Friction stir welding using the tools with polygonal pins is often found to improve the mechanical strength of weld joint in comparison to the tools with circular pins. However, the impacts of pin profile on the peak ...Friction stir welding using the tools with polygonal pins is often found to improve the mechanical strength of weld joint in comparison to the tools with circular pins. However, the impacts of pin profile on the peak temperature, tool torque and traverse force, and the resultant mechanical stresses experienced by the tool have been rarely reported in a systematic manner. An estimation of the rate of heat generation for the tools with polygonal pins is challenging due to their non-axisymmetric cross-section about the tool axis. A novel methodology is presented to analytically estimate the rate of heat generation for the tools with polygonal pins. A three-dimensional heat transfer analysis of friction stir welding is carried out using finite element method. The computed temperature field from the heat transfer model is used to estimate the torque, traverse force and the mechanical stresses experienced by regular triangular, square, pentagon and hexagon pins following the principles of solid mechanics. The computed results show that the peak temperature experienced by the tool pin increases with the number of pin sides. However, the resultant maximum shear stress experienced by the pin reduces from the triangular to hexagonal pins.展开更多
The paper analyzes the influence of a susceptible-infectious-susceptible （SIS） infectious disease affecting both fish and broiler species. The paper also considers a joint SIS project of fish and broiler in which th...The paper analyzes the influence of a susceptible-infectious-susceptible （SIS） infectious disease affecting both fish and broiler species. The paper also considers a joint SIS project of fish and broiler in which the growth rates of both species vary with available nutrients and environmental carrying capacities of biomasses. The nutrients for both species are functions of the biomasses of the two species. The harvesting rates of fish and broiler depend linearly on common effort function. It is assumed that the diseases are trans- mitted to the susceptible populations by direct contact with the infected populations. Using the medicine, some portion of the infected populations are transmitted to the sus- ceptible populations. The existence of steady states and their stability are investigated analytically. The joint profit of the SIS model is maximized using Pontryagin＇s max- imum principle and corresponding optimum harvesting rates are also obtained. Using Mathematica software~ the models are illustrated and the optimum results are obtained and presented in tabular and graphical forms.展开更多
In this paper, a two-species harvesting model has been considered and developed a solu- tion procedure which is able to calculate the equilibrium points of the model where some biological parameters of the model are i...In this paper, a two-species harvesting model has been considered and developed a solu- tion procedure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval numbers. A parametric mathematical pro- gram is formulated to find the biological equilibrium of the model for different values of parameters. This interval-valued problem is converted into an equivalent crisp model using interval mathematics. The main advantage of the proposed procedure is that dif- ferent characteristics of the model can be presented in a single framework. Analytically, the existence of steady state and stabilities are looked into. Using mathematical soft- ware, the model is illustrated and the results are obtained and presented in tabular and graphical forms.展开更多
In this paper, we consider three species harvesting model and develop a solution proce- dure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval nu...In this paper, we consider three species harvesting model and develop a solution proce- dure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval numbers. A parametric mathematical program is formulated to find the biological equilibrium of the model for different values of parame- ters. This interval-valued problem is converted into equivalent crisp model using interval operations. The main advantage of the proposed procedure is that we can present dif- ferent characteristics of the model in a single framework. Analytically, the existence of steady state and stabilities are looked into. Using mathematical software, the model is illustrated and the results are obtained and presented in tabular and graphical forms.展开更多
文摘Friction stir welding using the tools with polygonal pins is often found to improve the mechanical strength of weld joint in comparison to the tools with circular pins. However, the impacts of pin profile on the peak temperature, tool torque and traverse force, and the resultant mechanical stresses experienced by the tool have been rarely reported in a systematic manner. An estimation of the rate of heat generation for the tools with polygonal pins is challenging due to their non-axisymmetric cross-section about the tool axis. A novel methodology is presented to analytically estimate the rate of heat generation for the tools with polygonal pins. A three-dimensional heat transfer analysis of friction stir welding is carried out using finite element method. The computed temperature field from the heat transfer model is used to estimate the torque, traverse force and the mechanical stresses experienced by regular triangular, square, pentagon and hexagon pins following the principles of solid mechanics. The computed results show that the peak temperature experienced by the tool pin increases with the number of pin sides. However, the resultant maximum shear stress experienced by the pin reduces from the triangular to hexagonal pins.
文摘The paper analyzes the influence of a susceptible-infectious-susceptible （SIS） infectious disease affecting both fish and broiler species. The paper also considers a joint SIS project of fish and broiler in which the growth rates of both species vary with available nutrients and environmental carrying capacities of biomasses. The nutrients for both species are functions of the biomasses of the two species. The harvesting rates of fish and broiler depend linearly on common effort function. It is assumed that the diseases are trans- mitted to the susceptible populations by direct contact with the infected populations. Using the medicine, some portion of the infected populations are transmitted to the sus- ceptible populations. The existence of steady states and their stability are investigated analytically. The joint profit of the SIS model is maximized using Pontryagin＇s max- imum principle and corresponding optimum harvesting rates are also obtained. Using Mathematica software~ the models are illustrated and the optimum results are obtained and presented in tabular and graphical forms.
文摘In this paper, a two-species harvesting model has been considered and developed a solu- tion procedure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval numbers. A parametric mathematical pro- gram is formulated to find the biological equilibrium of the model for different values of parameters. This interval-valued problem is converted into an equivalent crisp model using interval mathematics. The main advantage of the proposed procedure is that dif- ferent characteristics of the model can be presented in a single framework. Analytically, the existence of steady state and stabilities are looked into. Using mathematical soft- ware, the model is illustrated and the results are obtained and presented in tabular and graphical forms.
文摘In this paper, we consider three species harvesting model and develop a solution proce- dure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval numbers. A parametric mathematical program is formulated to find the biological equilibrium of the model for different values of parame- ters. This interval-valued problem is converted into equivalent crisp model using interval operations. The main advantage of the proposed procedure is that we can present dif- ferent characteristics of the model in a single framework. Analytically, the existence of steady state and stabilities are looked into. Using mathematical software, the model is illustrated and the results are obtained and presented in tabular and graphical forms.
