Red clay,widely used as a subgrade material in southern China,requires a reliable evaluation of its dynamic behavior to ensure infrastructure safety.Long-term cyclic triaxial tests were conducted on red clay from typi...Red clay,widely used as a subgrade material in southern China,requires a reliable evaluation of its dynamic behavior to ensure infrastructure safety.Long-term cyclic triaxial tests were conducted on red clay from typical,complex subway subgrades to investigate its dynamic properties and shakedown behavior under intermittent cyclic loading.Results show that intermittent cyclic loading,especially with multiple amplitudes,causes greater axial plastic strain and lower post-cyclic strength than continuous loading.These effects diminish with increasing confining pressure.Notably,axial strain partially recovers during loading intervals,with recovery ratios depending on the number and sequence of pauses.Based on the rules of cumulative plastic strain rates and cumulative plastic strain increments,shakedown behavior for red clay under intermittent cyclic loading is divided into three categories:plastic shakedown,critical shakedown,and plastic creep.A quantitative shakedown limit criterion is proposed using the Boltzmann function.Shakedown behavior significantly influences the post-cyclic strengths,and the influence diminishes as confining pressure increases.Samples exhibiting plastic creep and plastic shakedown behavior have the lowest and highest strengths,and those with critical shakedown behaviors have medium strengths.Cyclic loading with relatively low-stress amplitude causes a hardening effect,while cyclic loading intermittence or cyclic loading with relatively high-stress amplitude causes a degradation effect,and both effects are mitigated by higher confining pressures.展开更多
The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design. Therefore, it is nece...The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design. Therefore, it is necessary to accurately predict the shakedown domains of these materials. The static shakedown theorem, also known as Melan's theorem, is a fundamental method used to predict the shakedown domains of structures and materials. Within this method, a key aspect lies in the construction and application of an appropriate self-equilibrium stress field(SSF). In the structural shakedown analysis, the SSF is typically constructed by governing equations that satisfy no external force(NEF) boundary conditions. However, we discover that directly applying these governing equations is not suitable for the shakedown analysis of heterogeneous materials. Researchers must consider the requirements imposed by the Hill-Mandel condition for boundary conditions and the physical significance of representative volume elements(RVEs). This paper addresses this issue and demonstrates that the sizes of SSFs vary under different boundary conditions, such as uniform displacement boundary conditions(DBCs), uniform traction boundary conditions(TBCs), and periodic boundary conditions(PBCs). As a result, significant discrepancies arise in the predicted shakedown domain sizes of heterogeneous materials. Built on the demonstrated relationship between SSFs under different boundary conditions, this study explores the conservative relationships among different shakedown domains, and provides proof of the relationship between the elastic limit(EL) factors and the shakedown loading factors under the loading domain of two load vertices. By utilizing numerical examples, we highlight the conservatism present in certain results reported in the existing literature. Among the investigated boundary conditions, the obtained shakedown domain is the most conservative under TBCs.Conversely, utilizing PBCs to construct an SSF for the shakedown analysis leads to less conservative lower bounds, indicating that PBCs should be employed as the preferred boundary conditions for the shakedown analysis of heterogeneous materials.展开更多
This paper proposes a novel numerical solution approach for the kinematic shakedown analysis of strain-hardening thin plates using the C^(1)nodal natural element method(C^(1)nodal NEM).Based on Koiter’s theorem and t...This paper proposes a novel numerical solution approach for the kinematic shakedown analysis of strain-hardening thin plates using the C^(1)nodal natural element method(C^(1)nodal NEM).Based on Koiter’s theorem and the von Mises and two-surface yield criteria,a nonlinear mathematical programming formulation is constructed for the kinematic shakedown analysis of strain-hardening thin plates,and the C^(1)nodal NEM is adopted for discretization.Additionally,König’s theory is used to deal with time integration by treating the generalized plastic strain increment at each load vertex.A direct iterative method is developed to linearize and solve this formulation by modifying the relevant objective function and equality constraints at each iteration.Kinematic shakedown load factors are directly calculated in a monotonically converging manner.Numerical examples validate the accuracy and convergence of the developed method and illustrate the influences of limited and unlimited strain-hardening models on the kinematic shakedown load factors of thin square and circular plates.展开更多
