An integral constitutive equation and a set of material functions for describing the strain history of polymer melts were formulated in terms of the Cauchy-Green and Finger tensors. A simple memory function and the de...An integral constitutive equation and a set of material functions for describing the strain history of polymer melts were formulated in terms of the Cauchy-Green and Finger tensors. A simple memory function and the dependence of ηo and τt on M3.4 were derived from the theory of non-linear viscoelasticity with constraints of entanglements for polymer melts and substituted into the Oldroye-Walters-Fredickson constitutive equation. An integral constitutive equation for polymer melts was consequently obtained. Some material functions of the constitutive equation related to certain 'test flow' are examined as follows : (1) simple steady shear flow; (2) steady elongation flow; (3) small-amplitude oscillatory shear flow; (4) stress growth upon the inception of steady shear elongation flow; (5) stress relaxation (modulus and compllance). These theoretical relations for simple steady shear flow were compared with experimental data from our laboratory and references for various polymer melts and concentrated solutions. A good agreement between the theory and experiment was achieved.展开更多
In order to get an approximation with better effect of pararneterization of Bezier curves, we proposed a method for arc-length parameterization and the corresponding algorithms by square approximation for the discrete...In order to get an approximation with better effect of pararneterization of Bezier curves, we proposed a method for arc-length parameterization and the corresponding algorithms by square approximation for the discrete even de-parameterization of the curves. This method is simple and easy to implement, and the property of the approximation has no change compared with the original curve. A quantitative criterion for estimating the effect of parameterization is also built to quantitatively characterize the parameterization effect of the algorithms. As a result, the nearly arc-length parameterized curve has a smaller relative deviation using either the algorithm with point constraint at endpoints or the algorithm with point constraint plus the first derivative constraint at endpoints. Experiments show that after re-parameterization with our algorithms, the relative deviation will have at least a 20% reduction.展开更多
This paper focuses on studying the integration method of a generalized Birkhoffian system.The method of variation on parameters for the dynamical equations of a generalized Birkhoffian system is presented.The procedur...This paper focuses on studying the integration method of a generalized Birkhoffian system.The method of variation on parameters for the dynamical equations of a generalized Birkhoffian system is presented.The procedure for solving the problem can be divided into two steps：the first step,a system of auxiliary equations is constructed and its general solution is given;the second step,the parameters are varied,and the solution of the problem is obtained by using the properties of generalized canonical transformation.The method of variation on parameters for the generalized Birkhoffian system is of universal significance,and we take a nonholonomic system and a nonconservative system as examples to illustrate the application of the results of this paper.展开更多
A new parameter coordination and robust optimization approach for multidisciplinary design is presented. Firstly, the constraints network model is established to support engineering change, coordination and optimizati...A new parameter coordination and robust optimization approach for multidisciplinary design is presented. Firstly, the constraints network model is established to support engineering change, coordination and optimization. In this model, interval boxes are adopted to describe the uncertainty of design parameters quantitatively to enhance the design robustness. Secondly, the parameter coordination method is presented to solve the constraints network model, monitor the potential conflicts due to engineering changes, and obtain the consistency solution space corresponding to the given product specifications. Finally, the robust parameter optimization model is established, and genetic arithmetic is used to obtain the robust optimization parameter. An example of bogie design is analyzed to show the scheme to be effective.展开更多
This paper discusses the problem that constructing a curve to satisfy the given endpoint constraints and chord-length parameters. Based on the research of Lu, the curve construction method for the entire tangent angle...This paper discusses the problem that constructing a curve to satisfy the given endpoint constraints and chord-length parameters. Based on the research of Lu, the curve construction method for the entire tangent angles region （α0, α1）∈（-r, r）×（-r, r） is given. Firstly, to ensure the weights are always positive, the three characteristics of cubic rational Bezier curve is proved, then the segment construction idea for the other tangent angles are presented in view of the three characteristics. The curve constructed with the new method satisfies the endpoint constraint and chord-length parameters, it＇s G1 continuous in every segment curve, and the shapes of the curve are well.展开更多
文摘An integral constitutive equation and a set of material functions for describing the strain history of polymer melts were formulated in terms of the Cauchy-Green and Finger tensors. A simple memory function and the dependence of ηo and τt on M3.4 were derived from the theory of non-linear viscoelasticity with constraints of entanglements for polymer melts and substituted into the Oldroye-Walters-Fredickson constitutive equation. An integral constitutive equation for polymer melts was consequently obtained. Some material functions of the constitutive equation related to certain 'test flow' are examined as follows : (1) simple steady shear flow; (2) steady elongation flow; (3) small-amplitude oscillatory shear flow; (4) stress growth upon the inception of steady shear elongation flow; (5) stress relaxation (modulus and compllance). These theoretical relations for simple steady shear flow were compared with experimental data from our laboratory and references for various polymer melts and concentrated solutions. A good agreement between the theory and experiment was achieved.
