A non-classical Timoshenko beam element for the postbuckling analysis of microbeams based on Mindlin’s strain gradient theory

2015 ◽  
Vol 85 (7) ◽  
pp. 937-953 ◽  
Author(s):  
R. Ansari ◽  
M. Faghih Shojaei ◽  
F. Ebrahimi ◽  
H. Rouhi
Keyword(s):  
Timoshenko Beam ◽  
Strain Gradient ◽  
Beam Element ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Mindlin’S Strain Gradient Theory ◽  
Timoshenko Beam Element

Nonlinear Forced Vibration Analysis of FG Cylindrical Nanopanels Based on Mindlin’s Strain Gradient Theory and 3D Elasticity

2020 ◽  
Vol 21 (6) ◽  
pp. 523-537 ◽  
Author(s):  
Y. Gholami ◽  
R. Ansari ◽  
R. Gholami ◽  
H. Rouhi
Keyword(s):  
Strain Gradient ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Solution Technique ◽  
Geometrical Parameters ◽  
Gradient Theory ◽  
Harmonic Load ◽  
Response Curves ◽  
Mindlin’S Strain Gradient Theory ◽  
3D Elasticity

AbstractA numerical approach is used herein to study the primary resonant dynamics of functionally graded (FG) cylindrical nanoscale panels taking the strain gradient effects into consideration. The basic relations of the paper are written based upon Mindlin’s strain gradient theory (SGT) and three-dimensional (3D) elasticity. Since the formulation is developed using Mindlin’s SGT, it is possible to reduce it to simpler size-dependent theories including modified forms of couple stress and strain gradient theories (MCST & MSGT). The governing equations is derived and directly discretized via the variational differential quadrature technique. Then, a numerical solution technique is employed to study the nonlinear resonance response of nanopanels with various edge conditions under a harmonic load. The impacts of length scale parameter, material and geometrical parameters on the frequency–response curves of nanopanels are investigated. In addition, comparisons are provided between the predictions of MSGT, MCST and the classical elasticity theory.

Lyapunov-Based Boundary Control of Strain Gradient Microscale Beams With Exponential Decay Rate

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Ramin Vatankhah ◽  
Ali Najafi ◽  
Hassan Salarieh ◽  
Aria Alasty
Keyword(s):  
Decay Rate ◽  
Boundary Control ◽  
Exponential Decay ◽  
Strain Gradient ◽  
Beam Element ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Exponential Decay Rate ◽  
Mass Matrices ◽  
Euler Bernoulli Beam

In nonclassical microbeams, the governing partial differential equation (PDE) of the system and corresponding boundary conditions are obtained based on the nonclassical continuum mechanics. In this study, exponential decay rate of a vibrating nonclassical microscale Euler–Bernoulli beam is investigated using a linear boundary control law and by implementing a proper Lyapunov functional. To illustrate the performance of the designed controllers, the closed-loop PDE model of the system is simulated via finite element method (FEM). To this end, new nonclassical beam element stiffness and mass matrices are developed based on the strain gradient theory and verification of this new beam element is accomplished in this work.

A novel size-dependent microbeam element based on Mindlin’s strain gradient theory

2015 ◽  
Vol 32 (1) ◽  
pp. 99-108 ◽  
Author(s):  
R. Ansari ◽  
M. Faghih Shojaei ◽  
F. Ebrahimi ◽  
H. Rouhi ◽  
M. Bazdid-Vahdati
Keyword(s):  
Strain Gradient ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Size Dependent ◽  
Mindlin’S Strain Gradient Theory
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