Analytical solutions for buckling of size-dependent Timoshenko beams

doi:10.1007/s10483-019-2494-8

Abstract

Abstract: 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.

Key words: satellite surface, explosion, jet How, aerosol, the amount of dust, strain gradient theory, boundary condition, buckling

2010 MSC Number:

74F15
35B34

Xiaojian XU, Mulian ZHENG. Analytical solutions for buckling of size-dependent Timoshenko beams. Applied Mathematics and Mechanics (English Edition), 2019, 40(7): 953-976.

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