Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are t...Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred.展开更多
In this paper,various aspects of the 2D and 3D nonlinear liquid sloshing problems in vertically excited containers have been studied numerically along with the help of a modified-transformation.Based on this new numer...In this paper,various aspects of the 2D and 3D nonlinear liquid sloshing problems in vertically excited containers have been studied numerically along with the help of a modified-transformation.Based on this new numerical algorithm,a numerical study on a regularly and randomly excited container in vertical direction was conducted utilizing four different cases： The first case was performed utilizing a 2D container with regular excitations.The next case examined a regularly excited 3D container with two different initial conditions for the liquid free surface,and finally,3D container with random excitation in the vertical direction.A grid independence study was performed along with a series of validation tests.An iteration error estimation method was used to stop the iterative solver（used for solving the discretized governing equations in the computational domain） upon reaching steady state of results at each time step.In the present case,this method was found to produce quite accurate results and to be more time efficient as compared to other conventional stopping procedures for iterative solvers.The results were validated with benchmark results.The wave elevation time history,phase plane diagram and surface plots represent the wave nonlinearity during its motion.展开更多
Overstraining gun tubes has a twofold advantage. First, it enables the increase of the Safe Maximum Pressure(SMP) in the tube, resulting in a higher muzzle velocity which extends the gun's range and its projectile...Overstraining gun tubes has a twofold advantage. First, it enables the increase of the Safe Maximum Pressure(SMP) in the tube, resulting in a higher muzzle velocity which extends the gun's range and its projectile kinetic energy. Second, it reduces the tube's susceptibility to internal cracking which prolongs its fatigue life. Unfortunately, autofrettage also bears an inherent detrimental effect as it considerably increases the tensile hoop stress at the outer portion of the barrel's wall, which enhances external cracking of the tube by increasing the prevailing Stress Intensity Factor(SIF). In order to quantify this disadvantageous effect, 3-D Mode I SIFs distributions along the front of a single external radial semielliptical crack initiating from the outer surface of an autofrettaged modern gun barrel, overstrained by either the Swage or the Hydraulic autofrettage processes, are evaluated. The analysis is performed by the finite element(FE) method, using singular elements along the crack front. Innovative residual stress fields(RSFs), incorporating the Bauschinger effect for both types of autofrettage are applied to the barrel.Hill's [1] RSF is also applied to the tube for comparison reasons. All three RSFs are incorporated in the FE analysis, using equivalent temperature fields, Values for K_(IA)-the SIF resulting from the tensile residual stresses induced by autofrettage are evaluated for: a typical barrel of radii ratio R_o/R_i = 2, crack depth to wall-thickness ratios(a/t = 0.005-0.1),crack ellipticities(a/c = 0.2-1.0),and five levels of Swage,Hydraulic and Hill's autofrettage(e = 40%,60%,70%,80%,and 100%). In total,375 different 3-D cases are analyzed. The analysis demonstrates undoubtedly the detrimental effect of all types of autofrettage in increasing the prevailing effective stress intensity factor of external cracks, resulting in crack initiation enhancement and crack growth rate acceleration which considerably shortens the total fatigue life of the barrel. Nonetheless, the detrimental effect is autofrettage-type dependent. Swage and Hydraulic autofrettage RSFs differ substantially from each other. The disadvantageous effect of Swage autofrettage is much greater than that resulting from Hydraulic autofrettage. The results also emphasize the significance of the Bauschinger effect and the importance of the 3-D analysis.展开更多
基金This work is supported by the Major State Basic Research Program of China (19990328), the National Tackling Key Problem Program, the National Science Foundation of China (10271066 and 0372052), and the Doctorate Foundation of the Ministry of Education of China (20030422047).
文摘Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred.
文摘In this paper,various aspects of the 2D and 3D nonlinear liquid sloshing problems in vertically excited containers have been studied numerically along with the help of a modified-transformation.Based on this new numerical algorithm,a numerical study on a regularly and randomly excited container in vertical direction was conducted utilizing four different cases： The first case was performed utilizing a 2D container with regular excitations.The next case examined a regularly excited 3D container with two different initial conditions for the liquid free surface,and finally,3D container with random excitation in the vertical direction.A grid independence study was performed along with a series of validation tests.An iteration error estimation method was used to stop the iterative solver（used for solving the discretized governing equations in the computational domain） upon reaching steady state of results at each time step.In the present case,this method was found to produce quite accurate results and to be more time efficient as compared to other conventional stopping procedures for iterative solvers.The results were validated with benchmark results.The wave elevation time history,phase plane diagram and surface plots represent the wave nonlinearity during its motion.
文摘Overstraining gun tubes has a twofold advantage. First, it enables the increase of the Safe Maximum Pressure(SMP) in the tube, resulting in a higher muzzle velocity which extends the gun's range and its projectile kinetic energy. Second, it reduces the tube's susceptibility to internal cracking which prolongs its fatigue life. Unfortunately, autofrettage also bears an inherent detrimental effect as it considerably increases the tensile hoop stress at the outer portion of the barrel's wall, which enhances external cracking of the tube by increasing the prevailing Stress Intensity Factor(SIF). In order to quantify this disadvantageous effect, 3-D Mode I SIFs distributions along the front of a single external radial semielliptical crack initiating from the outer surface of an autofrettaged modern gun barrel, overstrained by either the Swage or the Hydraulic autofrettage processes, are evaluated. The analysis is performed by the finite element(FE) method, using singular elements along the crack front. Innovative residual stress fields(RSFs), incorporating the Bauschinger effect for both types of autofrettage are applied to the barrel.Hill's [1] RSF is also applied to the tube for comparison reasons. All three RSFs are incorporated in the FE analysis, using equivalent temperature fields, Values for K_(IA)-the SIF resulting from the tensile residual stresses induced by autofrettage are evaluated for: a typical barrel of radii ratio R_o/R_i = 2, crack depth to wall-thickness ratios(a/t = 0.005-0.1),crack ellipticities(a/c = 0.2-1.0),and five levels of Swage,Hydraulic and Hill's autofrettage(e = 40%,60%,70%,80%,and 100%). In total,375 different 3-D cases are analyzed. The analysis demonstrates undoubtedly the detrimental effect of all types of autofrettage in increasing the prevailing effective stress intensity factor of external cracks, resulting in crack initiation enhancement and crack growth rate acceleration which considerably shortens the total fatigue life of the barrel. Nonetheless, the detrimental effect is autofrettage-type dependent. Swage and Hydraulic autofrettage RSFs differ substantially from each other. The disadvantageous effect of Swage autofrettage is much greater than that resulting from Hydraulic autofrettage. The results also emphasize the significance of the Bauschinger effect and the importance of the 3-D analysis.
