The main objective in this work is to study an application of the B-spline approximations in the Least Squares Method recovery of the structural response for boundary value problems in some linear elastic systems. These responses were approximated before using polynomial bases in the Stochastic perturbation-based Boundary Element Method and now are replaced with second or third order B-spline functions. A majority of such an approach is that the resulting expected values and standard deviations of structural response are obtained using analytical calculus of probability integrals, so that neither statistical nor expansion methods are necessary. Numerical illustration delivered in this paper includes fundamental eigenfrequencies of elastic thin homogeneous and isotropic plate immersed into Newtonian fluid subjected to various boundary conditions at its external edges.

这项工作的主要目标是研究 B 样条近似在某些线性弹性系统中边界值问题的结构响应的最小二乘法恢复中的应用。在基于随机微扰的边界元方法中使用多项式基之前，这些响应是近似的，现在被二阶或三阶 B 样条函数取代。大多数此类方法是使用概率积分的解析演算获得结构响应的预期值和标准偏差，因此不需要统计方法和扩展方法。