一种计算任意截面梁的等效截面参数的类有限元方法

By discretizing the cross-section beam using a finite element method, calculating the coordinates of the centroid and the moment of inertia, and determining the principal centroidal axis, the problem of calculating the equivalent cross-sectional parameters of beams with arbitrary cross-sections is solved. This method is applicable to both thin-walled and thick-walled cross-section beams, has small errors, and has broad application prospects.

CN116756853BActive Publication Date: 2026-07-17CHINA SHIP SCIENTIFIC RESEARCH CENTER

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
CHINA SHIP SCIENTIFIC RESEARCH CENTER
Filing Date
2023-07-06
Publication Date
2026-07-17

AI Technical Summary

Technical Problem

Existing technologies cannot effectively calculate the equivalent cross-sectional parameters of beams with arbitrary cross-sections, especially the complex shapes of thin-walled beams, which makes finite element analysis impossible.

Method used

The finite element method is used to discretize the cross-section beam into elements, calculate the coordinates of the centroid, establish a new coordinate system, calculate the moment of inertia and product of inertia, determine the centroid principal axis, calculate the equivalent torsional stiffness and polar moment of inertia based on the finite element algorithm, and determine the equivalent cross-section parameters.

Benefits of technology

It enables the calculation of equivalent section parameters for beams with arbitrary cross-sections, including moment of inertia and equivalent polar moment of inertia. It is applicable to both thin-walled and thick-walled beams, with small errors and broad application prospects.

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Abstract

本发明公开了一种计算任意截面梁的等效截面参数的类有限元方法,涉及截面梁参数计算领域,该方法包括:将薄壁截面梁的横截面用其中线代替,并离散为若干线单元;计算各单元的形心进而加权平均得到截面形心;将坐标原点放到截面形心上,计算各单元绕两个坐标轴的惯性矩和惯性积,求和得到截面的惯性矩和惯性积;旋转坐标轴到截面形心主轴的位置,计算最终的截面惯性矩;将单元沿着梁长度方向拉伸,一端全约束,另一端作为刚性面并施加单位转角,得到梁的等效扭转刚度,依据扭转刚度和截面等效极惯性矩的关系得到截面等效极惯性矩。由于采用类似于有限元方法的思想用线单元离散梁截面,所以不管梁截面是何种形状,均可采用本方法计算其截面参数。
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