具损伤正交各向异性板的后屈曲分析

基于代数不变量理论,推导了具各向异性损伤的正交各向异性材料的Helmholtz自由能的表达式,同时应用不可逆热力学理论,建立了其损伤本构关系及损伤演化方程.根据Von Karman板理论,建立了具损伤正交各向异性板的非线性压曲方程.数值计算结果表明:由于损伤和损伤演化,板在恒载下的挠度不再保持恒定不变,而是随着时间的增加而不断增大;随着外载荷的增大、初始挠度的增大或者长宽比的减小,损伤对板的挠度的影响越来越明显.

Post-Buckling Analysis of Orthotropic Plate Considering Damage

On the basis of algebra invariant theory,the expression of Helmholtz's free energy for orthotropic material considering damage effect was derived.Then,the corresponding constitutive relationship and damage evolution equations were obtained,based on irreversible thermodynamics theory.From Von Karman's plate theory, the nonlinear bulking equations for orthotropic material considering damage effect were founded.Numerical results have indicated that the deflection of the plate under constant load can not remain unchanged but increases with time due to the damage evolution,and the influences of damage on the deflection of the plate are more and more obvious with the load and initial deflection increase and the length-width ratio decrease.