Multivariate Rational Response Surface Approximation of Nodal Displacements of Truss Structures

Polynomial-basis response surface method has some shortcomings for truss structures in structural optimization,concluding the low fitting accuracy and the great computational effort. Based on the theory of approximation, a response surface method based on Multivariate Rational Function basis(MRRSM) is proposed. In order to further reduce the computational workload of MRRSM, focusing on the law between the cross-sectional area and the nodal displacements of truss structure, a conjecture that the determinant of the stiffness matrix and the corresponding elements of adjoint matrix involved in displacement determination are polynomials with the same order as their respective matrices, each term of which is the product of cross-sectional areas, is proposed. The conjecture is proved theoretically for statically determinate truss structure, and is shown corrected by a large number of statically indeterminate truss structures. The theoretical analysis and a large number of numerical examples show that MRRSM has a high fitting accuracy and less computational effort. Efficiency of the structural optimization of truss structures would be enhanced.

东北亚熊祭及其与满族家祭的比较研究

东北亚民族“饲养型熊祭”与满族以养猪为牺牲物的家祭,不仅在祭祀要素的准备上具有相同的特点,而且在祭祀过程的行为与思维模式上具有高度的一致性。在吸收满族先民动物饲养理念的同时,东北亚民族的熊祭祀仪式也影响了满族的家祭仪式。早期东北亚地区民族之间的交流纷繁复杂,各种文化因素陈陈相因,形成一个独特的文化区域。阿依努人的熊祭与满族家祭的相通性就是在东北亚各民族文化交流与影响过程中形成的。