考虑轴向均布载荷时线弹性支承压杆的稳定性计算

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1、InternationalJournalofMechanicsResearch力学研究,2015,4,7-14PublishedOnlineMarch2015inHans.http://www.hanspub.org/journal/ijmhttp://dx.doi.org/10.12677/ijm.2015.41002StabilityCalculationofLongColumnunderLinearElasticSupportsandExtraAxialUniformLoadKaizhiHuang*,XiaoliangChen,Zu’anTia

2、n,JianpingDingSchoolofMathematics&Physics,ChongqingUniversityofScience&Technology,Chongqing*Email:mocd361@163.comthrdthReceived:Mar.6,2015;accepted:Mar.23,2015;published:Mar.27,2015Copyright©2015byauthorsandHansPublishersInc.ThisworkislicensedundertheCreativeCommonsAttributionI

3、nternationalLicense(CCBY).http://creativecommons.org/licenses/by/4.0/AbstractForcalculatingthestabilityoflongcolumnunderlinearelasticsupportsandextraaxialuniformload,firstofall,withthestaticequilibriumconditionsofthemicrosectionoflongcolumn,theap-proximateequationsofdeformation

4、sandinternalforcesareestablished;Thenext,bytheboun-daryconditionsofdeformationsandinternalforces,andtherelationshipbetweeninternalforcesandexternalforces,andtherelationshipbetweenexternalforcesanddeformations,thehomoge-neouslinearequationsofcontaining12initialparametersareestab

5、lished,bytheconditionsofequationswithnon-zerosolution,thecharacteristicequationofcriticalloadarederived;Thelast,taking6linearelasticsupportslongcolumnsasexample,thestabilityiscalculated,theapprox-imaterelationcurvesbetweenaxialuniformloadandconcentratedloadaredrawn,andthenu-mer

6、icalsolutionsofinterceptsonCartesiancoordinatesystemaregiven,andfoundthatthetrendofeachcurve,andtherelationshipofsortingtostabilityrepresentedbythem,aremoreconsistentwiththeoreticalexpectations.KeywordsMechanicsofMaterials,LongColumn,Stability,CriticalLoad,LinearElasticSupport,

7、AxialUniformLoad考虑轴向均布载荷时线弹性支承压杆的稳定性计算*黄开志，陈小亮，田祖安，丁剑平*通讯作者。7考虑轴向均布载荷时线弹性支承压杆的稳定性计算重庆科技学院数理学院，重庆*Email:mocd361@163.com收稿日期：2015年3月6日；录用日期：2015年3月23日；发布日期：2015年3月27日摘要为了计算考虑轴向均布载荷时线弹性支承压杆的稳定性，首先用压杆微元段的静力平衡条件，建立了其变形和内力的近似方程；接着由变形边界条件、内力边界条件、内力与外力的关系、外力与变形的关系，确定了一个包含12个初参数的齐次线性方程组

8、，由方程组有非零解的条件，导出了临界载荷的特征方程；最后以6个线弹性支承的压杆为例，进行了稳定性计算，绘制了