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当不确定性信息量不足以精确确定概率模型时,基于凸模型的非概率可靠性理论为工程结构安全性提供一种有效的评估方法.论文基于材料、几何及荷载大小等不确定性因素扰动界限的多椭球模型描述,运用标准化变换和标准空间广义无穷范数度量,给出定义非概率可靠性指标的极小极大优化数学模型.该非概率可靠性指标可理解为结构所能容许的参数不确定范围与实际不确定范围的相对“长度”比值.通过对极限状态方程的线性化近似,推导优化问题的显式迭代公式,实现非概率可靠性指标的简便求解.数值算例验证了论文迭代算法的正确性和有效性.
When the amount of uncertainty information is not enough to accurately determine the probability model, the non-probabilistic reliability theory based on convex model provides an effective evaluation method for engineering structural safety.Based on the disturbance of uncertainties such as material, geometry and load size Boundary multi-ellipsoid model description, using standard transformation and standard space generalized infinite norm metric, gives the minimum and maximum optimization mathematical model to define the non-probabilistic reliability index, which can be understood as the structure can tolerate The relative “length” ratio of the uncertainty range of the parameter to the actual uncertainty range is derived.The explicit iterative formula of the optimization problem is deduced by linear approximation of the limit state equation, and the simple solution to the non-probabilistic reliability index is obtained. The example verifies the validity and validity of the paper iterative algorithm.