This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress...This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.展开更多
The incompatible elements presented in Ref. [1] are usually called Wilson’s incompatible elements. If we apply the elements to cantilever beam test problem, numerical results will be in agreement exactly with theory ...The incompatible elements presented in Ref. [1] are usually called Wilson’s incompatible elements. If we apply the elements to cantilever beam test problem, numerical results will be in agreement exactly with theory solution only when the element shape is regular (rectangular or right hexahedral). If the element shape is irregular, then the accuracy and convergence is no longer held. Various improvement elements have been presented for ten years. Unfortunately, the exact solution of the test problem is never achieved by these improvement elements for irregular elements.展开更多
This paper describes an incompatible finite element model satisfying the consistency condition of energy to solve the numerical precision problem of finite element solution in perfectly plastic analysis. In this paper...This paper describes an incompatible finite element model satisfying the consistency condition of energy to solve the numerical precision problem of finite element solution in perfectly plastic analysis. In this paper the reason and criterion of the application of the model to plastic limit analysis are discussed, and an algorithm of computing plastic limit load is given.展开更多
In this paper, based on the step reduction method and exaet analytic method, a new method, theexacl element method for constructing finite element, is presented. Since the near method doesn't need varialional prin...In this paper, based on the step reduction method and exaet analytic method, a new method, theexacl element method for constructing finite element, is presented. Since the near method doesn't need varialional principle, it can he applied to solve nun-positive and positive definite partial differcntial equations with arbitral varutble coefficients. By this method, a triangle noncompatible element with 15 degrees of freedom is derived to solve the bending of nonhomogenous Reissner's plate. Because the displacement parameters at the nodal point only contain deflection and rotation angle, it is convenient to deal with arbitrary boundary conditions. In this paper, the convergcnceof displacement and stress resultants is proved. The element obtained by the present method can be used for thin and thick plates as well, hour numerical examples are given at the end of this paper, which indicates that we can obtain satisfactory results and have higher numerical precision.展开更多
文摘This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.
文摘The incompatible elements presented in Ref. [1] are usually called Wilson’s incompatible elements. If we apply the elements to cantilever beam test problem, numerical results will be in agreement exactly with theory solution only when the element shape is regular (rectangular or right hexahedral). If the element shape is irregular, then the accuracy and convergence is no longer held. Various improvement elements have been presented for ten years. Unfortunately, the exact solution of the test problem is never achieved by these improvement elements for irregular elements.
文摘This paper describes an incompatible finite element model satisfying the consistency condition of energy to solve the numerical precision problem of finite element solution in perfectly plastic analysis. In this paper the reason and criterion of the application of the model to plastic limit analysis are discussed, and an algorithm of computing plastic limit load is given.
文摘In this paper, based on the step reduction method and exaet analytic method, a new method, theexacl element method for constructing finite element, is presented. Since the near method doesn't need varialional principle, it can he applied to solve nun-positive and positive definite partial differcntial equations with arbitral varutble coefficients. By this method, a triangle noncompatible element with 15 degrees of freedom is derived to solve the bending of nonhomogenous Reissner's plate. Because the displacement parameters at the nodal point only contain deflection and rotation angle, it is convenient to deal with arbitrary boundary conditions. In this paper, the convergcnceof displacement and stress resultants is proved. The element obtained by the present method can be used for thin and thick plates as well, hour numerical examples are given at the end of this paper, which indicates that we can obtain satisfactory results and have higher numerical precision.
基金Project(11972112)supported by the National Natural Science Foundation of ChinaProject(N2103024)supported by the Fundamental Research Funds for the Central Universities,China。
