This paper presents a novel fully edge-based smoothed finite element method for free vibration analysis of functionally graded plates,incorporating a quasi-weak form of smoothed integral within an edge-based finite el...This paper presents a novel fully edge-based smoothed finite element method for free vibration analysis of functionally graded plates,incorporating a quasi-weak form of smoothed integral within an edge-based finite element method framework.Employing first-order shear deformation plate theory,the present method accounts for transverse shear strain and rotary inertia effects while addressing exponentially graded material properties along the plate thickness.The formulation integrates a three-node Mindlin plate element(MIN3)with a shear stabilization technique to prevent shear locking.The quasi-weak form of smoothed integral necessitates the evaluation of indefinite integrals for shape functions,effectively tacking domain integrals related to the shape functions without partial derivatives.By applying both quasi-weak form of smoothed integral and strain smoothing technique,all domain integrals in stiffness and mass matrices are converted into boundary integrals over smoothing domains.Therefore,isoparametric mapping and computing of Jacobian matrix are completely eliminated throughout the solution process.The natural frequencies obtained using the present method are in good agreement with those reported in the literature,highlighting the versatility of the present method for free vibration analysis of functionally graded plates.Notably,the present method demonstrates advantages in eliminating shear locking and reducing sensitivity to mesh distortion.展开更多
基金financial support from the National Natural Science Foundation of China(12172131,12162014)the Jiangxi Provincial Cultivation Program for Academic and Technical Leaders of Major Subjects(20225BCJ22010)are gratefully acknowledged.
文摘This paper presents a novel fully edge-based smoothed finite element method for free vibration analysis of functionally graded plates,incorporating a quasi-weak form of smoothed integral within an edge-based finite element method framework.Employing first-order shear deformation plate theory,the present method accounts for transverse shear strain and rotary inertia effects while addressing exponentially graded material properties along the plate thickness.The formulation integrates a three-node Mindlin plate element(MIN3)with a shear stabilization technique to prevent shear locking.The quasi-weak form of smoothed integral necessitates the evaluation of indefinite integrals for shape functions,effectively tacking domain integrals related to the shape functions without partial derivatives.By applying both quasi-weak form of smoothed integral and strain smoothing technique,all domain integrals in stiffness and mass matrices are converted into boundary integrals over smoothing domains.Therefore,isoparametric mapping and computing of Jacobian matrix are completely eliminated throughout the solution process.The natural frequencies obtained using the present method are in good agreement with those reported in the literature,highlighting the versatility of the present method for free vibration analysis of functionally graded plates.Notably,the present method demonstrates advantages in eliminating shear locking and reducing sensitivity to mesh distortion.
