Kirchhoff stress tensor and its rates up to order m, resulting in a relaxation spectrum;4) incorporates second mechanism of memory or rheology due to nonclassical physics, interaction of microconstituents with the viscous medium and long chain molecules by considering rates of the contravariant second Piola-Kirchhoff moment tensor up to order m, resulting in relaxation of second Piola-Kirchhoff moment tensor. This results in another relaxation spectrum for the second Piola-Kirchhoff moment tensor due to microconstituents, referred to as micropolar relaxation spectrum consisting of micropolar relaxation time constants of the material. This nonlinear MPNCCT for TVES with memory is thermodynamically and mathematically consistent, and the mathematical model consisting of conservation and balance laws and the constitutive theories has closure and naturally reduces to linear MPNCCT based on infinitesimal deformation assumption. BMM is the essential balance law for all MPNCCT and is used in the present work as well. In the absence of this balance law, a valid thermodynamically and mathematically consistent nonlinear MPNCCT is not possible. The nonlinear MPNCCT based on rotations (cΘ+αΘ) and αΘ(ignoring cΘ) is not considered due to the fact that even the linear MPNCCT based on these rotations is invalid and is thermodynamically and mathematically inconsistent MPNCCT.展开更多
Objective: To compare the stress distribution in the periodontal ligament under different orthodontic forces during canine distalization using long-arm brackets, and to determine the optimal force value for this devic...Objective: To compare the stress distribution in the periodontal ligament under different orthodontic forces during canine distalization using long-arm brackets, and to determine the optimal force value for this device in orthodontic treatment. Methods: A finite element model was constructed after extracting the mandibular first premolar, and a long-arm bracket with a traction height of 6 mm was placed on the labial side of the mandibular canine. Three working conditions of 50 g, 100 g, and 150 g were simulated, and the magnitude and distribution of von Mises stress in the periodontal ligament were compared for each condition. Results: The maximum von Mises stress in the periodontal ligament was 0.013281 MPa in the 50 g condition, 0.02536 MPa in the 100 g condition, and 0.035549 MPa in the 150 g condition. As the orthodontic force increased, the stress distribution area in the periodontal ligament also expanded. Conclusion: A 100 g orthodontic force is the most suitable when using long-arm brackets, providing a relatively uniform stress distribution in the periodontal ligament and keeping the stress within a reasonable range.展开更多
This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practi...This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.展开更多
Design a precision electroplating mechanical structure for automobiles based on finite element analysis method and analyze its mechanical properties.Taking the automobile steering knuckle as the research object,ABAQUS...Design a precision electroplating mechanical structure for automobiles based on finite element analysis method and analyze its mechanical properties.Taking the automobile steering knuckle as the research object,ABAQUS parametric modeling technology is used to construct its three-dimensional geometric model,and geometric simplification is carried out.Two surface treatment processes,HK-35 zinc nickel alloy electroplating and pure zinc electroplating,were designed,and the influence of different coatings on the mechanical properties of steering knuckles was compared and analyzed through numerical simulation.At the same time,standard specimens were prepared for salt spray corrosion testing and scratch method combined strength testing to verify the numerical simulation results.The results showed that under emergency braking and composite working conditions,the peak Von Mises stress of the zinc nickel alloy coating was 119.85 MPa,which was lower than that of the pure zinc coating and the alkaline electroplated zinc layer.Its equivalent strain value was 652×10^(-6),which was lower than that of the pure zinc coating and the alkaline electroplated zinc layer.Experimental data confirms that zinc nickel alloy coatings exhibit significant advantages in stress distribution uniformity,strain performance,and load-bearing capacity in high stress zones.The salt spray corrosion test further indicates that the coating has superior corrosion resistance and coating substrate interface bonding strength,which can significantly improve the mechanical stability and long-term reliability of automotive precision electroplating mechanical structures.展开更多
Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment.Richards'equation,which describes the movement of water flow in the vadose zone,is highly nonlinear and ...Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment.Richards'equation,which describes the movement of water flow in the vadose zone,is highly nonlinear and challenging to solve.Existing numerical methods often face issues such as numerical dispersion,oscillation,and mass non-conservation when spatial and temporal discretization conditions are not appropriately configured.To address these problems and achieve accurate and stable numerical solutions,a finite analytic method based on water content-based Richards'equation(FAM-W)is proposed.The performance of the FAM-W is compared with analytical solutions,Finite Difference Method(FDM),and Finite Analytic Method based on the pressure Head-based Richards'equation(FAM-H).Compared to analytical solution and other numerical methods(FDM and FAM-H),FAM-W demonstrates superior accuracy and efficiency in controlling mass balance errors,regardless of spatial step sizes.This study introduces a novel approach for modelling water flow in the vadose zone,offering significant benefits for water resources management.展开更多
To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical c...To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 11071150)the Natural Science Foundation of Shanxi Province (Grant No. 2012011001-3)Shanxi Scholarship Council of China (Grant No. [2011]8-59)
文摘We classify up to isomorphism those finite p-groups, for odd primes p, which contain a cyclic subgroup of index p3.
