In this paper, we reexamine the method of successive approximation presented by Prof. Chien Wei-zangfor solving the problem of large deflection of a circular plate, and find that the method could be regarded as the me...In this paper, we reexamine the method of successive approximation presented by Prof. Chien Wei-zangfor solving the problem of large deflection of a circular plate, and find that the method could be regarded as the method of strained parameters in the singular perturbation theory. In terms of the parameter representing the ratio of the center deflection to the thickness of the plate, we make the asymptotic expansions of the deflection, membrane stress and the parameter of load as in Ref. [1], and then give the orthogonality conditions (i.e. the solvability conditions) for the resulting equations, by which the stiffness characteristics of the plate could be determined. It is pointed out that with the solutions for the small deflection problem of the circular plate and the orthogonality conditions, we can derive the third order approximate relations between the parameter of load and the center deflection and the first-term approximation of membrane stresses at the center and edge of the plate without solving the differential equations. For some special cases (i.e. under uniform load, under compound toad, with different boundary conditiors), we deduce the specific expressions and obtain the results in agreement with the previous ones given by Chien Wei-zang, Yeh kai-yuan and Hwang Chien in Refs. [1 - 4J.展开更多
In hot deformation, the flow stress curves of steels always present as two typical types: at relatively high temperature and low strain rate, the flow stress may first increase and then attain a steady value without r...In hot deformation, the flow stress curves of steels always present as two typical types: at relatively high temperature and low strain rate, the flow stress may first increase and then attain a steady value without reaching an obvious peak stress; in other situations, the flow stress decreases after reaching peak stress and then attains a steady value. A new phenomenological model,described by a sine-function equation, is proposed to define the relationship between flow stress and deformation parameters. A series of isothermal compressions for a carbon steel were carried out, as a case study, to obtain basic experimental data.Parameters of the new model were sequentially determined. The predicted results of the proposed model were compared with actual measured data. Good accuracy was found in the standard statistical parameters of correlation coefficient, root mean square error, and average absolute relative error with the values of 0.935, 7.137 MPa and 4.352%, respectively. Discussion of applications of different models in finite-element simulation demonstrated the benefit of the new model. When comparing the simulation results of three different deformation patterns with large strain, the new model showed 10%–20% lower predicted forming load than the original Arrhenius equation, and better applicability and reliability than modified Arrhenius equations.展开更多
A quasi-quasi-principal axis frame means a unit orthogonal frame in which the shear strains are small. As an extension of Hill's principal axis method we establish the approximate representations for various str...A quasi-quasi-principal axis frame means a unit orthogonal frame in which the shear strains are small. As an extension of Hill's principal axis method we establish the approximate representations for various strains. the.finite rotation tensor, spins, strain rates. conjugate stresses and their rates with respect to quasi-principal axes. The quasiprincipal axis method may function as a new basis of numerically analyzing finite deformation problems.展开更多
Numerical manifold method (NMM) is an effective method for simulating block system, however, significant errors are found in its simulation of rotation problems. Three kinds of errors, as volume expansion, stress vibr...Numerical manifold method (NMM) is an effective method for simulating block system, however, significant errors are found in its simulation of rotation problems. Three kinds of errors, as volume expansion, stress vibration, and attenuation of angular velocity, were observed in the original NMM. The first two kind errors are owing to the small deformation assumption and the last one is due to the numerical damping. A large deformation NMM is proposed based on large deformation theory. In this method, the governing equation is derived using Green strain, the large deformation iteration and the open-close iteration are combined, and an updating strategy is proposed. The proposed method is used to analyze block rotation, beam bending, and rock falling problems and the results prove that all three kinds of errors are eliminated in this method.展开更多
基金Project supported by the National Natural Science Foundation of China
文摘In this paper, we reexamine the method of successive approximation presented by Prof. Chien Wei-zangfor solving the problem of large deflection of a circular plate, and find that the method could be regarded as the method of strained parameters in the singular perturbation theory. In terms of the parameter representing the ratio of the center deflection to the thickness of the plate, we make the asymptotic expansions of the deflection, membrane stress and the parameter of load as in Ref. [1], and then give the orthogonality conditions (i.e. the solvability conditions) for the resulting equations, by which the stiffness characteristics of the plate could be determined. It is pointed out that with the solutions for the small deflection problem of the circular plate and the orthogonality conditions, we can derive the third order approximate relations between the parameter of load and the center deflection and the first-term approximation of membrane stresses at the center and edge of the plate without solving the differential equations. For some special cases (i.e. under uniform load, under compound toad, with different boundary conditiors), we deduce the specific expressions and obtain the results in agreement with the previous ones given by Chien Wei-zang, Yeh kai-yuan and Hwang Chien in Refs. [1 - 4J.
基金supported by the National Natural Science Foundation of China(Grant No.51475294)
文摘In hot deformation, the flow stress curves of steels always present as two typical types: at relatively high temperature and low strain rate, the flow stress may first increase and then attain a steady value without reaching an obvious peak stress; in other situations, the flow stress decreases after reaching peak stress and then attains a steady value. A new phenomenological model,described by a sine-function equation, is proposed to define the relationship between flow stress and deformation parameters. A series of isothermal compressions for a carbon steel were carried out, as a case study, to obtain basic experimental data.Parameters of the new model were sequentially determined. The predicted results of the proposed model were compared with actual measured data. Good accuracy was found in the standard statistical parameters of correlation coefficient, root mean square error, and average absolute relative error with the values of 0.935, 7.137 MPa and 4.352%, respectively. Discussion of applications of different models in finite-element simulation demonstrated the benefit of the new model. When comparing the simulation results of three different deformation patterns with large strain, the new model showed 10%–20% lower predicted forming load than the original Arrhenius equation, and better applicability and reliability than modified Arrhenius equations.
文摘A quasi-quasi-principal axis frame means a unit orthogonal frame in which the shear strains are small. As an extension of Hill's principal axis method we establish the approximate representations for various strains. the.finite rotation tensor, spins, strain rates. conjugate stresses and their rates with respect to quasi-principal axes. The quasiprincipal axis method may function as a new basis of numerically analyzing finite deformation problems.
基金This research was supported by the National Natural Science Foundation of China (Grant Nos. 51479001, 41471052)the IWHR Research & Development Support Program (GE0145B462017,GE0145B692017).
文摘Numerical manifold method (NMM) is an effective method for simulating block system, however, significant errors are found in its simulation of rotation problems. Three kinds of errors, as volume expansion, stress vibration, and attenuation of angular velocity, were observed in the original NMM. The first two kind errors are owing to the small deformation assumption and the last one is due to the numerical damping. A large deformation NMM is proposed based on large deformation theory. In this method, the governing equation is derived using Green strain, the large deformation iteration and the open-close iteration are combined, and an updating strategy is proposed. The proposed method is used to analyze block rotation, beam bending, and rock falling problems and the results prove that all three kinds of errors are eliminated in this method.
基金国家自然科学基金项目(No.51109092No.11272137)+5 种基金中国博士后基金项目(No.2013M530237No.2014T70479)supported by the National Natural Science Foundation of China(5110909211272137)the Foundation for Post-doctoral Scientists of China(2013M5302372014T70479)