The effect of kinematic hardening behavior on the shakedown behaviors of structure has been investigated by performing shakedown analysis for some specific problems. The results obtained only show that the shakedown l...The effect of kinematic hardening behavior on the shakedown behaviors of structure has been investigated by performing shakedown analysis for some specific problems. The results obtained only show that the shakedown limit loads of structures with kinematic hardening model are larger than or equal to those with perfectly plastic model of the same initial yield stress. To further investigate the rules governing the different shakedown behaviors of kinematic hardening structures, the extended shakedown theorem for limited kinematic hardening is applied, the shakedown condition is then proposed, and a general analytical solution for the structural shakedown limit load is thus derived. The analytical shakedown limit loads for fully reversed cyclic loading and non-fully reversed cyclic loading are then given based on the general solution. The resulting analytical solution is applied to some specific problems： a hollow specimen subjected to tension and torsion, a flanged pipe subjected to pressure and axial force and a square plate with small central hole subjected to biaxial tension. The results obtained are compared with those in literatures, they are consistent with each other. Based on the resulting general analytical solution, rules governing the general effects of kinematic hardening behavior on the shakedown behavior of structure are clearly.展开更多
Construction of the static admissible residual stress field and searching the optimal field are key tasks in the shakedown analysis methods applying the static theorem. These methods always meet dimension obstacles wh...Construction of the static admissible residual stress field and searching the optimal field are key tasks in the shakedown analysis methods applying the static theorem. These methods always meet dimension obstacles when dealing with complex problems. In this paper, a novel shakedown criterion is proposed employing actual residual stress field based on the static shakedown theorem. The actual residual stress field used here is produced under a specified load path, which is a sequence of proportional loading and unloading from zero to all the vertices of the given load domain. This ensures that the shakedown behavior in the whole load domain can be determined based on the theorem proposed by K6nig. The shakedown criterion is then implemented in numerical shakedown analysis, The actual residual stress fields are calculated by incremental finite element elastic-plastic analysis technique for finite deformation under the specified load path with different load levels. The shakedown behavior and the shakedown limit load are determined according to the proposed criterion. The validation of the criterion is performed by a benchmark shakedown example, which is a square plate with a central hole under biaxial loading. The results are consistent with existing results in the literatures and are validated by full cyclic elastic-plastic finite element analysis. The numerical shakedown analysis applying the proposed criterion avoids processing dimension obstacles and performing full cyclic elastic-plastic analysis under arbitrary load paths which should be accounted for appearing. The effect of material model and geometric changes on shakedown behavior can he considered conveniently.展开更多
Unbound granular material specifications for road pavements in Australia are primarily based on physical material specification rather than mechanical characterisation. This simplified approach does not reflect the ac...Unbound granular material specifications for road pavements in Australia are primarily based on physical material specification rather than mechanical characterisation. This simplified approach does not reflect the actual material performance under repeated dynamic traffic loads. There is a little information available on the influence of the local crushed rock properties and compacted layer properties on permanent deformation (PD). This study aims to characterise the local unbound granular materials in Victoria according to their PD behaviour under repeated loads and to develop a suitable shakedown criterion that could describe the PD of the tested materials to simplify the flexible pavement design. Repeated-load triaxial tests were conducted over several samples with a range of moisture contents, gradations, densities, and stress conditions. The laboratory test results showed that PD behaviour was influenced by several factors. In addition, the tested subbase-specified unbound granular materials reflect high PD resistance that is almost equivalent to basequality unbound