基金Supported by the NSF of China(11171194)by the NSF of Shanxi Province(2012011001-1)
文摘For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.
基金Supported by National Natural Science Foundation of China(Grant No.11601121,12171142).
文摘Let G be a group and A and B be subgroups of G.If G=AB,then G is said to be factorized by A and B.Let p be a prime number.The factorization numbers of a 2-generators abelian p-group and a modular p-group have been determined.Further,suppose that G is a finite p-group as follows G=<a,b|a^(p)^(n)=b^(p)^(m)=1,a^(b)=a^(p^(n-1)+1)>,where n≥2,m≥1.In this paper,the factorization number of G is computed completely,which is a generalization of the result of Saeedi and Farrokhi.
基金Supported by National Natural Science Foundation of China(11601121)Henan Provincial Natural Science Foundation of China(162300410066)
文摘Let p be a prime number and f_2(G) be the number of factorizations G = AB of the group G, where A, B are subgroups of G. Let G be a class of finite p-groups as follows,G = a, b | a^(p^n)= b^(p^m)= 1, a^b= a^(p^(n-1)+1), where n > m ≥ 1. In this article, the factorization number f_2(G) of G is computed, improving the results of Saeedi and Farrokhi in [5].
基金Supported by the National Natural Science Foundation of China(Grant Nos.1152611411601245)+3 种基金the Natural Science Foundation of Guangdong Province(Grant No.2015A030313791)the Innovative Team Project of Guangdong Province(CHINA)(Grant No.2014KTSCX196)Guangdong Province Innovation Talent Project for Youths(Grant No.2015KQNCX107)the Appropriative Researching Fund for Doctors,Guangdong University of Education(Grant No.2013ARF07)
文摘A p-group G is called a JC-group if the normal closure HG of every cyclic subgroup H satisfies｜G：HG｜≤p or｜HG：H｜≤p.In this paper, we classify the non-Dedekindian JC-groups for p 〉 2.
文摘Assume that G is a finite non-abelian p-group.If G has an abelian maximal subgroup whose number of Generators is at least n,then G is called an M_(n)-group.For p=2,M_(2)-groups have been classified.For odd prime p,this paper provides the isomorphism classification of M_(2)-groups,thereby achieving a complete classification of M_(2)-groups.
基金This work was supported by NSFC(Nos.11371232,11471198)by NSF of Shanxi Province(No.2013011001).
文摘Suppose that G is a finite p-group.If all subgroups of index p^(t)of G are abelian and at least one subgroup of index p^(t−1)of G is not abelian,then G is called an A_(t)-group.We useA0-group to denote an abelian group.From the definition,we know every finite non-abelian p-group can be regarded as an A_(t)-group for some positive integer t.A_(1)-groups and A_(2)-groups have been classified.Classifying A_(3)-groups is an old problem.In this paper,some general properties about A_(t)-groups are given.A_(3)-groups are completely classified up to isomorphism.Moreover,we determine the Frattini subgroup,the derived subgroup and the center of every A_(3)-group,and give the number of A_(1)-subgroups and the triple(μ_(0),μ_(1),μ_(2))of every A_(3)-group,whereμi denotes the number of A_(i)-subgroups of index p of A_(3)-groups.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11471198, 11771258）.
文摘Suppose that G is a finite p-group. If G is not a Dedekind group, then G has a non-normal subgroup. We use p^M（G） and p^m（G） to denote the maximum and minimum of the orders of the non-normal subgroups of G, respectively. In this paper, we classify groups G such that M（G） 〈 2m（G） ^- 1. As a by-product, we also classify p-groups whose orders of non-normal subgroups are p^k and p^k＋1.
