This paper deals with the capabilities of linear and nonlinear beam theories in predicting the dynamic response of an elastically supported thin beam traversed by a moving mass. To this end, the discrete equations of ...This paper deals with the capabilities of linear and nonlinear beam theories in predicting the dynamic response of an elastically supported thin beam traversed by a moving mass. To this end, the discrete equations of motion are developed based on Lagrange＇s equations via reproducing kernel particle method （RKPM）. For a particular case of a simply supported beam, Galerkin method is also employed to verify the results obtained by RKPM, and a reasonably good agreement is achieved. Variations of the maximum dynamic deflection and bending moment associated with the linear and nonlinear beam theories are investigated in terms of moving mass weight and velocity for various beam boundary conditions. It is demonstrated that for majority of the moving mass velocities, the differences between the results of linear and nonlinear analyses become remarkable as the moving mass weight increases, particularly for high levels of moving mass velocity. Except for the cantilever beam, the nonlinear beam theory predicts higher possibility of moving mass separation from the base beam compared to the linear one. Furthermore, the accuracy levels of the linear beam theory are determined for thin beams under large deflections and small rotations as a function of moving mass weight and velocity in various boundary conditions.展开更多
A meshfree method based on reproducing kernel approximation and point collocation is presented for analysis of metal ring compression. The point collocation method is a true meshfree method without the employment of a...A meshfree method based on reproducing kernel approximation and point collocation is presented for analysis of metal ring compression. The point collocation method is a true meshfree method without the employment of a background mesh. It is shown that, in a point collocation approach, the remesh problem because of the mesh distortion in FEM （finite element method） and the low efficiency in Galerkin-based meshfree method are avoided. The corrected kernel functions are introduced to the stabilization of free-surface boundary conditions. The solution of symmetric ring compression problem is compared with a conventional finite element solution, and reasonable results have been obtained.展开更多
Reproducing kernel particle Method （RKPM） is a meshless technology which has proven very useful for solving problems of elastic plastic fracture mechanics. The mode I plastic zone shape at the crack-tip in a work-ha...Reproducing kernel particle Method （RKPM） is a meshless technology which has proven very useful for solving problems of elastic plastic fracture mechanics. The mode I plastic zone shape at the crack-tip in a work-hard ening material is obtained using RKPM. Ramberg-Osgood stress-strain relation is assumed and the crack-tip stress intensity factor （SIF） before and after formation of the plastic zone are examined. To impose the essential boundary conditions, penalty method is used. To construct the shape functions in the vicinity of the crack and crack-tip, both the diffraction and visibility criteria are employed. A comparison between two conventional treatments, visibility and diffraction, to crack discontinuity is conducted. The effects of different dilation parameters on SIF under plane-stress and plane-strain conditions are ~tudied. Results including plastic zone shape are compared with finite element method （FEM） to show the accuracy of RKPM. The main objective is to study the effects of different dilation parameters on SIF under plane stress and plane strain conditions and to obtain the mode I plastic zone shape at the crack-tip in a work hardening material using RKPM.展开更多
The complex variable reproducing kernel particle method （CVRKPM） of solving two-dimensional variable coefficient advection-diffusion problems is presented in this paper. The advantage of the CVRKPM is that the shape...The complex variable reproducing kernel particle method （CVRKPM） of solving two-dimensional variable coefficient advection-diffusion problems is presented in this paper. The advantage of the CVRKPM is that the shape function of a two-dimensional problem is formed with a one-dimensional basis function. The Galerkin weak form is employed to obtain the discretized system equation, and the penalty method is used to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional variable coefficient advection-diffusion problems are obtained. Two numerical examples are given to show that the method in this paper has greater accuracy and computational efficiency than the conventional meshless method such as reproducing the kernel particle method （RKPM） and the element- free Galerkin （EFG） method.展开更多
文摘This paper deals with the capabilities of linear and nonlinear beam theories in predicting the dynamic response of an elastically supported thin beam traversed by a moving mass. To this end, the discrete equations of motion are developed based on Lagrange＇s equations via reproducing kernel particle method （RKPM）. For a particular case of a simply supported beam, Galerkin method is also employed to verify the results obtained by RKPM, and a reasonably good agreement is achieved. Variations of the maximum dynamic deflection and bending moment associated with the linear and nonlinear beam theories are investigated in terms of moving mass weight and velocity for various beam boundary conditions. It is demonstrated that for majority of the moving mass velocities, the differences between the results of linear and nonlinear analyses become remarkable as the moving mass weight increases, particularly for high levels of moving mass velocity. Except for the cantilever beam, the nonlinear beam theory predicts higher possibility of moving mass separation from the base beam compared to the linear one. Furthermore, the accuracy levels of the linear beam theory are determined for thin beams under large deflections and small rotations as a function of moving mass weight and velocity in various boundary conditions.
基金the National Natural Science Foundation of China （No. 50275059）.
文摘A meshfree method based on reproducing kernel approximation and point collocation is presented for analysis of metal ring compression. The point collocation method is a true meshfree method without the employment of a background mesh. It is shown that, in a point collocation approach, the remesh problem because of the mesh distortion in FEM （finite element method） and the low efficiency in Galerkin-based meshfree method are avoided. The corrected kernel functions are introduced to the stabilization of free-surface boundary conditions. The solution of symmetric ring compression problem is compared with a conventional finite element solution, and reasonable results have been obtained.
文摘Reproducing kernel particle Method （RKPM） is a meshless technology which has proven very useful for solving problems of elastic plastic fracture mechanics. The mode I plastic zone shape at the crack-tip in a work-hard ening material is obtained using RKPM. Ramberg-Osgood stress-strain relation is assumed and the crack-tip stress intensity factor （SIF） before and after formation of the plastic zone are examined. To impose the essential boundary conditions, penalty method is used. To construct the shape functions in the vicinity of the crack and crack-tip, both the diffraction and visibility criteria are employed. A comparison between two conventional treatments, visibility and diffraction, to crack discontinuity is conducted. The effects of different dilation parameters on SIF under plane-stress and plane-strain conditions are ~tudied. Results including plastic zone shape are compared with finite element method （FEM） to show the accuracy of RKPM. The main objective is to study the effects of different dilation parameters on SIF under plane stress and plane strain conditions and to obtain the mode I plastic zone shape at the crack-tip in a work hardening material using RKPM.
基金supported by the National Natural Science Foundation of China (Grant No. 11171208)the Leading Academic Discipline Project of Shanghai City,China (Grant No. S30106)
文摘The complex variable reproducing kernel particle method （CVRKPM） of solving two-dimensional variable coefficient advection-diffusion problems is presented in this paper. The advantage of the CVRKPM is that the shape function of a two-dimensional problem is formed with a one-dimensional basis function. The Galerkin weak form is employed to obtain the discretized system equation, and the penalty method is used to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional variable coefficient advection-diffusion problems are obtained. Two numerical examples are given to show that the method in this paper has greater accuracy and computational efficiency than the conventional meshless method such as reproducing the kernel particle method （RKPM） and the element- free Galerkin （EFG） method.