granular materials. This may indicate that current requirements for the subbase-quality unbound granular materials are over-prescribe. Moreover, as the existing shakedown criterion was not applicable for the multi-stage repeated-load triaxial test and the local tested materials, a new shakedown criterion and new boundaries are proposed based on the PD behaviour. In the proposed criterion, the shakedown ranges are identified based on the curve angle of the PD vs. logarithm of the number of loading cycles, and this new criterion was validated using several materials from existing literature. The local tested base and subbase materials can be assigned as Range A when PD\1%, Range B when 1%\PD\3%, and Range C when PD[3%. The proposed criterion could provide a useful and quick approach to assess the PD of the unbound granular materials with both single and multistages of stresses.展开更多
The shakedown analysis of structures under variable multi-loadings is considered, and the corresponding simple shakedown condition is presented in this paper. Distribution of fixed stresses field is given, and the sel...The shakedown analysis of structures under variable multi-loadings is considered, and the corresponding simple shakedown condition is presented in this paper. Distribution of fixed stresses field is given, and the self-equilibrium of fixed stresses field is analyzed. Elastic shakedown and plastic shakedown conditions are presented based on the fixed stresses field. The theorem is convenient to evaluate the shakedown limit of structures under cyclical variable multiloadings through solving positive scalar fields and fixed stresses field factors at a series of dangerous positions of the structure, and tedious computations are avoided. Finally the theorem is applied to a thick-walled cylindrical tube under variable pressure and temperature, and the rolling contact problem. The results are in good agreement with some computational results.展开更多
The symmetric Galerkin boundary element method (SGBEM) instead ofthe finite element method is used t perform lower bound limit andshakedown analysis of structures. The self-equilibrium stress fieldsare constructed by ...The symmetric Galerkin boundary element method (SGBEM) instead ofthe finite element method is used t perform lower bound limit andshakedown analysis of structures. The self-equilibrium stress fieldsare constructed by a linear combination of several basicself-equilibrium stress fields with parameters to be determined.These basic self-equilibrium stress fields are expressed as elasticresponses of the body to im- posed permanent strains and obtainedthrough elastic-plastic incremental analysis.展开更多
In aerospace engineering,design and optimization of mechanical structures are usually performed with respect to elastic limit.Besides causing insufcient use of the material,such design concept fails to meet the ever g...In aerospace engineering,design and optimization of mechanical structures are usually performed with respect to elastic limit.Besides causing insufcient use of the material,such design concept fails to meet the ever growing needs of the light weight design.To remedy this problem,in the present study,a shakedown theory based numerical approach for performing parametric optimization is presented.Within this approach,strength of the structure is measured by its shakedown limit calculated from the direct method.The numerical method developed for the structural optimization consists of nested loops:the inner loop adopts the interior point method to solve shakedown problems pertained to fxed design parameters,while the outer loop employs the genetic algorithm to fnd optimal design parameters leading to the greatest shakedown limit.The method established is frst verifed by the classic plate-with-a-circular-hole example,and after that it is applied to an airtight module for determining few key design parameters.By carefully analyzing results generated during the optimization process,it is convinced that the approach can become a viable means for designing similar aerospace structures.展开更多
This paper proposes a numerical solution method for upper bound shakedown analysis of perfectly elasto-plastic thin plates by employing the C^(1) natural element method.Based on the Koiter’s theorem and von Mises yie...This paper proposes a numerical solution method for upper bound shakedown analysis of perfectly elasto-plastic thin plates by employing the C^(1) natural element method.Based on the Koiter’s theorem and von Mises yield criterion,the nonlinear mathematical programming formulation for upper bound shakedown analysis of thin plates is established.In this formulation,the trail function of residual displacement increment is approximated by using the C^(1) shape functions,the plastic incompressibility condition is satisfied by introducing a constant matrix in the objective function,and the time integration is resolved by using the Konig’s technique.Meanwhile,the objective function is linearized by distinguishing the non-plastic integral points from the plastic integral points and revising the objective function and associated equality constraints at each iteration.Finally,the upper bound shakedown load multipliers of thin plates are obtained by direct iterative and monotone convergence processes.Several benchmark examples verify the good precision and fast convergence of this proposed method.展开更多
