Exact solutions for multilayer functionally graded beams bonded by viscoelastic interlayer considering memory effect

2020 ◽  
Vol 249 ◽  
pp. 112492
Author(s):  
Peng Wu ◽  
Zhiyuan Yang ◽  
Xi Huang ◽  
Weiqing Liu ◽  
Hai Fang
Keyword(s):  
Exact Solutions ◽  
Memory Effect ◽  
Functionally Graded ◽  
Viscoelastic Interlayer

Analysis of Elasticity Solution of Bi-Direction Functionally Graded Piezoelectric Beam Subject to Voltage

2012 ◽  
Vol 166-169 ◽  
pp. 824-827 ◽  
Author(s):  
Y Z Yang
Keyword(s):  
Hamiltonian System ◽  
Exact Solutions ◽  
Material Properties ◽  
Functionally Graded ◽  
Symplectic Method ◽  
Elasticity Solution ◽  
Numerical Examples ◽  
Piezoelectric Beam ◽  
Functionally Graded Piezoelectric

This paper presents symplectic method for the derivation of exact solutions of functionally graded piezoelectric beam with the material properties varying exponentially both along the axial and transverse coordinates. In the approach, the related equations and formulas are developed in terms of dual equations, which can be solved by variables separation and symplectic expansion in Hamiltonian system. To verify advantages of the method, numerical examples of bi-directional functionally piezoelectric beam are discussed.

scholarly journals Nonlocal strain gradient exact solutions for functionally graded inflected nano-beams

2019 ◽  
Vol 164 ◽  
pp. 667-674 ◽  
Author(s):  
A. Apuzzo ◽  
R. Barretta ◽  
S.A. Faghidian ◽  
R. Luciano ◽  
F. Marotti de Sciarra
Keyword(s):  
Exact Solutions ◽  
Strain Gradient ◽  
Functionally Graded ◽  
Nonlocal Strain Gradient
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