A Non-Classical Kirchhoff Plate Model Incorporating the Couple Stress and Strain Gradient Effets

2021 ◽  
Author(s):  
Gongye Zhang ◽  
Xin-Lin Gao
Keyword(s):  
Strain Gradient ◽  
Couple Stress ◽  
Kirchhoff Plate ◽  
Stress And Strain ◽  
Plate Model ◽  
Kirchhoff Plate Model

scholarly journals DG approach to large bending plate deformations with isometry constraint

2021 ◽  
pp. 1-43
Author(s):  
Andrea Bonito ◽  
Ricardo H. Nochetto ◽  
Dimitrios Ntogkas
Keyword(s):  
Discontinuous Galerkin ◽  
Minimization Problem ◽  
Numerical Experiments ◽  
Gradient Flow ◽  
Kirchhoff Plate ◽  
Geometrically Nonlinear ◽  
Plate Model ◽  
Global Minimizers ◽  
Dg Method ◽  
Kirchhoff Plate Model

We propose a new discontinuous Galerkin (dG) method for a geometrically nonlinear Kirchhoff plate model for large isometric bending deformations. The minimization problem is nonconvex due to the isometry constraint. We present a practical discrete gradient flow that decreases the energy and computes discrete minimizers that satisfy a prescribed discrete isometry defect. We prove [Formula: see text]-convergence of the discrete energies and discrete global minimizers. We document the flexibility and accuracy of the dG method with several numerical experiments.

INVESTIGATION OF SIZE EFFECTS ON STATIC RESPONSE OF SINGLE-WALLED CARBON NANOTUBES BASED ON STRAIN GRADIENT ELASTICITY

2012 ◽  
Vol 09 (02) ◽  
pp. 1240032 ◽  
Author(s):  
B. AKGÖZ ◽  
Ö. CİVALEK
Keyword(s):  
Carbon Nanotubes ◽  
Strain Gradient ◽  
Couple Stress ◽  
Gradient Elasticity ◽  
Single Walled Carbon Nanotubes ◽  
Stress And Strain ◽  
Strain Gradient Elasticity ◽  
Single Walled Carbon ◽  
Modified Couple Stress ◽  
Walled Carbon Nanotubes

This paper is concerned with the bending analysis of single-walled carbon nanotubes (CNT) based on modified couple stress and strain gradient elasticity theories and Euler–Bernoulli beam theory. The size effect is taken into consideration using the modified couple stress and strain gradient elasticity theories. The governing equations and boundary conditions are derived using the variational approach. Deflections of CNT are obtained and presented in graphical form. Results are presented to show the effect of small-scale effect on bending of CNT. It is the first time in the literature, analytical expression and their solutions for the bending analysis based on strain gradient elasticity and couple stress theories are given for CNT under uniformly distributed load and concentrated end load.

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