The shakedown behavior of structures subjected to a combined loading of constant and cyclic loads has been well researched.For some specified problems,shakedown limit loads have been obtained.However,the general effec...The shakedown behavior of structures subjected to a combined loading of constant and cyclic loads has been well researched.For some specified problems,shakedown limit loads have been obtained.However,the general effect of combined loading on the structural shakedown has not yet been presented.The general analytic solution of the elastic shakedown limit load is thus derived for a structure subjected to combined loading.Polizzotto's extended static shakedown theorem for combined loading is applied.The stress field in equilibrium with the external constant load required in Polizzotto's extended theorem is constructed by subtracting the reference elastic stress field of the peak cyclic load from the elastic-plastic stress field of the combined constant load and peak cyclic load.The shakedown condition of the stress field is then derived according to the extended theorem.Through the analytical analysis of the shakedown condition,the structural shakedown behavior under combined loading is investigated.A general solution of the shakedown limit load is then derived,and the effects of the combined loading on the shakedown behavior are proposed.The obtained general analytical result is applied to a hollow tension specimen under constant tension and alternating torsion and a plate with a central hole under constant and cyclic tension.The results are consistent with the solutions reported in the literature.展开更多
The static and kinematic shakedown of a functionally graded （FG） Bree plate is analyzed. The plate is subjected to coupled constant mechanical load and cyclically varying temperature. The material is assumed linearl...The static and kinematic shakedown of a functionally graded （FG） Bree plate is analyzed. The plate is subjected to coupled constant mechanical load and cyclically varying temperature. The material is assumed linearly elastic and nonlinear isotropic hardening with elastic modulus,yield strength and the thermal expansion coeffcient varying exponentially through the thickness of the plate. The boundaries between the shakedown area and the areas of elasticity,incremental collapse and reversed plasticity are determined,respectively. The shakedown of the counterpart made of homogeneous material with average material properties is also analyzed. The comparison between the results obtained in the two cases exhibits distinct qualitative and quantitative difference,indicating the importance of shakedown analysis for FG structures. Since FG structures are usually used in the cases where severe coupled cyclic thermal and mechanical loadings are applied,the approach developed and the results obtained are significant for the analysis and design of such kind of structures.展开更多
In this paper, a formulation for shakedown analysis of elastic-plastic offshore structures under cyclic wave loading is presented. In this formulation, a fast numerical solution method is used, suitable for the Finite...In this paper, a formulation for shakedown analysis of elastic-plastic offshore structures under cyclic wave loading is presented. In this formulation, a fast numerical solution method is used, suitable for the Finite Element Method (FEM) analysis of large offshore structures on which shear effects in addition to bending and axial effects are taken into account. The Morison equation is adopted for converting the velocity and acceleration terms into resultant forces and it is extended to consider arbitrary orientations of the structural members. The theoretical methods of the shakedown analysis are discussed in detail and the formulation is applied to an offshore structure to verify the concept employed and its analytical capabilities.展开更多
It is of great practical importance to analyze the shakedown of shell structures under cyclic loading, especially of those made of strain hardening materials.In this paper, same further understanding of the shakedown ...It is of great practical importance to analyze the shakedown of shell structures under cyclic loading, especially of those made of strain hardening materials.In this paper, same further understanding of the shakedown theorem for kinematic hardening materials has been made, and it is applied to analyze the shakedown of shell structures Though the residual stress of a real stale is related to plastic strain, the time-independent residual stress field as we will show in the theorem may be unrelated to the time-independent kinematically admissible plastic