Instead of the biharmonic type equation, a set of new governing equations and solving method for circular sector plate bending is presented based on the analogy between plate bending and plane elasticity problems. So ...Instead of the biharmonic type equation, a set of new governing equations and solving method for circular sector plate bending is presented based on the analogy between plate bending and plane elasticity problems. So the Hamiltonian system can also be applied to plate bending problems by introducing bending moment functions. The new method presents the analytical solution for the circular sector plate. The results show that the new method is effective.展开更多
A new effective path has been proposed to formulate thin plate element by using the similarity theory between plane elasticity and plate bending.Because of avoiding the difficulty of c(1)continuity,the construction of...A new effective path has been proposed to formulate thin plate element by using the similarity theory between plane elasticity and plate bending.Because of avoiding the difficulty of c(1)continuity,the construction of thin plate elements becomes easier.The similarity theory and its applications were discussed more deeply,and a new four nodes,sixteen D.O.F.(degree of freedom)thin plate element was presented on the base of the similarity theory.Numerical results for typical problems show that this new element can pass the patch test and has a very good convergence and a high precision.展开更多
Based on analogy between plane elasticity and plate bending as well as variational principles of mixed energy, Hamiltonian system is further led to orthotropic plate bending problems in this paper. Thus many effective...Based on analogy between plane elasticity and plate bending as well as variational principles of mixed energy, Hamiltonian system is further led to orthotropic plate bending problems in this paper. Thus many effective methods of mathematical physics such as separation of variables and eigenfunction expansion can be employed in orthotropic plate bending problems as they are used in plane elasticity. Analytical solutions of rectangular plate are presented directly, which expands the range of analytical solutions. There is an essential distinction between this method and traditional semi-inverse method. Numerical results of orthotropic plate with two lateral sides fixed are included to demonstrate the effectiveness and accuracy of this method.展开更多
基金National Natural Science Foundation(No.19732020)the Doctoral Research Foundation of China
文摘Instead of the biharmonic type equation, a set of new governing equations and solving method for circular sector plate bending is presented based on the analogy between plate bending and plane elasticity problems. So the Hamiltonian system can also be applied to plate bending problems by introducing bending moment functions. The new method presents the analytical solution for the circular sector plate. The results show that the new method is effective.
基金the National Natural Science Foundation of China(19732020)
文摘A new effective path has been proposed to formulate thin plate element by using the similarity theory between plane elasticity and plate bending.Because of avoiding the difficulty of c(1)continuity,the construction of thin plate elements becomes easier.The similarity theory and its applications were discussed more deeply,and a new four nodes,sixteen D.O.F.(degree of freedom)thin plate element was presented on the base of the similarity theory.Numerical results for typical problems show that this new element can pass the patch test and has a very good convergence and a high precision.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19732020) .
文摘Based on analogy between plane elasticity and plate bending as well as variational principles of mixed energy, Hamiltonian system is further led to orthotropic plate bending problems in this paper. Thus many effective methods of mathematical physics such as separation of variables and eigenfunction expansion can be employed in orthotropic plate bending problems as they are used in plane elasticity. Analytical solutions of rectangular plate are presented directly, which expands the range of analytical solutions. There is an essential distinction between this method and traditional semi-inverse method. Numerical results of orthotropic plate with two lateral sides fixed are included to demonstrate the effectiveness and accuracy of this method.
