This paper aims to present the critical top tension for static equilibrium configurations of a steel catenary riser（SCR） by using the finite element method. The critical top tension is the minimum top tension that c...This paper aims to present the critical top tension for static equilibrium configurations of a steel catenary riser（SCR） by using the finite element method. The critical top tension is the minimum top tension that can maintain the equilibrium of the SCR. If the top tension is smaller than the critical value, the equilibrium of the SCR does not exist. If the top tension is larger than the critical value, there are two possible equilibrium configurations. These two configurations exhibit the nonlinear large displacement. The configuration with the smaller displacement is stable, while the one with larger displacement is unstable. The numerical results show that the increases in the riser＇s vertical distances, horizontal offsets, riser＇s weights, internal flow velocities, and current velocities increase the critical top tensions of the SCR. In addition, the parametric studies are also performed in order to investigate the limit states for the analysis and design of the SCR.展开更多
In the GaN-based heterostructures, this paper reports that the strong electric fields induced by polarization effects at the structure boundaries complicate the electric-static equilibrium and the boundary conditions....In the GaN-based heterostructures, this paper reports that the strong electric fields induced by polarization effects at the structure boundaries complicate the electric-static equilibrium and the boundary conditions. The basic requirements of electric-static equilibrium for the heterostructure systems are discussed first, and it is deduced that in the application of the coupled Schroedinger-Poisson model to the heterostructures of electric static equilibrium state, zero external electric field guarantees the overall electric neutrality, and there is no need to introduce the charge balance equation. Then the relation between the screening of the polar charges in GaN-based heterostructures and the possible boundary conditions of the Poisson equation is analysed, it is shown that the various boundary conditions are equivalent to each other, and the surface charge, which can be used in studying the screening of the polar charges, can be precisely solved even if only the conduction band energy is correctly known at the surface. Finally, through the calculations on an AlGaN/GaN heterostructure with typical structure parameters by the coupled Schroedinger-Poisson model under the various boundary conditions, the correctness of the above analyses are validated.展开更多
On the basis of the Young-Laplace Equation that describes the pressure difference between each side of a curved liquid surface, a static equilibrium model is established to describe the surface shape of the weld bead....On the basis of the Young-Laplace Equation that describes the pressure difference between each side of a curved liquid surface, a static equilibrium model is established to describe the surface shape of the weld bead. The geometrical model for the molten pool is included, which is essential to explain the undercut phenomenon during high speed bead-on-plate welding. The results got from an iteration algorithm show that it is the force balance on the liquid mixture of the deposited metal and the molten base metal that causes the undercut. Some factors and their effects are also analyzed.展开更多
The development of a theoretical model to predict the four equilibrium forces of reaction on a simple ladder of non-adjustable length leaning against a wall has long remained an unresolved matter. The difficulty is th...The development of a theoretical model to predict the four equilibrium forces of reaction on a simple ladder of non-adjustable length leaning against a wall has long remained an unresolved matter. The difficulty is that the problem is statically indeterminate and therefore requires complementary information to obtain a unique solution. This paper reports 1) a comprehensive theoretical analysis of the three fundamental models based on treating the ladder as a single Euler-Bernoulli beam, and 2) a detailed experimental investigation of the forces of reaction as a function of applied load and location of load. In contrast to previous untested proposals that the solution to the ladder problem lay in the axial constraint on compression or the transverse constraint on flexure, the experimental outcome of the present work showed unambiguously that 1) the ladder could be modeled the best by a pinned support at the base (on the ground) and a roller support at the top (at the wall), and 2) the only complementary relation needed to resolve the static indeterminacy is the force of friction at the wall. Measurements were also made on the impact loading of a ladder by rapid ascent and descent of a climber. The results obtained were consistent with a simple dynamical model of the ladder as a linear elastic medium subject to a pulse perturbation. The solution to the ladder problem herein presented provides a basis for theoretical extension to other types of ladders. Of particular importance, given that accidents involving ladders in the workplace comprise a significant fraction of all industrial accidents, the theoretical relations reported here can help determine whether a collapsed structure, against which a ladder was applied, met regulatory safety limits or not.展开更多
In a recent publication the author derived and experimentally tested several theoretical models, distinguished by different boundary conditions at the contacts with horizontal and vertical supports, that predicted the...In a recent publication the author derived and experimentally tested several theoretical models, distinguished by different boundary conditions at the contacts with horizontal and vertical supports, that predicted the forces of reaction on a fixed (i.e. inextensible) ladder. This problem is statically indeterminate since there are 4 forces of reaction and only 3 equations of static equilibrium. The model that predicted the empirical reactions correctly used a law of static friction to complement the equations of static equilibrium. The present paper examines in greater theoretical and experimental detail the role of friction in accounting for the forces of reaction on a fixed ladder. The reported measurements confirm that forces parallel and normal to the support at the top of the ladder are linearly proportional with a constant coefficient of friction irrespective of the magnitude or location of the load, as assumed in the theoretical model. However, measurements of forces parallel and normal to the support at the base of the ladder are linearly proportional with coefficients that depend sensitively on the location (although not the magnitude) of the load. This paper accounts quantitatively for the different effects of friction at the top and base of the ladder under conditions of usual use whereby friction at the vertical support alone is insufficient to keep the ladder from sliding. A theoretical model is also proposed for the unusual circumstance in which friction at the vertical support can keep the ladder from sliding.展开更多
