Many displacement-based quadrilateral plate elements based on Mindlin-Reissner plate theory have been proposed to analyze the thin and moderately thick plate problems. However, numerical inaccuracies of some elements ...Many displacement-based quadrilateral plate elements based on Mindlin-Reissner plate theory have been proposed to analyze the thin and moderately thick plate problems. However, numerical inaccuracies of some elements appear since the presence of shear locking and spurious zero energy modes for thin plate problems. To overcome these shortcomings, we employ the large increment method(LIM) for the analyses of the plate bending problems, and propose a force-based 8-node quadrilateral plate(8NQP) element which is based on MindlinReissner plate theory and has no extra spurious zero energy mode. Several benchmark plate bending problems are presented to illustrate the accuracy and convergence of the plate element by comparing with the analytical solutions and displacement-based plate elements. The results show that the 8-node plate element produces fast convergence and accurate stress distributions in both the moderately thick and thin plate bending problems. The plate element is insensitive to mesh distortion and it can avoid the shear locking for thin plate analysis.展开更多
A force-based quadrilateral plate element( 4NQP13) for the analysis of the plate bending problems using large increment method( LIM) was proposed. The LIM, a force-based finite element method( FEM),has been successful...A force-based quadrilateral plate element( 4NQP13) for the analysis of the plate bending problems using large increment method( LIM) was proposed. The LIM, a force-based finite element method( FEM),has been successfully developed for the analysis of truss,beam,frame,and 2D continua problems. In these analyses,LIMcan provide more precise stress results and less computational time consumption compared with displacement-based FEM. The plate element was based on the Mindlin-Reissner plate theory which took into account the transverse shear effects.Numerical examples were presented to study its performance including accuracy and convergence behavior,and the results were compared with the results have been obtained from the displacementbased quadrilateral plate elements and the analytical solutions. The4NQP13 element can analyze the moderately thick plates and the thin plates using LIMand is free from spurious zero energy modes and free from shear locking for thin plate analysis.展开更多
The combination of a 4-node quadrilateral mixed interpolation of tensorial components element(MITC4)and the cell-based smoothed finite element method(CSFEM)was formulated and implemented in this work for the analysis ...The combination of a 4-node quadrilateral mixed interpolation of tensorial components element(MITC4)and the cell-based smoothed finite element method(CSFEM)was formulated and implemented in this work for the analysis of free vibration and unidirectional buckling of shell structures.This formulation was applied to numerous numerical examples of non-woven fabrics.As CSFEM schemes do not require coordinate transformation,spurious modes and numerical instabilities are prevented using bilinear quadrilateral element subdivided into two,three and four smoothing cells.An improvement of the original CSFEM formulation was made regarding the calculation of outward unit normal vectors,which allowed to remove the integral operator in the strain smoothing operation.This procedure conducted both to the simplification of the developed formulation and the reduction of computational cost.A wide range of values for the thickness-to-length ratio and edge boundary conditions were analysed.The developed numerical model proved to overcome the shear locking phenomenon with success,revealing both reduced implementation effort and computational cost in comparison to the conventional FEM approach.The cell-based strain smoothing technique used in this work yields accurate results and generally attains higher convergence rate in energy at low computational cost.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11472137,U2141246,12002065,and 12002066)Hunan Natural Science Foundation(Grant No.2021JJ40556).
基金the National Natural Science Foundation of China(No.10872128)
文摘Many displacement-based quadrilateral plate elements based on Mindlin-Reissner plate theory have been proposed to analyze the thin and moderately thick plate problems. However, numerical inaccuracies of some elements appear since the presence of shear locking and spurious zero energy modes for thin plate problems. To overcome these shortcomings, we employ the large increment method(LIM) for the analyses of the plate bending problems, and propose a force-based 8-node quadrilateral plate(8NQP) element which is based on MindlinReissner plate theory and has no extra spurious zero energy mode. Several benchmark plate bending problems are presented to illustrate the accuracy and convergence of the plate element by comparing with the analytical solutions and displacement-based plate elements. The results show that the 8-node plate element produces fast convergence and accurate stress distributions in both the moderately thick and thin plate bending problems. The plate element is insensitive to mesh distortion and it can avoid the shear locking for thin plate analysis.
基金National Natural Science Foundation of China(No.10872128)
文摘A force-based quadrilateral plate element( 4NQP13) for the analysis of the plate bending problems using large increment method( LIM) was proposed. The LIM, a force-based finite element method( FEM),has been successfully developed for the analysis of truss,beam,frame,and 2D continua problems. In these analyses,LIMcan provide more precise stress results and less computational time consumption compared with displacement-based FEM. The plate element was based on the Mindlin-Reissner plate theory which took into account the transverse shear effects.Numerical examples were presented to study its performance including accuracy and convergence behavior,and the results were compared with the results have been obtained from the displacementbased quadrilateral plate elements and the analytical solutions. The4NQP13 element can analyze the moderately thick plates and the thin plates using LIMand is free from spurious zero energy modes and free from shear locking for thin plate analysis.
基金supported by the Portuguese Foundation for Science and Technology(FCT)through project UID/CTM/00264/2019 of 2C2T—Centro de Ciência e Tecnologia Têxtil,hold by National Founds of FCT/MCTES,and project UID/EEA/04436/2013,COMPETE 2020 with the code POCI-01-0145-FEDER-006941.
文摘The combination of a 4-node quadrilateral mixed interpolation of tensorial components element(MITC4)and the cell-based smoothed finite element method(CSFEM)was formulated and implemented in this work for the analysis of free vibration and unidirectional buckling of shell structures.This formulation was applied to numerous numerical examples of non-woven fabrics.As CSFEM schemes do not require coordinate transformation,spurious modes and numerical instabilities are prevented using bilinear quadrilateral element subdivided into two,three and four smoothing cells.An improvement of the original CSFEM formulation was made regarding the calculation of outward unit normal vectors,which allowed to remove the integral operator in the strain smoothing operation.This procedure conducted both to the simplification of the developed formulation and the reduction of computational cost.A wide range of values for the thickness-to-length ratio and edge boundary conditions were analysed.The developed numerical model proved to overcome the shear locking phenomenon with success,revealing both reduced implementation effort and computational cost in comparison to the conventional FEM approach.The cell-based strain smoothing technique used in this work yields accurate results and generally attains higher convergence rate in energy at low computational cost.