strain field For the engineering application, it will lie much more convenient to point this out clearly and definitely, otherwise it will be very difficult. Also, we have proposed a new method of proving this theorem.The above theorem is applied to the shakedown analysis of a cylindrical shell with hemispherical ends. According to the elastic solution, various possible residual sfcss and plastic strain Jlelds, the shakedown analysis of the structure can be reduced to a mathematical programming problem.The results of calculation show that the shakedown load oj strain hardening materials is about 30-40% higher than that of ideal plastic materials. So it is very important to consider the hardening of materials in the shakedown analysis,for it can greatly increase the structure design capacity, and meanwhile provide ascicntific basis to improve the design of shell structures.展开更多
基金the support of the National Natural Science Foundation of China(Grant No.52108319)the Natural Science Foundation of Jiangxi Province(20224BAB214069)。
文摘Red clay,widely used as a subgrade material in southern China,requires a reliable evaluation of its dynamic behavior to ensure infrastructure safety.Long-term cyclic triaxial tests were conducted on red clay from typical,complex subway subgrades to investigate its dynamic properties and shakedown behavior under intermittent cyclic loading.Results show that intermittent cyclic loading,especially with multiple amplitudes,causes greater axial plastic strain and lower post-cyclic strength than continuous loading.These effects diminish with increasing confining pressure.Notably,axial strain partially recovers during loading intervals,with recovery ratios depending on the number and sequence of pauses.Based on the rules of cumulative plastic strain rates and cumulative plastic strain increments,shakedown behavior for red clay under intermittent cyclic loading is divided into three categories:plastic shakedown,critical shakedown,and plastic creep.A quantitative shakedown limit criterion is proposed using the Boltzmann function.Shakedown behavior significantly influences the post-cyclic strengths,and the influence diminishes as confining pressure increases.Samples exhibiting plastic creep and plastic shakedown behavior have the lowest and highest strengths,and those with critical shakedown behaviors have medium strengths.Cyclic loading with relatively low-stress amplitude causes a hardening effect,while cyclic loading intermittence or cyclic loading with relatively high-stress amplitude causes a degradation effect,and both effects are mitigated by higher confining pressures.
基金Project supported by the National Natural Science Foundation of China (Nos. 52075070 and12302254)the Dalian City Supports Innovation and Entrepreneurship Projects for High-Level Talents (No. 2021RD16)the Liaoning Revitalization Talents Program (No. XLYC2002108)。
文摘The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design. Therefore, it is necessary to accurately predict the shakedown domains of these materials. The static shakedown theorem, also known as Melan's theorem, is a fundamental method used to predict the shakedown domains of structures and materials. Within this method, a key aspect lies in the construction and application of an appropriate self-equilibrium stress field(SSF). In the structural shakedown analysis, the SSF is typically constructed by governing equations that satisfy no external force(NEF) boundary conditions. However, we discover that directly applying these governing equations is not suitable for the shakedown analysis of heterogeneous materials. Researchers must consider the requirements imposed by the Hill-Mandel condition for boundary conditions and the physical significance of representative volume elements(RVEs). This paper addresses this issue and demonstrates that the sizes of SSFs vary under different boundary conditions, such as uniform displacement boundary conditions(DBCs), uniform traction boundary conditions(TBCs), and periodic boundary conditions(PBCs). As a result, significant discrepancies arise in the predicted shakedown domain sizes of heterogeneous materials. Built on the demonstrated relationship between SSFs under different boundary conditions, this study explores the conservative relationships among different shakedown domains, and provides proof of the relationship between the elastic limit(EL) factors and the shakedown loading factors under the loading domain of two load vertices. By utilizing numerical examples, we highlight the conservatism present in certain results reported in the existing literature. Among the investigated boundary conditions, the obtained shakedown domain is the most conservative under TBCs.Conversely, utilizing PBCs to construct an SSF for the shakedown analysis leads to less conservative lower bounds, indicating that PBCs should be employed as the preferred boundary conditions for the shakedown analysis of heterogeneous materials.
基金supported by the Chinese Postdoctoral Science Foundation(2013M540934).