A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance ...A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance summation to every fixed point arbitrarily given on each force line with a weighing factor proportional to corresponding force value. Especially the mechanical simulating technique for its inverse problem has been realized by means of pulley block. The conclusions for the inverse problem derived from mechanic method are in accordance with that given by the pure mathematical method, and the self-consistence of the theorem and its inverse problem has been demonstrated. Some application examples in engineering, economy and mathematics have been discussed, especially the possible application in the research of molecular structure, has also been predicted.展开更多
Fix n electrons on the disk ｜z｜≤R. They generate a static electric field. Let a be an electron located in the disk ｜z｜≤R sin π/n. It shows that the closed disk with center a and radius R contains at least one s...Fix n electrons on the disk ｜z｜≤R. They generate a static electric field. Let a be an electron located in the disk ｜z｜≤R sin π/n. It shows that the closed disk with center a and radius R contains at least one static equilibrium point.展开更多
An engineering application tool for prediction of the static equilibrium bay （ Beach Mod） is established to describe two bay shape formulas by use of the programming software ＂MATLAB＂ with a graphic user interface...An engineering application tool for prediction of the static equilibrium bay （ Beach Mod） is established to describe two bay shape formulas by use of the programming software ＂MATLAB＂ with a graphic user interface （ GUI）. The tool is user-friendly for engineering students for the design of beach shapes. This tool was tested through application on three types of beaches in Taiwan and Australia. By implementing the concept of Headland Control, the Beach Mod program allows users to draw a structure and create an ＇artificial headland. The results indicate that Beach Mod can efficiently forecast beach changes as well as MEPBAY, a competing software package, while boasting a better user interface.展开更多
On the basis of Karman's theory of thin plates with large deflection, the Boltzmann law on linear viscoelastic materials and the mathematical model of dynamic analysis on viscoelastic thin plates, a set of nonline...On the basis of Karman's theory of thin plates with large deflection, the Boltzmann law on linear viscoelastic materials and the mathematical model of dynamic analysis on viscoelastic thin plates, a set of nonlinear integro partial differential equations is first presented by means of a structural function introduced in this paper. Then, by using the Galerkin technique in spatial field and a backward difference scheme in temporal field, the set of nonlinear integro partial differential equations reduces to a system of nonlinear algebraic equations. After solving the algebraic equations, the buckling behavior and multiple equilibrium states can be obtained.展开更多
1 INTRODUCTIONVapor-liquid equilibrium(VLE)relations are required for practical use,such as in the designand operation of disitillation equipment.In the conventional experimental methods of vapor-liquid equilibria,som...1 INTRODUCTIONVapor-liquid equilibrium(VLE)relations are required for practical use,such as in the designand operation of disitillation equipment.In the conventional experimental methods of vapor-liquid equilibria,some analytical instruments are applied.They are time-consuming and dif-ficult for multicomponent system because the proper method for the composition analysis isnot easy to be set up.展开更多
基金supported by the Thailand Research Fund(TRF)through the Royal Golden Jubilee Ph.D.Program(Grant No.PHD/0112/2553)the National Research University(NRU)initiative
文摘This paper aims to present the critical top tension for static equilibrium configurations of a steel catenary riser（SCR） by using the finite element method. The critical top tension is the minimum top tension that can maintain the equilibrium of the SCR. If the top tension is smaller than the critical value, the equilibrium of the SCR does not exist. If the top tension is larger than the critical value, there are two possible equilibrium configurations. These two configurations exhibit the nonlinear large displacement. The configuration with the smaller displacement is stable, while the one with larger displacement is unstable. The numerical results show that the increases in the riser＇s vertical distances, horizontal offsets, riser＇s weights, internal flow velocities, and current velocities increase the critical top tensions of the SCR. In addition, the parametric studies are also performed in order to investigate the limit states for the analysis and design of the SCR.
文摘In the GaN-based heterostructures, this paper reports that the strong electric fields induced by polarization effects at the structure boundaries complicate the electric-static equilibrium and the boundary conditions. The basic requirements of electric-static equilibrium for the heterostructure systems are discussed first, and it is deduced that in the application of the coupled Schroedinger-Poisson model to the heterostructures of electric static equilibrium state, zero external electric field guarantees the overall electric neutrality, and there is no need to introduce the charge balance equation. Then the relation between the screening of the polar charges in GaN-based heterostructures and the possible boundary conditions of the Poisson equation is analysed, it is shown that the various boundary conditions are equivalent to each other, and the surface charge, which can be used in studying the screening of the polar charges, can be precisely solved even if only the conduction band energy is correctly known at the surface. Finally, through the calculations on an AlGaN/GaN heterostructure with typical structure parameters by the coupled Schroedinger-Poisson model under the various boundary conditions, the correctness of the above analyses are validated.
