摘要
本文基于非局部连续统场论和非线性连续体力学理论,建立了非局部非对称弹性固体的非线性理论.它完善和发展了Eringen等人所建立的非局部弹性场论.将文献[1]中所建立的非局部非对称弹性力学的线性理论推广到有限变形.证明了在非局部弹性固体中存在着非局部体力矩.非局部体力矩引起应力的非对称性,而非局部体力矩则由原子晶格相互作用形成的共价键所产生的.并应用本文建立的理论合理地解释了平面横波和纵波色散系关的不相似性.
In this paper, a nonlinear theory of nonlocal asymmetric elastic solids is developed on the basis of basic theories of nonlocal continuum field theory and nonlinear continuum mechanics. It perfects and expands the nonlocal elastic field theory developed by Eringen and others. The linear theory of nonlocal asymmetric elasticity developed in [1] expands to the finite deformation. It is shown that there is the nonlocal body moment in the nonlocal elastic solids. The nonlocal body moment causes the stress asymmetric and itself is caused by the covalent bond formed by the reaction between atoms. The theory developed in this paper is applied to explain reasonably that curves of dispersion relation of one-dimensional plane longitudinal waves are not similar to those of transverse waves.
出处
《应用数学和力学》
EI
CSCD
北大核心
1992年第9期765-774,共10页
Applied Mathematics and Mechanics
关键词
非对称应力
非局部理论
弹性固体
non-symmetrical stress, nonlocal theory, body couple stress