基金The National Natural Science Foundationof China (No.60672135)the Natural Science Foundation of Department of Education of Shaanxi Province, China(No.09JK809)
文摘In order to get an approximation with better effect of pararneterization of Bezier curves, we proposed a method for arc-length parameterization and the corresponding algorithms by square approximation for the discrete even de-parameterization of the curves. This method is simple and easy to implement, and the property of the approximation has no change compared with the original curve. A quantitative criterion for estimating the effect of parameterization is also built to quantitatively characterize the parameterization effect of the algorithms. As a result, the nearly arc-length parameterized curve has a smaller relative deviation using either the algorithm with point constraint at endpoints or the algorithm with point constraint plus the first derivative constraint at endpoints. Experiments show that after re-parameterization with our algorithms, the relative deviation will have at least a 20% reduction.
基金supported by the National Natural Science Foundation of China (10972151)
文摘This paper focuses on studying the integration method of a generalized Birkhoffian system.The method of variation on parameters for the dynamical equations of a generalized Birkhoffian system is presented.The procedure for solving the problem can be divided into two steps：the first step,a system of auxiliary equations is constructed and its general solution is given;the second step,the parameters are varied,and the solution of the problem is obtained by using the properties of generalized canonical transformation.The method of variation on parameters for the generalized Birkhoffian system is of universal significance,and we take a nonholonomic system and a nonconservative system as examples to illustrate the application of the results of this paper.
基金This project is supported by National Natural Science Foundation of China (No.60304015, No.50575142).
文摘A new parameter coordination and robust optimization approach for multidisciplinary design is presented. Firstly, the constraints network model is established to support engineering change, coordination and optimization. In this model, interval boxes are adopted to describe the uncertainty of design parameters quantitatively to enhance the design robustness. Secondly, the parameter coordination method is presented to solve the constraints network model, monitor the potential conflicts due to engineering changes, and obtain the consistency solution space corresponding to the given product specifications. Finally, the robust parameter optimization model is established, and genetic arithmetic is used to obtain the robust optimization parameter. An example of bogie design is analyzed to show the scheme to be effective.
基金Supported by Shandong Province Higher Educational Science and Technology Program(No.J12LN34)Shandong Ji'nan College and Institute Independent Innovation Project(No.201303011,No.201303021,No.201303016)
文摘This paper discusses the problem that constructing a curve to satisfy the given endpoint constraints and chord-length parameters. Based on the research of Lu, the curve construction method for the entire tangent angles region （α0, α1）∈（-r, r）×（-r, r） is given. Firstly, to ensure the weights are always positive, the three characteristics of cubic rational Bezier curve is proved, then the segment construction idea for the other tangent angles are presented in view of the three characteristics. The curve constructed with the new method satisfies the endpoint constraint and chord-length parameters, it＇s G1 continuous in every segment curve, and the shapes of the curve are well.