基金Supported by National Natural Science Foundation of China(Grant Nos.11471198,11501045 and 11371232)
文摘Assume G is a finite group and H a subgroup of G. If there exists a subgroup K of G such that G = HK and H ∩ K = 1, then K is said to be a complement to H in G. A finite p-group G is called an NC-group if all its proper normal subgroups not contained in de（G） have complements. In this paper, some properties of NC-groups are investigated and some classes of NC-groups are classified. Keywords Finite p-groups, normal subgroups, subgroup complement
基金supported by the National Natural Science Foundation of China(Nos.11371232,11371177)
文摘A subgroup of index p^k of a finite p-group G is called a k-maximal subgroup of G.Denote by d(G) the number of elements in a minimal generator-system of G and by δ_k(G) the number of k-maximal subgroups which do not contain the Frattini subgroup of G.In this paper,the authors classify the finite p-groups with δ_(d(G))(G) ≤ p^2 and δ_(d(G)-1)(G) = 0,respectively.
基金supported by the National Natural Science Foundation of China(Nos.11371232,11101252)the Shanxi Provincial Natural Science Foundation of China(No.2013011001)the Fundamental Research Funds for the Central Universities(No.BUPT2013RC0901)
文摘The groups as mentioned in the title are classified up to isomorphism. This is an answer to a question proposed by Berkovich and Janko.
文摘Let G be a group and G＇ be its commutator subgroup. An automorphism α of a group G is called an IA-automorphism if x^-1α（x） ∈G＇ for each x∈G. The set of all IA-automorphisms of G is denoted by IA（G）. A group G is called semicomplete if and only if IA（G） = Inn（G）, where Inn（G） is the inner automorphism group of G. In this paper we completely characterize semicomplete finite p-groups of class 2; we also classify all semicomplete finite p-groups of order p^n （n≤5）, where p is an odd prime. This completes our work in 2011.
文摘In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided into,by the work of Amiot[Bull.Soc.Math.France,2007,135(3):435-474](see also[Adv.Math.,2008,217(6):2443-2484]and[J.Algebra,2016,446:426-449]),three classes:type A,type D and type E.
文摘This paper presents a nonlinear micropolar nonclassical continuum theory (MPNCCT) for finite deformation, finite strain deformation physics of thermosviscoelastic solid medium with memory (polymeric micropolar solids) based on classical rotations cΘand their rates. Contravariant second Piola-Kirchhoff stress and moment tensors, in conjunction with finite deformation measures derived by the authors in recent paper, are utilized in deriving the conservation and balance laws and the constitutive theories based on conjugate pairs in entropy inequality and the representation theorem. This nonlinear MPNCCT for TVES with rheology: 1) incorporates nonlinear ordered rate dissipation mechanism based on Green’s strain rates up to order n;2) also incorporates an additional ordered rate dissipation mechanism due to microconstituents, the viscosity of the medium and the rates of the symmetric part of the rotation gradient (of cΘ) tensor up to order n, referred to as micropolar dissipation or micropolar viscous dissipation mechanism;3) incorporates the primary mechanism of memory or rheology due to long chain molecules of the polymer and the viscosity of the medium by using the contravaraint second Piola-Kirchhoff stress tensor and its rates up to order m, resulting in a relaxation spectrum;4) incorporates second mechanism of memory or rheology due to nonclassical physics, interaction of microconstituents with the viscous medium and long chain molecules by considering rates of the contravariant second Piola-Kirchhoff moment tensor up to order m, resulting in relaxation of second Piola-Kirchhoff moment tensor. This results in another relaxation spectrum for the second Piola-Kirchhoff moment tensor due to microconstituents, referred to as micropolar relaxation spectrum consisting of micropolar relaxation time constants of the material. This nonlinear MPNCCT for TVES with memory is thermodynamically and mathematically consistent, and the mathematical model consisting of conservation and balance laws and the constitutive theories has closure and naturally reduces to linear MPNCCT based on infinitesimal deformation assumption. BMM is the essential balance law for all MPNCCT and is used in the present work as well. In the absence of this balance law, a valid thermodynamically and mathematically consistent nonlinear MPNCCT is not possible. The nonlinear MPNCCT based on rotations (cΘ+αΘ) and αΘ(ignoring cΘ) is not considered due to the fact that even the linear MPNCCT based on these rotations is invalid and is thermodynamically and mathematically inconsistent MPNCCT.
