摘要
研究Hooke材料在大位移下的轴对称平面应力问题的空穴分岔现象 .根据Lia punov第一方法的基本思想 ,列出该非线性问题的线性化扰动方程 ,找到了这个线性化扰动方程封闭解 .由于在分岔点扰动方程具有非零解 ,结合边界条件得到临界载荷满足的特征方程 .用二分法搜索特征方程的最小正根 ,即临界载荷 .其中得到Poisson比为 1 2时微孔萌生临界载荷的精确解 .计算了Poisson比从 0到 1 2变化时材料的微孔萌生和微孔突变的临界载荷以及失稳模态 .
Studies on cavitation and catastrophy of a pre exist micro hole for Hooke materials are much less than those for hyperelastic materials. The bifurcation of cavitation in Hooke material under large displacement is studied for axisymmetric plane stress problem. The closed form solution of the perturbation equation of the nonlinear system is found. According to the boundary condition, the eigen equation for the bifurcation load is obtained. The exact critical load is found in the material in which Poissons ratio is 1/2. The critical load of cavitation and catastrophy of the micro hole where Poissons ration varies from zero to 1/2 and the buckling mode are also calculated. The results agree with some phenomena obtained in the hyperelastic materials.
出处
《固体力学学报》
CAS
CSCD
北大核心
2001年第3期281-286,共6页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金 (No .19990 5 10 )资助
