分析恒载效应的有限元方法

本文在Takabatake关于恒载对梁静、动力影响的研究工作的基础上,导出了梁考虑恒载效应的动力分析有限元公式,提出了荷载影响刚度矩阵的概念。分析了分布和集中两种恒载型式对简支梁和悬臂梁自振特性的影响。计算结果表明,用本文方法与Takabatake应用Galerkin方法和近似闭合解方法的结果吻合良好。同时由于本文采用了矩阵形式,不仅便于编制计算机程序,且使方法有更广泛的适用性和灵活性,可更方便地用于各种不同的构造和边界条件下的实际结构。

A FINITE ELEMENT METHOD FOR ANALYZING THE EFFECT OF DEAD LOADS

Based on Takabatake' s works, in this paper, a conception of load-induced stiffness matrix is proposed, and a beam element with the effect of dead loads included is developed. The effects of dead loads on natural frequencies are presented by the FEM for simply supported and cantilever beams. Two types of dead load, uniform load per unit length and concentrated load, are considered in the analysis. The validity of the proposed procedure is confirmed in the numerical examples. It is shown that the proposed method is applicable to practical structures under various support conditions due to the advantages of the FEM.