First integrals of the equilibrium equations in one-dimensional problems of nonlinear elasticity theory

被引:4
作者
Zelenina, A. A. [1 ]
Zubov, L. M. [1 ]
机构
[1] So Fed Univ, Rostov Na Donu, Russia
关键词
D O I
10.1134/S1028335808070112
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
The first integrals of the equilibrium equations in one-dimensional problems of nonlinear elasticity theory is discussed. The theory describes the bending, tension and torsion of an elastic anisotropic layer under the conservation laws of the finite strain theory. These integrals can be used to reduce the order of such systems of differential equations, obtaining exact solutions, and checking. The exact solution of the nonlinear problem of the pure bending of an elastic plate is universal, and valid for any material from the class of incompressible isotropic micropolar bodies.
引用
收藏
页码:379 / 382
页数:4
相关论文
共 9 条
[1]  
ESHELBY JD, 1956, SOLID STATE PHYS, V3, P79
[2]  
Green AE., 1960, LARGE ELASTIC DEFORM
[3]  
KNOWLES JK, 1972, ARCH RATION MECH AN, V44, P187
[4]  
Lur'e A.I., 1980, Nonlinear Theory of Elasticity
[5]   Conservation laws and conjugate solutions in the elasticity of simple materials and materials with couple stress [J].
Nikitin E. ;
Zubov L.M. .
Journal of Elasticity, 1998, 51 (1) :1-22
[6]   THEORIES OF ELASTICITY WITH COUPLE-STRESS [J].
TOUPIN, RA .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1964, 17 (02) :85-112
[7]  
Zubov L. M., 1981, Soviet Physics - Doklady, V26, P111
[8]  
ZUBOV LM, 2006, CALCULUS TENSORS FUN
[9]  
Zubov LM., 1997, NONLINEAR THEORY DIS