基于有限材料参数试验数据的横观各向同性板结构随机有限元分析与验证

当材性试验数据有限时，为了研究各力学参数的离散性和不确定性对结构性能计算的影响，需要对材料参数采用随机变量建模并基于概率理论构建刚度矩阵的随机模型。为此，首先将随机弹性张量分解为一组基张量和由材料参数构成的随机系数的线性组合，以考虑刚度矩阵各分量间的统计相关性；并利用最大熵原理确定由上述随机系数组成的随机向量的概率密度函数。采用基于Metropolis-Hasting算法的马尔科夫链蒙特卡罗方法用于计算与之相关的概率模型的拉格朗日乘子，并通过Matlab生成材料参数的随机样本。最后采用蒙特卡罗随机有限元法对横观各向同性材料构成的板式结构在不同荷载下的力学行为进行了数值分析。以刨花板材料为典型案例，与试验结果对比，验证了本文方法的效果和实用性。

Stochastic finite element analysis and verification of transversely isotropic plate structure based on limited material parameter test data

When material property test date is limited,in order to study the influences of the dispersion and uncertainty of various mechanical parameters on the structural performance,it is extremely necessary to adopt a probabilistic model for material parameters as random variables and construct a random model of stiffness matrix based on probability theory.To this aim,the random elasticity tensor was firstly decomposed into a linear combination of basis tensors and a set of random coefficients which were expressed as functions of material parameters,to take into account the statistical dependence between stiffness components;and probability density function of the random vector composed of the mentioned random coefficients was determined based on the principle of maximum entropy.Then a Monte Carlo Markov Chain method based on Metropolis-Hasting algorithm was used for the estimation of the Lagrange multipliers involved in the probabilistic model and random samples of material parameters were generated in Matlab.Finally,the mechanical behavior of a plate structure composed of transversely isotropic materials under different loads is numerically simulated by Monte Carlo stochastic finite element method.A typical example of particleboard was used to verify the effectiveness and practicability of the approach used in the present work by comparison with test results.