Partial Decoupling Finite Element Method Study

The finite element method(FEM)is one of the important means to solve various physical problems in engineering practice.It is a numerical method.At present,the most widely adopted method in commercial software is the displacement finite element method,which performs better displacement accuracy and lower computing resource consumption,especially in large-scale calculation.However,the stress values calculated by the displacement method tend to be discontinuous between elements,thus leading to inaccurate calculation of stress values.For cracks,damage,failure,destruction,penetration which are often encountered in engineering,these problems are often inextricably linked with the stress value.In order to obtain a reliable numerical result,the mesh must be thin and dense.The calculation time and computing resource consumption are corresponding increased,and which is contradictory to computational efficiency.Mixed-FEM treats displacement and stress as two types of variables,which are solved simultaneously in a mixed equation.Thus stress accuracy is improved.Even so,the total number of variables in mixed equation in a three-dimensional problem redoubled.Partial decoupled finite element method is a method between displacement method and mixed finite element method,which has the advantages of both.Based on the modified H-R variational principle and the elastic mechanics symplectic theory,a block mixed isoparametric elemental equation including two kinds of variables of stress and displacement is established.Based on the physical equations of elastic materials,the two types of variables contained in the physical equations are also spatially separated,and the coupling relationship between the two types of variables is partially canceled in the isoparametric equations.The two equations obtained by the partially decoupled finite element method can be solved separately for two types of variables.The solving process is similar to the displacement method for solving the displacement variables,that is,the form of solving linear equations.The stress variables here are ensured continuously between the elements and the result is more accurate.Therefore,the partial decoupling finite element method has the characteristics of simple solution,low computational resource consumption and high precision.In addition,for common bending problems of flexible structures in engineering,nonconforming method can eliminate the phenomenon of shear self-locking.Due to simple character,the Partial Decoupled Finite Element Method is easily generalized to the nonconforming form,which makes this method more complete and can be adapted to solve various engineering problems.The numerical results show that the non-conforming form of the Partial Decoupled Finite Element Method has a very high accuracy in extremely distorted elements issue.