OPTIMIZATION OF THE STRAIN-ENERGY DENSITY IN LINEAR ANISOTROPIC ELASTICITY

被引:34
作者
COWIN, SC [1 ]
机构
[1] CUNY CITY COLL,GRAD SCH,NEW YORK,NY 10031
关键词
D O I
10.1007/BF00042425
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
The problem considered here is that of extremizing the strain energy density of a linear anisotropic material by varying the relative orientation between a fixed stress state and a fixed material symmetry. It is shown that the principal axes of stress must coincide with the principal axes of strain in order to minimize or maximize the strain energy density in this situation. Specific conditions for maxima and minima are obtained. These conditions involve the stress state and the elastic constants. It is shown that the symmetry coordinate system of cubic symmetry is the only situation in linear anisotropic elasticity for which a strain energy density extremum can exist for all stress states. The conditions for the extrema of the strain energy density for transversely isotropic and orthotropic materials with respect to uniaxial normal stress states are obtained and illustrated with data on the elastic constants of some composite materials. Not surprisingly, the results show that a uniaxial normal stress in the grain direction in wood minimizes the strain energy in the set of all uniaxial stress states. These extrema are of interest in structural and material optimization.
引用
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页码:45 / 68
页数:24
相关论文
共 14 条
[1]   KINEMATICS OF FINITE RIGID-BODY DISPLACEMENTS [J].
BEATTY, MF .
AMERICAN JOURNAL OF PHYSICS, 1966, 34 (10) :949-&
[2]   VECTOR ANALYSIS OF FINITE RIGID ROTATIONS [J].
BEATTY, MF .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1977, 44 (03) :501-502
[3]   GENERATING OPTIMAL TOPOLOGIES IN STRUCTURAL DESIGN USING A HOMOGENIZATION METHOD [J].
BENDSOE, MP ;
KIKUCHI, N .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1988, 71 (02) :197-224
[4]   ON THE IDENTIFICATION OF MATERIAL SYMMETRY FOR ANISOTROPIC ELASTIC-MATERIALS [J].
COWIN, SC ;
MEHRABADI, MM .
QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 1987, 40 :451-476
[5]  
COWIN SC, 1989, BONE MECHANICS
[6]  
Fedorov F.I., 2013, THEORY ELASTIC WAVES
[7]   A UNIFYING PRINCIPLE RELATING STRESS TO TRABECULAR BONE MORPHOLOGY [J].
FYHRIE, DP ;
CARTER, DR .
JOURNAL OF ORTHOPAEDIC RESEARCH, 1986, 4 (03) :304-317
[8]  
HANCOCK H., 1917, THEORY MAXIMA MINIMA
[9]  
HUO YZ, 1987, COMPLETENESS CRYSTAL
[10]  
Kollmann F, 1968, PRINCIPLES WOOD SCI