为了验证双向蒙特卡罗法模拟热辐射传递，与文献中其它方法计算结果进行了比较。

To validate the Bidirectional Monte-Carlo simulation for radiative heat transfer, the solution obtained from this method is compared with that from other methods.

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针对材料性能的随机性和裂缝分布的随机性，引入了随机性模型，采用蒙特卡罗法来模拟其随机性。

Aiming at the randomicity of concrete crack, the author adopt the randomicity finite element model and Monte-Carlomethod to simulate the randomicity of material character and crack distribution.

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为了减少随机抽样的次数并保证蒙特卡罗法的数值模拟精度，对比引入了重要抽样法和拉丁超立方体抽样方法；

To reduce sampling number and assure simulation precision, Importance Sampling method and Latin Hypercube Sampling method are coupled with Neumann expansion SFEM respectively.

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