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
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 lea展开更多
In order to investigate the ratcheting behavior of T225NG alloy, a series of ratcheting tests under uniaxial long-cyclic stressing were performed. The results show that the ratcheting strain of this alloy can get into...In order to investigate the ratcheting behavior of T225NG alloy, a series of ratcheting tests under uniaxial long-cyclic stressing were performed. The results show that the ratcheting strain of this alloy can get into shakedown after tens （or hundreds） of thousand cycles. After the ratcheting strain is saturated under the condition that stress amplitude is half of peak stress, it will bring about subsequent fatigue failure, and relationship between fatigue life and one of peak stress and saturated ratcheting （SR） strain meets power law. As the alloy is under stress jiggling with stress amplitude that is 1%-2.5% of peak stress, the ratcheting strain still become remarkable and goes into shakedown after several hundreds of thousand cycles but there exists little accessional strain caused by creep effect. It is notable that, when the peak stress is 85%-100% of yield stress, the long-cyclic stressing will lead SR strain to be from 1.4% to 2.5% even if the initial ratio of ratcheting strain is zero. Based on ratcheting threshold property of peak stress and monotonicity of relationship between the peak stress and SR strain, a saturated ratcheting model （SRM） is developed to predict SR strain and to estimate saturated creep strain also. In addition, the classes of ratcheting evolutions of metals are discussed.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
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
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.
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 lea
文摘In order to investigate the ratcheting behavior of T225NG alloy, a series of ratcheting tests under uniaxial long-cyclic stressing were performed. The results show that the ratcheting strain of this alloy can get into shakedown after tens （or hundreds） of thousand cycles. After the ratcheting strain is saturated under the condition that stress amplitude is half of peak stress, it will bring about subsequent fatigue failure, and relationship between fatigue life and one of peak stress and saturated ratcheting （SR） strain meets power law. As the alloy is under stress jiggling with stress amplitude that is 1%-2.5% of peak stress, the ratcheting strain still become remarkable and goes into shakedown after several hundreds of thousand cycles but there exists little accessional strain caused by creep effect. It is notable that, when the peak stress is 85%-100% of yield stress, the long-cyclic stressing will lead SR strain to be from 1.4% to 2.5% even if the initial ratio of ratcheting strain is zero. Based on ratcheting threshold property of peak stress and monotonicity of relationship between the peak stress and SR strain, a saturated ratcheting model （SRM） is developed to predict SR strain and to estimate saturated creep strain also. In addition, the classes of ratcheting evolutions of metals are discussed.
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 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.