文摘On the basis of the Young-Laplace Equation that describes the pressure difference between each side of a curved liquid surface, a static equilibrium model is established to describe the surface shape of the weld bead. The geometrical model for the molten pool is included, which is essential to explain the undercut phenomenon during high speed bead-on-plate welding. The results got from an iteration algorithm show that it is the force balance on the liquid mixture of the deposited metal and the molten base metal that causes the undercut. Some factors and their effects are also analyzed.
文摘The development of a theoretical model to predict the four equilibrium forces of reaction on a simple ladder of non-adjustable length leaning against a wall has long remained an unresolved matter. The difficulty is that the problem is statically indeterminate and therefore requires complementary information to obtain a unique solution. This paper reports 1) a comprehensive theoretical analysis of the three fundamental models based on treating the ladder as a single Euler-Bernoulli beam, and 2) a detailed experimental investigation of the forces of reaction as a function of applied load and location of load. In contrast to previous untested proposals that the solution to the ladder problem lay in the axial constraint on compression or the transverse constraint on flexure, the experimental outcome of the present work showed unambiguously that 1) the ladder could be modeled the best by a pinned support at the base (on the ground) and a roller support at the top (at the wall), and 2) the only complementary relation needed to resolve the static indeterminacy is the force of friction at the wall. Measurements were also made on the impact loading of a ladder by rapid ascent and descent of a climber. The results obtained were consistent with a simple dynamical model of the ladder as a linear elastic medium subject to a pulse perturbation. The solution to the ladder problem herein presented provides a basis for theoretical extension to other types of ladders. Of particular importance, given that accidents involving ladders in the workplace comprise a significant fraction of all industrial accidents, the theoretical relations reported here can help determine whether a collapsed structure, against which a ladder was applied, met regulatory safety limits or not.
文摘In a recent publication the author derived and experimentally tested several theoretical models, distinguished by different boundary conditions at the contacts with horizontal and vertical supports, that predicted the forces of reaction on a fixed (i.e. inextensible) ladder. This problem is statically indeterminate since there are 4 forces of reaction and only 3 equations of static equilibrium. The model that predicted the empirical reactions correctly used a law of static friction to complement the equations of static equilibrium. The present paper examines in greater theoretical and experimental detail the role of friction in accounting for the forces of reaction on a fixed ladder. The reported measurements confirm that forces parallel and normal to the support at the top of the ladder are linearly proportional with a constant coefficient of friction irrespective of the magnitude or location of the load, as assumed in the theoretical model. However, measurements of forces parallel and normal to the support at the base of the ladder are linearly proportional with coefficients that depend sensitively on the location (although not the magnitude) of the load. This paper accounts quantitatively for the different effects of friction at the top and base of the ladder under conditions of usual use whereby friction at the vertical support alone is insufficient to keep the ladder from sliding. A theoretical model is also proposed for the unusual circumstance in which friction at the vertical support can keep the ladder from sliding.
文摘A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance summation to every fixed point arbitrarily given on each force line with a weighing factor proportional to corresponding force value. Especially the mechanical simulating technique for its inverse problem has been realized by means of pulley block. The conclusions for the inverse problem derived from mechanic method are in accordance with that given by the pure mathematical method, and the self-consistence of the theorem and its inverse problem has been demonstrated. Some application examples in engineering, economy and mathematics have been discussed, especially the possible application in the research of molecular structure, has also been predicted.
文摘Fix n electrons on the disk ｜z｜≤R. They generate a static electric field. Let a be an electron located in the disk ｜z｜≤R sin π/n. It shows that the closed disk with center a and radius R contains at least one static equilibrium point.
文摘An engineering application tool for prediction of the static equilibrium bay （ Beach Mod） is established to describe two bay shape formulas by use of the programming software ＂MATLAB＂ with a graphic user interface （ GUI）. The tool is user-friendly for engineering students for the design of beach shapes. This tool was tested through application on three types of beaches in Taiwan and Australia. By implementing the concept of Headland Control, the Beach Mod program allows users to draw a structure and create an ＇artificial headland. The results indicate that Beach Mod can efficiently forecast beach changes as well as MEPBAY, a competing software package, while boasting a better user interface.
文摘On the basis of Karman's theory of thin plates with large deflection, the Boltzmann law on linear viscoelastic materials and the mathematical model of dynamic analysis on viscoelastic thin plates, a set of nonlinear integro partial differential equations is first presented by means of a structural function introduced in this paper. Then, by using the Galerkin technique in spatial field and a backward difference scheme in temporal field, the set of nonlinear integro partial differential equations reduces to a system of nonlinear algebraic equations. After solving the algebraic equations, the buckling behavior and multiple equilibrium states can be obtained.
基金Supported by the National Natural Science Foundation of China
文摘1 INTRODUCTIONVapor-liquid equilibrium(VLE)relations are required for practical use,such as in the designand operation of disitillation equipment.In the conventional experimental methods of vapor-liquid equilibria,some analytical instruments are applied.They are time-consuming and dif-ficult for multicomponent system because the proper method for the composition analysis isnot easy to be set up.