文摘This paper proposes a novel numerical solution approach for the kinematic shakedown analysis of strain-hardening thin plates using the C^(1)nodal natural element method(C^(1)nodal NEM).Based on Koiter’s theorem and the von Mises and two-surface yield criteria,a nonlinear mathematical programming formulation is constructed for the kinematic shakedown analysis of strain-hardening thin plates,and the C^(1)nodal NEM is adopted for discretization.Additionally,König’s theory is used to deal with time integration by treating the generalized plastic strain increment at each load vertex.A direct iterative method is developed to linearize and solve this formulation by modifying the relevant objective function and equality constraints at each iteration.Kinematic shakedown load factors are directly calculated in a monotonically converging manner.Numerical examples validate the accuracy and convergence of the developed method and illustrate the influences of limited and unlimited strain-hardening models on the kinematic shakedown load factors of thin square and circular plates.
基金Supported by National Science and Technology Major Project of China(Grant No.2013ZX04003031)National Natural Science Foundation of China(Grant No.51575474)+1 种基金Hebei Provincial College Innovation Team Leader Training Program of China(Grant No.LJRC012)Hebei Provincial Natural Science Foundation of China(Grant No.E2015203223)
文摘The effect of kinematic hardening behavior on the shakedown behaviors of structure has been investigated by performing shakedown analysis for some specific problems. The results obtained only show that the shakedown limit loads of structures with kinematic hardening model are larger than or equal to those with perfectly plastic model of the same initial yield stress. To further investigate the rules governing the different shakedown behaviors of kinematic hardening structures, the extended shakedown theorem for limited kinematic hardening is applied, the shakedown condition is then proposed, and a general analytical solution for the structural shakedown limit load is thus derived. The analytical shakedown limit loads for fully reversed cyclic loading and non-fully reversed cyclic loading are then given based on the general solution. The resulting analytical solution is applied to some specific problems： a hollow specimen subjected to tension and torsion, a flanged pipe subjected to pressure and axial force and a square plate with small central hole subjected to biaxial tension. The results obtained are compared with those in literatures, they are consistent with each other. Based on the resulting general analytical solution, rules governing the general effects of kinematic hardening behavior on the shakedown behavior of structure are clearly.
基金Supported by National Science and Technology Major Project of China(Grant No.2013ZX04003031)National Natural Science Foundation of China(Grant No.51475408)+1 种基金Hebei Provincial College Innovation Team Leader Training Program of China(Grant No.LJRC012)Hebei Provincial Natural Science Foundation of China(Grant No.E2012203045)
文摘Construction of the static admissible residual stress field and searching the optimal field are key tasks in the shakedown analysis methods applying the static theorem. These methods always meet dimension obstacles when dealing with complex problems. In this paper, a novel shakedown criterion is proposed employing actual residual stress field based on the static shakedown theorem. The actual residual stress field used here is produced under a specified load path, which is a sequence of proportional loading and unloading from zero to all the vertices of the given load domain. This ensures that the shakedown behavior in the whole load domain can be determined based on the theorem proposed by K6nig. The shakedown criterion is then implemented in numerical shakedown analysis, The actual residual stress fields are calculated by incremental finite element elastic-plastic analysis technique for finite deformation under the specified load path with different load levels. The shakedown behavior and the shakedown limit load are determined according to the proposed criterion. The validation of the criterion is performed by a benchmark shakedown example, which is a square plate with a central hole under biaxial loading. The results are consistent with existing results in the literatures and are validated by full cyclic elastic-plastic finite element analysis. The numerical shakedown analysis applying the proposed criterion avoids processing dimension obstacles and performing full cyclic elastic-plastic analysis under arbitrary load paths which should be accounted for appearing. The effect of material model and geometric changes on shakedown behavior can he considered conveniently.
