任意轴向荷载作用下高耸结构P-Δ效应高阶精确分析方法  

Method of High-Order Precise Analysis for the P-△ Effect in Tall Structures due to Arbitrary Axial Loads

作　　者：陆言 李鸿晶[1] 杨筱朋 翟银泉 Yan Lu;Hongjing Li;Xiaopeng Yang;Yinquan Zhai(Institute of Engineering Mechanics,Nanjing Tech University,Nanjing,211816)

机构地区：[1]南京工业大学工程力学研究所,南京211816

出　　处：《固体力学学报》2025年第1期79-92,共14页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(52378519)资助。

摘　　要：高耸结构P-Δ效应的传统分析方法一般难以考虑时变轴力作用,有可能会低估P-Δ效应对结构安全性的影响.本文应用求积单元法(weak form quadrature element method,QEM),针对分布质量结构体系和含有集中质量的结构体系分别建立Hermite型求积单元模型,发展了一种高耸结构P-Δ效应高阶精确分析方法.该方法能够应用于具有突变质量的结构体系,可处理任意轴向荷载引起的动力P-Δ效应问题,无需迭代计算即可获得高精度的P-Δ效应解答,同时能准确地揭示竖向荷载以及时变轴力对高耸结构特性的影响规律.通过对3个不同类型案例的比较分析,验证了本文方法的可行性和准确性.数值分析结果表明,本文方法可以实现高精度的P-Δ效应分析,对于质量均匀分布和含有集中质量的结构体系仅需使用一个求积单元即可获得非常精确的动态响应结果.Traditional methods for analyzing the P-effect in tall structures often fail to adequately account for time-varying axial forces,which can lead to an underestimation of its impact on structural safety.This paper introduces a high-order accurate analysis method based on the weak-form quadrature element method(QEM).We develop Hermite-type quadrature element models for both distributed and concentrated mass structures.The proposed method is capable of addressing dynamic P-△ effects caused by arbitrary axial loads without iterative computations,yielding precise solutions.Its efficacy and accuracy are validated through comparative analysis involving three distinct case studies.Numerical results confirm that the proposed approach delivers highly accurate P-effect analyses,achieving exceptional precision in dynamic response with a single quadrature element,even in complex structural systems.Overall,this method offers a novel and efficient solution for detailed analysis of P-effects in tall structures.

关 键 词：高耸结构 P-Δ效应 求积单元 时变轴力 Hermite型插值 

分 类 号：TU311.3[建筑科学—结构工程]