This paper presents three boundary meshless methods for solving problems of steady-state and transient heat conduction in nonlinear functionally graded materials(FGMs).The three methods are,respectively,the method of ...This paper presents three boundary meshless methods for solving problems of steady-state and transient heat conduction in nonlinear functionally graded materials(FGMs).The three methods are,respectively,the method of fundamental solution(MFS),the boundary knot method(BKM),and the collocation Trefftz method(CTM)in conjunction with Kirchhoff transformation and various variable transformations.In the analysis,Laplace transform technique is employed to handle the time variable in transient heat conduction problem and the Stehfest numerical Laplace inversion is applied to retrieve the corresponding time-dependent solutions.The proposed MFS,BKM and CTM are mathematically simple,easyto-programming,meshless,highly accurate and integration-free.Three numerical examples of steady state and transient heat conduction in nonlinear FGMs are considered,and the results are compared with those from meshless local boundary integral equation method(LBIEM)and analytical solutions to demonstrate the effi-ciency of the present schemes.展开更多
The basic relations in linear isotropic photoviscoelasticity have been theoretically discussed in de- tails.A new routine has been found to obtain the time-dependent principal stress without the measurement of isoclin...The basic relations in linear isotropic photoviscoelasticity have been theoretically discussed in de- tails.A new routine has been found to obtain the time-dependent principal stress without the measurement of isoclinics.As a test of our method,examples are given at the end of this paper.展开更多
Thermoelastic transient response of multilayered annular cylinders of infinite lengths subjected to known inner pressure and outer surfaces cooling are considered. A method based on the Laplace transformation and fini...Thermoelastic transient response of multilayered annular cylinders of infinite lengths subjected to known inner pressure and outer surfaces cooling are considered. A method based on the Laplace transformation and finite difference method has been developed to analyze the thermoelasticity problem. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. Solutions for the temperature and thermal stress distributions in a transient state were obtained. It was found that the temperature distribution, the displacement and the thermal stresses change slightly as time increases.展开更多
In this study, the closed form of series solutions of the original and modified nonlinear time-fractional Fornberg-Whitham equations are derived by means of the Laplace decomposition method (LDM). The fractional order...In this study, the closed form of series solutions of the original and modified nonlinear time-fractional Fornberg-Whitham equations are derived by means of the Laplace decomposition method (LDM). The fractional order derivatives are expressed in the sense of Caputo. For the specific choice of parameters, the obtained solutions are compared with the exact solutions to validate the accuracy of this method. Numerical solutions are represented graphically which illustrate the behavior of the solutions. Further, the computations express that the above method is straightforward, and it desires the smaller size of computation.展开更多
We investigate an analytical solution for the Schr o¨dinger equation with a position-dependent mass distribution, with the Morse potential via Laplace transformations. We considered a mass function localized arou...We investigate an analytical solution for the Schr o¨dinger equation with a position-dependent mass distribution, with the Morse potential via Laplace transformations. We considered a mass function localized around the equilibrium position.The mass distribution depends on the energy spectrum of the state and the intrinsic parameters of the Morse potential. An exact bound state solution is obtained in the presence of this mass distribution.展开更多
文摘This paper presents three boundary meshless methods for solving problems of steady-state and transient heat conduction in nonlinear functionally graded materials(FGMs).The three methods are,respectively,the method of fundamental solution(MFS),the boundary knot method(BKM),and the collocation Trefftz method(CTM)in conjunction with Kirchhoff transformation and various variable transformations.In the analysis,Laplace transform technique is employed to handle the time variable in transient heat conduction problem and the Stehfest numerical Laplace inversion is applied to retrieve the corresponding time-dependent solutions.The proposed MFS,BKM and CTM are mathematically simple,easyto-programming,meshless,highly accurate and integration-free.Three numerical examples of steady state and transient heat conduction in nonlinear FGMs are considered,and the results are compared with those from meshless local boundary integral equation method(LBIEM)and analytical solutions to demonstrate the effi-ciency of the present schemes.
文摘The basic relations in linear isotropic photoviscoelasticity have been theoretically discussed in de- tails.A new routine has been found to obtain the time-dependent principal stress without the measurement of isoclinics.As a test of our method,examples are given at the end of this paper.
文摘Thermoelastic transient response of multilayered annular cylinders of infinite lengths subjected to known inner pressure and outer surfaces cooling are considered. A method based on the Laplace transformation and finite difference method has been developed to analyze the thermoelasticity problem. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. Solutions for the temperature and thermal stress distributions in a transient state were obtained. It was found that the temperature distribution, the displacement and the thermal stresses change slightly as time increases.
文摘In this study, the closed form of series solutions of the original and modified nonlinear time-fractional Fornberg-Whitham equations are derived by means of the Laplace decomposition method (LDM). The fractional order derivatives are expressed in the sense of Caputo. For the specific choice of parameters, the obtained solutions are compared with the exact solutions to validate the accuracy of this method. Numerical solutions are represented graphically which illustrate the behavior of the solutions. Further, the computations express that the above method is straightforward, and it desires the smaller size of computation.
文摘We investigate an analytical solution for the Schr o¨dinger equation with a position-dependent mass distribution, with the Morse potential via Laplace transformations. We considered a mass function localized around the equilibrium position.The mass distribution depends on the energy spectrum of the state and the intrinsic parameters of the Morse potential. An exact bound state solution is obtained in the presence of this mass distribution.
