含缺陷轴对称体的安定与极限分析

SHAKEDOWN AND LIMIT ANALYSIS OF AXI-SYMMETRIC STRUCTURE CONTAINED DEFECTS

利用静力安定定理得到了计算轴对称体安定与极限载荷的统一格式，采用温度参数法构造安定分析所需的残余应力场．为了克服对工程实际问题进行安定分析时解题规模与计算精度的矛盾，针对轴对称体的特点，采用两种线性化方案对屈服面进行线性化处理，即直接内接法和在降维的应力偏量空间中对屈服面的线性化处理，使安定分析转化为一线性规划问题．在简化过程中合理选择线性化方案以便使应力校核点接近精确的屈服面；为了减小计算量，在求解过程中直接求其对偶规划．对于退化问题的数值困难采用了摄动方法来克服．本文的方法与程序通过算例验证是可靠的，并利用此方法计算了含凹坑和气孔缺陷球壳的安定与极限载荷，初步得到了含缺陷球壳的塑性承载能力与缺陷参数的关系．

A unified method for computing shakedown and limit loads of axi-symmetric bodies is given based on the static shakedown theorem.The pseudo-residual stress field is simulated by temperature parameter method.In the shakedown analysis of engineer Structures,the difficulty of largecomputative quantities is in company With the raising of solution's accuracy.In order to get over the difficulty,the yield cowhtion is linearized through two kinds of paths,one is directiy obtained by inscribed polyhedron,and the other is dealt with in the reduced 3-D sauce of devistoric stress,so that the shakedown analysis is transformed into a linear programming problem, then its dual programming is also set up.The linearized yield surface should be chosen carefully on which the stress of inspected points closes to the original yield surface. Perturbations of right-hand side of the cohstraining equations are added for overcoming the numerical difficulty.TWo examples show that the numerical solutions are in good agreement with the theoretical solutions.Finally,the shakedown and the limit limit of spherical shells contsined pert-through slots and gas holes are computed by this method, then the dependence of the carrying capocities of vessels on the geometric parameters of shells and defects is obtained.