Some analytical solutions of functionally graded Kirchhoff plates

被引：63

作者：

Apuzzo, Andrea ^{[1
]}

Barretta, Raffaele ^{[2
]}

Luciano, Raimondo ^{[1
]}

机构：

[1] Univ Cassino & Southern Lazio, Dept Civil & Mech Engn, I-03043 Cassino, FR, Italy

[2] Univ Naples Federico II, Dept Struct Engn & Architecture, I-80125 Naples, Italy

来源：

COMPOSITES PART B-ENGINEERING | 2015年 / 68卷

关键词：

Plates; Elasticity; Analytical modeling; SHEAR DEFORMATION-THEORY; THERMOELASTIC DEFORMATIONS; MICROMECHANICAL MODELS; CARBON NANOTUBES; ANALOGIES; EQUATIONS;

D O I：

10.1016/j.compositesb.2014.08.048

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The elastostatic problem of a functionally graded KIRCHHOFF plate, with no kinematic constraints on the boundary, under constant distributions of transverse loads per unit area and of boundary bending couples is investigated. Closed-form expressions are provided for displacements, bending twisting curvatures and moments of an isotropic plate with elastic stiffness and boundary distributed shear forces, assigned respectively in terms of the stress function and of its normal derivative of a corresponding SAINT-VENANT beam under torsion. The methodology is adopted to solve circular plates with local and ERINGEN-type elastic constitutive behaviors, providing thus new benchmarks for computational mechanics. The proposed approach can be used to obtain other exact solutions for plates whose planform coincides with the cross-section of beams for which the PRANDTL stress function is known in an analytical form. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：266 / 269

页数：4

共 55 条

[31]

Nadai A, 1925, ELASTICHEN PLATTEN

[32]

Navier C., 1823, B SCI SOC PHILOMATHI

[33] Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique [J].

Neves, A. M. A. ;

Ferreira, A. J. M. ;

Carrera, E. ;

Cinefra, M. ;

Roque, C. M. C. ;

Jorge, R. M. N. ;

Soares, C. M. M. .

COMPOSITES PART B-ENGINEERING, 2013, 44 (01) :657-674

[34] Functionally graded materials for biomedical applications [J].

Pompe, W ;

Worch, H ;

Epple, M ;

Friess, W ;

Gelinsky, M ;

Greil, P ;

Hempel, U ;

Scharnweber, D ;

Schulte, K .

MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, 2003, 362 (1-2) :40-60

[35]

Prandtl L., 1903, Phys. Z, V4, P758

[36] On the modeling of carbon nanotubes: A critical review [J].

Rafiee, Roham ;

Moghadam, Reza Maleki .

COMPOSITES PART B-ENGINEERING, 2014, 56 :435-449

[37]

Reddy J.N., 2009, An Introduction to the Finite Element Method, Vthird

[38] Thermomechanical analysis of functionally graded cylinders and plates [J].

Reddy, JN ;

Chin, CD .

JOURNAL OF THERMAL STRESSES, 1998, 21 (06) :593-626

[39]

Reddy JN, 2000, INT J NUMER METH ENG, V47, P663, DOI 10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO

[40]

2-8

← 1 2 3 4 5 6 →