The family of Falk-Neilan P_(k)finite elements,combined with the Argyris P_(k+1)finite elements,solves the Reissner-Mindlin plate equation quasi-optimally and locking-free,on triangular meshes.The method is truly conf...The family of Falk-Neilan P_(k)finite elements,combined with the Argyris P_(k+1)finite elements,solves the Reissner-Mindlin plate equation quasi-optimally and locking-free,on triangular meshes.The method is truly conforming or consistent in the sense that no projection/reduction is introduced.Theoretical proof and numerical confirmation are presented.展开更多
The Tangential-Displacement Normal-Normal-Stress(TDNNS)method is a finite element method that was originally introduced for elastic solids and later extended to piezoelectric materials.It uses tangential components of...The Tangential-Displacement Normal-Normal-Stress(TDNNS)method is a finite element method that was originally introduced for elastic solids and later extended to piezoelectric materials.It uses tangential components of the displacement and normal components of the normal stress vector as degrees of freedom for elasticity.For the electric field,the electric potential is used.The TDNNS method has been shown to provide elements which do not suffer from shear locking.Therefore thin structures(e.g.piezoelectric patch actuators)can be modeled efficiently.Hexahedral and prismatic elements of arbitrary polynomial order are provided in the current contribution.We show that these elements can be used to discretize curved,shelllike geometries by curved elements of high aspect ratio.The order of geometry approximation can be chosen independently from the polynomial order of the shape functions.We present two examples of curved geometries,a circular patch actuator and a radially polarized piezoelectric semi-cylinder.Simulation results of the TDNNS method are compared to results gained in ABAQUS.We obtain good results for displacements and electric potential as well as for stresses,strains and electric field when using only one element in thickness direction.展开更多
文摘The family of Falk-Neilan P_(k)finite elements,combined with the Argyris P_(k+1)finite elements,solves the Reissner-Mindlin plate equation quasi-optimally and locking-free,on triangular meshes.The method is truly conforming or consistent in the sense that no projection/reduction is introduced.Theoretical proof and numerical confirmation are presented.
基金supported by the Linz Institute of Technology[MiFESMS].
文摘The Tangential-Displacement Normal-Normal-Stress(TDNNS)method is a finite element method that was originally introduced for elastic solids and later extended to piezoelectric materials.It uses tangential components of the displacement and normal components of the normal stress vector as degrees of freedom for elasticity.For the electric field,the electric potential is used.The TDNNS method has been shown to provide elements which do not suffer from shear locking.Therefore thin structures(e.g.piezoelectric patch actuators)can be modeled efficiently.Hexahedral and prismatic elements of arbitrary polynomial order are provided in the current contribution.We show that these elements can be used to discretize curved,shelllike geometries by curved elements of high aspect ratio.The order of geometry approximation can be chosen independently from the polynomial order of the shape functions.We present two examples of curved geometries,a circular patch actuator and a radially polarized piezoelectric semi-cylinder.Simulation results of the TDNNS method are compared to results gained in ABAQUS.We obtain good results for displacements and electric potential as well as for stresses,strains and electric field when using only one element in thickness direction.