文摘Objective: To compare the stress distribution in the periodontal ligament under different orthodontic forces during canine distalization using long-arm brackets, and to determine the optimal force value for this device in orthodontic treatment. Methods: A finite element model was constructed after extracting the mandibular first premolar, and a long-arm bracket with a traction height of 6 mm was placed on the labial side of the mandibular canine. Three working conditions of 50 g, 100 g, and 150 g were simulated, and the magnitude and distribution of von Mises stress in the periodontal ligament were compared for each condition. Results: The maximum von Mises stress in the periodontal ligament was 0.013281 MPa in the 50 g condition, 0.02536 MPa in the 100 g condition, and 0.035549 MPa in the 150 g condition. As the orthodontic force increased, the stress distribution area in the periodontal ligament also expanded. Conclusion: A 100 g orthodontic force is the most suitable when using long-arm brackets, providing a relatively uniform stress distribution in the periodontal ligament and keeping the stress within a reasonable range.
文摘This paper mainly studies the well-posedness of steady incompressible impinging jet flow problem through a 3D axisymmetric finitely long nozzle.This problem originates from the physical phenomena encountered in practical engineering fields,such as in short take-off and vertical landing(STOVL)aircraft.Nowadays many intricate phenomena associated with impinging jet flows remain inadequately elucidated,which limits the ability to optimize aircraft design.Given a boundary condition in the inlet,the impinging jet problem is transformed into a Bernoulli-type free boundary problem according to the stream function.Then the variational method is used to study the corresponding variational problem with one parameter,thereby the wellposedness is established.The main conclusion is as follows.For a 3D axisymmetric finitely long nozzle and an infinitely long vertical wall,given an axial velocity in the inlet of nozzle,there exists a unique smooth incom‑pressible impinging jet flow such that the free boundary initiates smoothly at the endpoint of the nozzle and extends to infinity along the vertical wall at far fields.The key point is to investigate the regularity of the corner where the nozzle and the vertical axis intersect.
文摘Design a precision electroplating mechanical structure for automobiles based on finite element analysis method and analyze its mechanical properties.Taking the automobile steering knuckle as the research object,ABAQUS parametric modeling technology is used to construct its three-dimensional geometric model,and geometric simplification is carried out.Two surface treatment processes,HK-35 zinc nickel alloy electroplating and pure zinc electroplating,were designed,and the influence of different coatings on the mechanical properties of steering knuckles was compared and analyzed through numerical simulation.At the same time,standard specimens were prepared for salt spray corrosion testing and scratch method combined strength testing to verify the numerical simulation results.The results showed that under emergency braking and composite working conditions,the peak Von Mises stress of the zinc nickel alloy coating was 119.85 MPa,which was lower than that of the pure zinc coating and the alkaline electroplated zinc layer.Its equivalent strain value was 652×10^(-6),which was lower than that of the pure zinc coating and the alkaline electroplated zinc layer.Experimental data confirms that zinc nickel alloy coatings exhibit significant advantages in stress distribution uniformity,strain performance,and load-bearing capacity in high stress zones.The salt spray corrosion test further indicates that the coating has superior corrosion resistance and coating substrate interface bonding strength,which can significantly improve the mechanical stability and long-term reliability of automotive precision electroplating mechanical structures.
基金supported by the National Natural Science Foundation of China(No.42372287 and No.U24A20178)the Fundamental Research Funds for the Central Universities CHD(No.2024SHEEAR002)+3 种基金the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shaanxi Province(No.2020024)the China Postdoctoral Science Foundation(GZC20232955,2024M753472,and 2024MD763937)the Science-Technology Foundation for Young Scientists of Gansu Province,China(No.24JRRA097)the Study of biodiversity survey and limiting factor analysis of Yinkentala(2023ZL01).
文摘Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment.Richards'equation,which describes the movement of water flow in the vadose zone,is highly nonlinear and challenging to solve.Existing numerical methods often face issues such as numerical dispersion,oscillation,and mass non-conservation when spatial and temporal discretization conditions are not appropriately configured.To address these problems and achieve accurate and stable numerical solutions,a finite analytic method based on water content-based Richards'equation(FAM-W)is proposed.The performance of the FAM-W is compared with analytical solutions,Finite Difference Method(FDM),and Finite Analytic Method based on the pressure Head-based Richards'equation(FAM-H).Compared to analytical solution and other numerical methods(FDM and FAM-H),FAM-W demonstrates superior accuracy and efficiency in controlling mass balance errors,regardless of spatial step sizes.This study introduces a novel approach for modelling water flow in the vadose zone,offering significant benefits for water resources management.
基金Supported by Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)+3 种基金National Natural Science Foundation of China(12301556)Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)Basic Research Plan of Shanxi Province(202203021211129)。
文摘To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.