文摘Unbound granular material specifications for road pavements in Australia are primarily based on physical material specification rather than mechanical characterisation. This simplified approach does not reflect the actual material performance under repeated dynamic traffic loads. There is a little information available on the influence of the local crushed rock properties and compacted layer properties on permanent deformation (PD). This study aims to characterise the local unbound granular materials in Victoria according to their PD behaviour under repeated loads and to develop a suitable shakedown criterion that could describe the PD of the tested materials to simplify the flexible pavement design. Repeated-load triaxial tests were conducted over several samples with a range of moisture contents, gradations, densities, and stress conditions. The laboratory test results showed that PD behaviour was influenced by several factors. In addition, the tested subbase-specified unbound granular materials reflect high PD resistance that is almost equivalent to basequality unbound granular materials. This may indicate that current requirements for the subbase-quality unbound granular materials are over-prescribe. Moreover, as the existing shakedown criterion was not applicable for the multi-stage repeated-load triaxial test and the local tested materials, a new shakedown criterion and new boundaries are proposed based on the PD behaviour. In the proposed criterion, the shakedown ranges are identified based on the curve angle of the PD vs. logarithm of the number of loading cycles, and this new criterion was validated using several materials from existing literature. The local tested base and subbase materials can be assigned as Range A when PD\1%, Range B when 1%\PD\3%, and Range C when PD[3%. The proposed criterion could provide a useful and quick approach to assess the PD of the unbound granular materials with both single and multistages of stresses.
文摘The shakedown analysis of structures under variable multi-loadings is considered, and the corresponding simple shakedown condition is presented in this paper. Distribution of fixed stresses field is given, and the self-equilibrium of fixed stresses field is analyzed. Elastic shakedown and plastic shakedown conditions are presented based on the fixed stresses field. The theorem is convenient to evaluate the shakedown limit of structures under cyclical variable multiloadings through solving positive scalar fields and fixed stresses field factors at a series of dangerous positions of the structure, and tedious computations are avoided. Finally the theorem is applied to a thick-walled cylindrical tube under variable pressure and temperature, and the rolling contact problem. The results are in good agreement with some computational results.
基金the National Natural Science Foundation of China(No.19902007)the National Foundation for Excellent Doctorial Dissertation of China(No.200025)the Basic Research Foundation of Tsinghua University
文摘The symmetric Galerkin boundary element method (SGBEM) instead ofthe finite element method is used t perform lower bound limit andshakedown analysis of structures. The self-equilibrium stress fieldsare constructed by a linear combination of several basicself-equilibrium stress fields with parameters to be determined.These basic self-equilibrium stress fields are expressed as elasticresponses of the body to im- posed permanent strains and obtainedthrough elastic-plastic incremental analysis.
基金Supported by National Natural Science Foundation of China(Grant No.52075033)Fundamental Research Funds for the Central Universities of China(Grant No.2020RC202).
文摘In aerospace engineering,design and optimization of mechanical structures are usually performed with respect to elastic limit.Besides causing insufcient use of the material,such design concept fails to meet the ever growing needs of the light weight design.To remedy this problem,in the present study,a shakedown theory based numerical approach for performing parametric optimization is presented.Within this approach,strength of the structure is measured by its shakedown limit calculated from the direct method.The numerical method developed for the structural optimization consists of nested loops:the inner loop adopts the interior point method to solve shakedown problems pertained to fxed design parameters,while the outer loop employs the genetic algorithm to fnd optimal design parameters leading to the greatest shakedown limit.The method established is frst verifed by the classic plate-with-a-circular-hole example,and after that it is applied to an airtight module for determining few key design parameters.By carefully analyzing results generated during the optimization process,it is convinced that the approach can become a viable means for designing similar aerospace structures.
基金supported by the Chinese Postdoctoral Science Foundation(2013M540934)supported by the National Key Research and Development Program of China(2016YFC0801905,2017YFF0210704).
文摘This paper proposes a numerical solution method for upper bound shakedown analysis of perfectly elasto-plastic thin plates by employing the C^(1) natural element method.Based on the Koiter’s theorem and von Mises yield criterion,the nonlinear mathematical programming formulation for upper bound shakedown analysis of thin plates is established.In this formulation,the trail function of residual displacement increment is approximated by using the C^(1) shape functions,the plastic incompressibility condition is satisfied by introducing a constant matrix in the objective function,and the time integration is resolved by using the Konig’s technique.Meanwhile,the objective function is linearized by distinguishing the non-plastic integral points from the plastic integral points and revising the objective function and associated equality constraints at each iteration.Finally,the upper bound shakedown load multipliers of thin plates are obtained by direct iterative and monotone convergence processes.Several benchmark examples verify the good precision and fast convergence of this proposed method.
