On simplified deformation gradient theory of modified gradient elastic Kirchhoff–Love plate

Zhou，Yucheng; Huang，Kefu

2023-07-01

10.1016/j.euromechsol.2023.105014

European Journal of Mechanics, A/Solids   影响因子和分区

0997-7538

1873-7285

A concise modified gradient elastic Kirchhoff–Love plate model with two length-scale parameters is proposed based on simplified deformation gradient theory. A sixth-order basic differential equation and boundary conditions applicable to arbitrary shapes are obtained by applying the principle of minimum potential energy and combining with the generalized strain energy related to classical strain, strain gradient and rotation gradient. By introducing couple stress, the classical bending stiffness corresponding to the fourth-order terms and force-related boundary conditions in the typical gradient elastic Kirchhoff–Love plate model are modified, and the bending deformation of thin plates can be described more flexibly. Under certain conditions, the modified gradient elastic Kirchhoff–Love plate model can be reduced to typical gradient elastic thin plate model, couple stress thin plate model and classical Kirchhoff–Love plate model. The bending boundary value problems of gradient elastic thin plates are further studied, and the specific modified classical boundary conditions and non-classical higher-order boundary condition acceptable to the sixth-order basic equation in Cartesian coordinates are derived. The analytical and numerical bending solutions to gradient Navier-type and Levy-type thin plates with various boundary conditions, including simply supported, clamped and free boundaries are presented, and the size-dependent bending stiffness that is jointly determined by geometric dimensions and length-scale parameters is defined to describe the size effect of thin plates comprehensively.

Bending stiffness Deformation gradient Gradient elastic Kirchhoff–Love plate Size effect

SCI ; EI

英语

第一 ; 通讯

null[11521202]

Mechanics

Mechanics

WOS:001053019700001

ELSEVIER

20231914059610

Bending (deformation) ; Boundary value problems ; Potential energy ; Stiffness ; Strain energy

Mechanics:931.1 ; Materials Science:951

ENGINEERING

2-s2.0-85156221578

Scopus

Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,1088 Xueyuan Boulevard, Guangdong,518055,China

Zhou，Yucheng,Huang，Kefu. On simplified deformation gradient theory of modified gradient elastic Kirchhoff–Love plate[J]. European Journal of Mechanics, A/Solids,2023,100.

Zhou，Yucheng,&Huang，Kefu.(2023).On simplified deformation gradient theory of modified gradient elastic Kirchhoff–Love plate.European Journal of Mechanics, A/Solids,100.

Zhou，Yucheng,et al."On simplified deformation gradient theory of modified gradient elastic Kirchhoff–Love plate".European Journal of Mechanics, A/Solids 100(2023).