Pisuttawan Sripirom. การแอ่นตัวมากของคานยื่นโดยวิธีไฟไนต์เอลิเมนต์ระบบพิกัดอินทรินสิก. Master's Degree(Applied Mathematics). มหาวิทยาลัยเทคโนโลยีพระจอมเกล้าธนบุรี. : King Mongkut's University of Technology Thonburi, 2544.
Abstract:
This thesis presents a finite elcinent approach for solviilg large deflections ofEL ca~ltilevcrb eam subjectcd to the applied forces which are the non-follower forcesand follower forces. The non-follower forces are a concentrated load and a uniformlydistributed load applied in thc vcrtical direction. 'The follower forces are acoiccntrated load and a u~liforinly distributed load applied in the position makingangle with respect to thc deforined shape of the beam. The model of the cantileverbeam is foril~ulatcd based on Bcr~loulli-Euler beam theory. In case of the followerload, thc principle virtual work is used to formulate the virtual work energyfunctional. 'rl~isi i~volvcsv irtual strain cnergy duc to bending, and virtual work doneof the applied forces. Thc problem is for~llulated using intrinsic coordinate in whichrotation is used as a variable while the arc-length of beam is an independent variable.The shape function of a rotatioils at nodal points are approximated by Lagrange'sinterpolation. The first variation of energy functional yields a non-linear system ofequations. The Newton-Raphson itcrative procedure is used to solve this system ofequations. Thc llumerical results arc compared with those obtained from otherresearch work, they are found to be in good agreement. Numerical examples of thebeam subjected to combincd load are provided in two cases which are (1)coi~centrated end load and uniforn~lyd istributed load, and (2) follower concentratedclld load and followcr uniforlllly distributed load.