基金Sponsored by the National Natural Science Foundation of China(Grant No.51575474)the College Innovation Team Leader Training Program of Province(Grant No.LJRC012)the Natural Science Foundation of Hebei Province,China(Grant No.E2015203220)
文摘The shakedown behavior of structures subjected to a combined loading of constant and cyclic loads has been well researched.For some specified problems,shakedown limit loads have been obtained.However,the general effect of combined loading on the structural shakedown has not yet been presented.The general analytic solution of the elastic shakedown limit load is thus derived for a structure subjected to combined loading.Polizzotto's extended static shakedown theorem for combined loading is applied.The stress field in equilibrium with the external constant load required in Polizzotto's extended theorem is constructed by subtracting the reference elastic stress field of the peak cyclic load from the elastic-plastic stress field of the combined constant load and peak cyclic load.The shakedown condition of the stress field is then derived according to the extended theorem.Through the analytical analysis of the shakedown condition,the structural shakedown behavior under combined loading is investigated.A general solution of the shakedown limit load is then derived,and the effects of the combined loading on the shakedown behavior are proposed.The obtained general analytical result is applied to a hollow tension specimen under constant tension and alternating torsion and a plate with a central hole under constant and cyclic tension.The results are consistent with the solutions reported in the literature.
基金supported by the National Natural Science Foundation of China (No.10872220)Japan Society for the Promotion of Science (No.L08538)
文摘The static and kinematic shakedown of a functionally graded （FG） Bree plate is analyzed. The plate is subjected to coupled constant mechanical load and cyclically varying temperature. The material is assumed linearly elastic and nonlinear isotropic hardening with elastic modulus,yield strength and the thermal expansion coeffcient varying exponentially through the thickness of the plate. The boundaries between the shakedown area and the areas of elasticity,incremental collapse and reversed plasticity are determined,respectively. The shakedown of the counterpart made of homogeneous material with average material properties is also analyzed. The comparison between the results obtained in the two cases exhibits distinct qualitative and quantitative difference,indicating the importance of shakedown analysis for FG structures. Since FG structures are usually used in the cases where severe coupled cyclic thermal and mechanical loadings are applied,the approach developed and the results obtained are significant for the analysis and design of such kind of structures.
文摘In this paper, a formulation for shakedown analysis of elastic-plastic offshore structures under cyclic wave loading is presented. In this formulation, a fast numerical solution method is used, suitable for the Finite Element Method (FEM) analysis of large offshore structures on which shear effects in addition to bending and axial effects are taken into account. The Morison equation is adopted for converting the velocity and acceleration terms into resultant forces and it is extended to consider arbitrary orientations of the structural members. The theoretical methods of the shakedown analysis are discussed in detail and the formulation is applied to an offshore structure to verify the concept employed and its analytical capabilities.
文摘It is of great practical importance to analyze the shakedown of shell structures under cyclic loading, especially of those made of strain hardening materials.In this paper, same further understanding of the shakedown theorem for kinematic hardening materials has been made, and it is applied to analyze the shakedown of shell structures Though the residual stress of a real stale is related to plastic strain, the time-independent residual stress field as we will show in the theorem may be unrelated to the time-independent kinematically admissible plastic strain field For the engineering application, it will lie much more convenient to point this out clearly and definitely, otherwise it will be very difficult. Also, we have proposed a new method of proving this theorem.The above theorem is applied to the shakedown analysis of a cylindrical shell with hemispherical ends. According to the elastic solution, various possible residual sfcss and plastic strain Jlelds, the shakedown analysis of the structure can be reduced to a mathematical programming problem.The results of calculation show that the shakedown load oj strain hardening materials is about 30-40% higher than that of ideal plastic materials. So it is very important to consider the hardening of materials in the shakedown analysis,for it can greatly increase the structure design capacity, and meanwhile provide ascicntific basis to improve the design of shell structures.
