利用全局薄板样条径向基配点法分析了功能梯度梁的弯曲问题,径向基函数的形状参数对近似精度有很大的影响,而薄板样条径向基函数的形状参数选取比其他径向基函数要容易.利用高阶剪切变形理论推导了控制微分方程,将该文的计算结果与已有参考文献中的结果进行了对比,以验证该文方法的精度.

This paper focuses on the bending analysis of functionally graded beams using a meshless global thin plate spline radial basis function collocation method.The shape parameter of the radial basis function plays an important role in the numerical accuracy.The determination of the shape parameter in the thin plate spline radial basis function is easier than that in other radial basis functions.The governing differential equations are derived based on the higher order shear deformation theory.The present results are compared with available published results which demonstrates the accuracy of the present method.

针对舰船装备保障过程中备件数量的确定方法缺乏科学性和实际操作繁琐的现状，分析了影响舰船备件数量主要因素，研究了径向基神经网络的工作原理，提出基于径向基函数神经网络的舰船备件需求预测方法。最后给出了预测实例，并与BP神经网络预测结果进行对比。结果表明，径向基神经网络预测方法操作简单，预测结果符合实际情况，拟合效果优于BP。

Due to the fact that in ship maintenance process, the method of determining the number of spare parts is not scientific and the actual operation is complicated, this paper analyzes the 4 major factors affecting the number of ship’s spare parts (number of planned main operations, total times of disassembling in maintenance, accumulated working time, mean time between failures), it also establishes the spare parts demand forecast model based on the affecting factors and RBF nerve network. Finally, the paper provides forecast examples and makes a comparison between the examples with the BP nerve network forecast results. It shows that the operation of radial basis function nerve network forecast is simple, the forecast result fits the actual situation and the fitting effect is better than BP.

根据弹性力学基本方程，研究了不均匀干燥时水泥基材料弹性模量对径向位移分布、径向应变分布、环向应变分布、径向应力分布和环向应力分布的影响，并与均匀干燥情况进行了比较。通过比较发现，不均匀干燥时的最大径向位移、最大径向应变、最大环向应变和最大径向应力都比均匀干燥时的小。采用实芯钢芯时，不均匀干燥时的最大环向拉应力也比均匀干燥时的小；采用空芯钢芯时，不均匀干燥时的最大环向拉应力有可能超过均匀干燥时的最大环向拉应力。水泥基材料的弹性模量越高，这种可能性就越大。

According to the equations of elasticity, the influences of the elastic modulus of cement-based material on the distribution of the radial displacement, radial strain, circumferential strain, radial stress and circumferential stress un-der the drying inhomogeneous condition are studied, and they are compared with these under the drying homogeneous con-dition. It is discovered by comparison that the maxima of the radial displacement, the radial strain, the circumferential strain and the radial stress under the drying inhomogeneous condition are less than that under the drying homogeneous condition. If solid steel core is used, the maximum of the circumferential tensile stress under the drying inhomogeneous condition is also less than that under the drying homogeneous condition. However, if hollow steel core is used, it is possi-ble that the maximum of the circumferential tensile stress under the drying inhomogeneous condition is over that under the drying homogeneous condition. The high

针对代理模型优化技术在结构耐撞性优化中的应用问题,开展了径向基函数和响应面的预测精度检测和适用性研究,并针对径向基函数中散布常数取值机制不明确的问题进行数值分析,提出基于优化计算的选取策略。具体实施为,先使用遗传算法（Genetic algorithm,GA）直接进行搜寻优化,得到的结果可认为是最优结果,并作为代理模型优化方法的参照;通过实例证实代理模型精度检测的必要性,并检验均匀试验设计、中心复合试验设计、析因试验设计在碰撞问题中的适用性;在构造径向基函数时将散布常数设为变量,再以几个随机样点处的数值结果为目标进行模型修正,得到修正的散布常数,代入构造的径向基函数中。结果表明该方案得到的散布常数能够使得径向基函数更好地表征结构耐撞性问题。

The prediction accuracy and applicability of the radial basis function (RBF) and the response surface method (RSM) are studied, and an optimization idea is put forward to solve the problem of selecting an applicable shaping parameter of the RBF model when the surrogate model technology is employed in structure crashworthiness optimization. The genetic algorithm (GA) is used to optimize the crashing energy absorption of a thin-walled structure and find the global optimum which can be viewed as the target of the surrogate model. The necessity of testing surrogate model’s prediction accuracy via numerical examples is demonstrated and the applicability of several methods of design of experiments is tested. Thaping parameter of RBF model is treated as a variable, and a few random sample points are used to update radial basis function model suitable. The results show that the updated radial basis function model will be more suitable for structure crashworthiness problem.

利用弹性力学方法分析了抗裂圆环在水泥基材料发生均匀干缩变形时的径向位移分布、径向应变分布、环向应变分布、径向应力分布和环向应力分布。给出了这些分布的数学表达式,并对这些表达式进行了分析。研究结果表明,在均匀干燥过程中,水泥基材料圆环径向受压,环向受拉,最大环向拉应力在圆环的内侧。环向应变是多种应变的叠加,而不仅是环向拉应力作用的结果。

The method of elasticity is used to analyze the distribution of the radial displacement, radial strain, circum-ferential strain, radial stress and circumferential stress in breaking ring due to the homogeneous dry shrinkage of cement-ing material. The mathematical equations of these distributions are given. The results show that in homogeneously drying process, the ring of cement-based material is compressive in radial direction and tensile in circumferential direction. The maximum circumferential tensile stress is at the internal surface of the ring. The circumferential strain is the superposition of a lot of strain, not only the elastic strain due to the circumferential tensile stress.