Stiffness formula of cable element under general situations and its application 一般情況下小垂度索的剛度方程及其應(yīng)用
Based on the force - method equation , the stiffness matrix and fixed - end nodal displacement and force vector are derived 在力法方程的基礎(chǔ)上,給出了組合梁單元的剛度矩陣、桿端位移向量及桿端荷載向量并建立了剛度方程。
By using 3 - d isoparametric element , the global stiffness matrix equation for the piezoelectric laminate is obtained on the bases of minimum principle of total potential energy 由于最小勢能原理,建立了單元?jiǎng)偠染仃嚭蛪弘姴牧系恼w剛度方程。并且推導(dǎo)了壓電層合板的邊界條件。
On the basis of the virtual work principles and nonlinear finite element theory , the author introduces a plausible method which analyzes the double nonlinear problem of structure by importing the elastic - plastic constitutive relationship matrix into geometric nonlinear fea equation 摘要從非線性有限元理論出發(fā),基于虛功原理,闡述在幾何非線性剛度方程有限元列式中引入非線性本構(gòu)關(guān)系矩陣、合理考慮結(jié)構(gòu)雙重非線性問題的理論方法。
When analyzing skew support continuous curved box girder bridge , curved grid girder analyzing method considering warping effect is applied . matrix displacement method is applied in analyzing skew support continuous curved thin - walled box girder bridge with restrained bearing . in order to convert original rigidity equations to structural rigidi ty equations that can be solved , bearing nodal displacement matrix can be introduced , then unknown quantities at the edge of beams can be consistent with the restrained directions of skew bearings , unit rigidity matrix and unit nodal forces can be gained . structural rigidity matrix can be composed according to matrix displacement method , so nodal displacements and inner forces on the end of the rod that are unknown can be gained calculating equations of inner forces on any cross - section can be solved 分析斜支承連續(xù)曲線箱梁橋時(shí),采用考慮翹曲作用的曲線格子梁分析方法,應(yīng)用矩陣位移法對(duì)具有約束支承形式的斜支承連續(xù)曲線薄壁箱梁橋進(jìn)行分析,考慮到支座的約束條件并不與梁端彎曲角位移和扭轉(zhuǎn)角位移的方向一致,引入支座節(jié)點(diǎn)坐標(biāo)矩陣,使得梁端的位移未知量與斜支座約束方向一致,來計(jì)算單元?jiǎng)偠染仃嚭蛦卧?jié)點(diǎn)力,然后按照矩陣位移法組集總剛并建立結(jié)構(gòu)剛度方程,根據(jù)結(jié)構(gòu)剛度方程即可求解未知的節(jié)點(diǎn)位移及桿端力,推導(dǎo)出任意截面處的內(nèi)力計(jì)算公式。
This paper studied the material nonlinear problems , geometric nonlinear problems and double nonlinear problems , which includes both material and geometric nonlinear problems , of tall frames . at first i built up the stiffness equations of nonlinear problems by qr - method , then solved them by incremental iterative method , finally wrote the corresponding programs by c and calculated some examples 本文研究高層框架的材料非線性問題、幾何非線性問題及雙重非線性問題,即既含材料非線性問題又含幾何非線性問題,先利用qr法建立非線性問題的剛度方程,然后利用增量迭代法求解非線性剛度方程,并用c語言編制計(jì)算程序,計(jì)算了一些例題。
In order to solve the static , dynamic and material nonlinear problems of mega - frame structure , this paper analyzes mega - frame structure by qr - method and sets up a new computational form . in this paper , the author adopts the method of repeated increment and no limit stabilization to handle t he elastic - plastic rigid equation and dynamic equation 然后,利用qr法對(duì)巨型框架結(jié)構(gòu)進(jìn)行分析,解決該結(jié)構(gòu)的靜力、動(dòng)力及材料非線性問題,利用增量迭代法及樣條無條件穩(wěn)定算法分別求解彈塑性剛度方程及動(dòng)力方程,建立了高層巨型框架結(jié)構(gòu)分析的新的計(jì)算格式。
Secondly the author ' s study are introduced in this paper . the author study mainly the linear static and dynamic , elastic - plastic static and dynamic problems of cfst arc - bridge . firstly , the author establish the linear static equation on the based of the rigid equation of element by qr - method , and then analysis the inner force of arc bridge , establish the linear dynamic equation and elastic - plastic rigid equation and dynamic equation , then solve respectively the elastic - plastic rigid and dynamic equation by the method of repeated increment and no limit stabilization , arithmetic 本文主要研究大跨度鋼管混凝土桁架拱線性靜力問題和線性動(dòng)力問題以及彈塑性靜力問題和彈塑性動(dòng)力問題,先利用qr法按照梁單元的剛度方程建立桁架拱的線性靜力方程,進(jìn)行桁架拱內(nèi)力分析,建立桁架拱線性動(dòng)力方程、彈塑性剛度方程及彈塑性動(dòng)力方程,然后利用增量迭代法及樣條無條件穩(wěn)定算法分別求解彈塑性剛度方程及動(dòng)力方程。