Analytical solutions for buckling of size-dependent Timoshenko beams  

作　　者：Xiaojian XU Mulian ZHENG 

机构地区：[1]Key Laboratory for Special Area Highway Engineering of Ministry of Education, School of Highway, Chang'an University, Xi'an 710064, China [2]Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2019年第7期953-976,共24页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(No.11602032);the China Postdoctoral Science Foundation(No.2016M602733);the Shaanxi Postdoctoral Science Foundation(No.2017BSHEDZZ123);the Fundamental Research Funds for the Central Universities of Ministry of Education of China(Nos.310821163502 and 300102219315)

摘　　要：The inconsistences of the higher-order shear resultant expressed in terms of displacement(s) and the complete boundary value problems of structures modeled by the nonlocal strain gradient theory have not been well addressed. This paper develops a size-dependent Timoshenko beam model that considers both the nonlocal effect and strain gradient effect. The variationally consistent boundary conditions corresponding to the equations of motion of Timoshenko beams are reformulated with the aid of the weighted residual method. The complete boundary value problems of nonlocal strain gradient Timoshenko beams undergoing buckling are solved in closed forms. All the possible higher-order boundary conditions induced by the strain gradient are selectively suggested based on the fact that the buckling loads increase with the increasing aspect ratios of beams from the conventional mechanics point of view. Then, motivated by the expression for beams with simply-supported (SS) boundary conditions, some semiempirical formulae are obtained by curve fitting procedures.The inconsistences of the higher-order shear resultant expressed in terms of displacement(s) and the complete boundary value problems of structures modeled by the nonlocal strain gradient theory have not been well addressed. This paper develops a size-dependent Timoshenko beam model that considers both the nonlocal effect and strain gradient effect. The variationally consistent boundary conditions corresponding to the equations of motion of Timoshenko beams are reformulated with the aid of the weighted residual method. The complete boundary value problems of nonlocal strain gradient Timoshenko beams undergoing buckling are solved in closed forms. All the possible higher-order boundary conditions induced by the strain gradient are selectively suggested based on the fact that the buckling loads increase with the increasing aspect ratios of beams from the conventional mechanics point of view. Then, motivated by the expression for beams with simply-supported(SS) boundary conditions, some semiempirical formulae are obtained by curve fitting procedures.

关 键 词：BUCKLING STRAIN GRADIENT theory BOUNDARY condition 

分 类 号：O343.1[理学—固体力学] O326[理学—力学]