Theory of Elasticity
نویسنده
چکیده
2 Kinematics 12 2.1 Geometric interpretation of the deformation gradient . . . . . . . . . . . . . . . . . . 12 2.2 Small strain and linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 Transformations of a deformation gradient . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4 Compatibility conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
منابع مشابه
Static analysis of rectangular nanoplates using exponential shear deformation theory based on strain gradient elasticity theory
In this research, the bending analysis of rectangular nanoplates subjected to mechanical loading is investigated. For this purpose, the strain gradient elasticity theory with one gradient parameter is presented to study the nanoplates. From the best knowledge of authors, it is the first time that the exponential shear deformation formulation based on strain gradient elasticity theory is carried...
متن کاملFree Vibration Analysis of Microtubules as Orthotropic Elastic Shells Using Stress and Strain Gradient Elasticity Theory
In this paper, vibration of the protein microtubule, one of the most important intracellular elements serving as one of the common components among nanotechnology, biotechnology and mechanics, is investigated using stress and strain gradient elasticity theory and orthotropic elastic shells model. Microtubules in the cell are influenced by internal and external stimulation and play a part in con...
متن کاملON MAXWELL'S STRESS FUNCTIONS FOR SOLVING THREE DIMENSIONAL ELASTICITY PROBLEMS IN THE THEORY OF ELASTICITY
The governing equations of three dimensional elasticity problems include the six Beltrami-Michell stress compatibility equations, the three differential equations of equilibrium, and the six material constitutive relations; and these are usually solved subject to the boundary conditions. The system of fifteen differential equations is usually difficult to solve, and simplified methods are usual...
متن کاملWave Propagation in Rectangular Nanoplates Based on a New Strain Gradient Elasticity Theory with Considering in-Plane Magnetic Field
In this paper, on the basis of a new strain gradient elasticity theory, wave propagation in rectangular nanoplates by considering in-plane magnetic field is studied. This strain gradient theory has two gradient parameters and has the ability to compare with the nonlocal elasticity theory. From the best knowledge of author, it is the first time that this theory is used for investigating wave pro...
متن کاملBuckling analysis of graphene nanosheets based on nonlocal elasticity theory
This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...
متن کاملExact analytical approach for free longitudinal vibration of nanorods based on nonlocal elasticity theory from wave standpoint
In this paper, free longitudinal vibration of nanorods is investigated from the wave viewpoint. The Eringen’s nonlocal elasticity theory is used for nanorods modelling. Wave propagation in a medium has a similar formulation as vibrations and thus, it can be used to describe the vibration behavior. Boundaries reflect the propagating waves after incident. Firstly, the governing quation of nanoro...
متن کامل