Back to Search
Start Over
Stability of a flat form of bending of a hinged beam
- Publication Year :
- 2022
- Publisher :
- СанкÑ-ÐеÑеÑбÑÑгÑкий полиÑÐµÑ Ð½Ð¸ÑеÑкий ÑнивеÑÑиÑÐµÑ ÐеÑÑа Ðеликого, 2022.
-
Abstract
- Тема вÑпÑÑкной квалиÑикаÑионной ÑабоÑÑ: «УÑÑойÑивоÑÑÑ Ð¿Ð»Ð¾Ñкой ÑоÑÐ¼Ñ Ð¸Ð·Ð³Ð¸Ð±Ð° ÑаÑниÑно-опеÑÑой балки».ÐÐ°Ð½Ð½Ð°Ñ ÑабоÑа поÑвÑÑена иÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð³ÐµÐ¾Ð¼ÐµÑÑиÑеÑки нелинейной ÑаÑниÑно-опеÑÑой балки пÑи ÑиÑÑом изгибе. ÐадаÑи, коÑоÑÑе ÑеÑалиÑÑ Ð² Ñ Ð¾Ð´Ðµ иÑÑледованиÑ:РеÑение геомеÑÑиÑеÑки нелинейной пÑÐ¾Ð±Ð»ÐµÐ¼Ñ ÑÑаÑики ÑаÑниÑно-опеÑÑой балки пÑи ÑиÑÑом изгибе;РеÑение задаÑи ÑÑÑойÑивоÑÑи ÑаÑниÑно-опеÑÑой балки пÑи ÑиÑÑом изгибе в ÑоÑной поÑÑановке;РеÑение задаÑи ÑÑÑойÑивоÑÑи ÑаÑниÑно-опеÑÑой балки пÑи ÑиÑÑом изгибе в ÑилÑно-линеаÑизованной поÑÑановке;ÐолÑÑение кÑиÑеÑÐ¸Ñ Ð´Ð»Ñ Ð½Ð°Ñ Ð¾Ð¶Ð´ÐµÐ½Ð¸Ñ ÐºÑиÑиÑеÑкого моменÑа.   Рданной ÑабоÑе Ð´Ð»Ñ ÑеÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°Ñи ÑÑÑойÑивоÑÑи пÑименÑеÑÑÑ Ð¿ÑоÑÑÑанÑÑÐ²ÐµÐ½Ð½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ ÑÑеÑжнÑ, ÑÑиÑÑваÑÑÐ°Ñ Ð²Ñе Ð²Ð¸Ð´Ñ Ð´ÐµÑоÑмаÑии (ÑаÑÑÑжение, Ñдвиг, изгиб и кÑÑÑение) и, ÑооÑвеÑÑÑвенно, ÑаÑÑмаÑÑиваÑÑÑÑ ÑазлиÑнÑе Ð²Ð¸Ð´Ñ Ð¶ÐµÑÑкоÑÑей. Рданной ÑабоÑе бÑла пÑименена ваÑиаÑÐ¸Ð¾Ð½Ð½Ð°Ñ Ð¿Ð¾ÑÑановка задаÑи ÑÑÑойÑивоÑÑи, коÑоÑÐ°Ñ ÑÑоÑмÑлиÑована, как поиÑк ÑоÑки минимÑма ÑÑнкÑионала ÐагÑанжа. ФÑнкÑионал ÑÑÑойÑивоÑÑи Ñавен вÑоÑой ваÑиаÑии ÑÑнкÑионала ÐагÑанжа, а в ÑÐ²Ð¾Ñ Ð¾ÑеÑÐµÐ´Ñ ÑÑавнение ÑÑÑойÑивоÑÑи â ÑÑо ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð­Ð¹Ð»ÐµÑа Ð´Ð»Ñ ÑÑнкÑионала ÑÑÑойÑивоÑÑи.   Рданной ÑабоÑе бÑло полÑÑено ÑеÑение задаÑи ÑÑÑойÑивоÑÑи. РкаÑеÑÑве ÑезÑлÑÑаÑа полÑÑен кÑиÑеÑий Ð½Ð°Ñ Ð¾Ð¶Ð´ÐµÐ½Ð¸Ñ ÐºÑиÑиÑеÑкого моменÑа в виде пÑоÑÑого ÑÑигономеÑÑиÑеÑкого ÑÑавнениÑ. Ðанное ÑÑавнение неÑложно ÑеÑиÑÑ ÑиÑленнÑми меÑодами Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð»Ñбого пÑогÑаммного комплекÑа. ÐолÑÑеннÑе в Ñ Ð¾Ð´Ðµ дипломной ÑабоÑÑ ÑеÑÐµÐ½Ð¸Ñ Ð¼Ð¾Ð³ÑÑ Ð¿ÑименÑÑÑÑÑ Ð¿Ñи пÑоекÑиÑовании новÑÑ ÐºÐ¾Ð½ÑÑÑÑкÑий, а Ñакже пÑи ÑеконÑÑÑÑкÑии ÑооÑÑжений ÑазлиÑного назнаÑениÑ.  Â<br />The subject of the graduate qualification work is âStability of a flat form of bending of a hinged beamâ.The given work is devoted to studying a geometrically nonlinear articulated beam with pure bending. Tasks that were solved in the course of the study:Solution of the geometrically nonlinear problem of the statics of a hinged beam under pure bending;Solution of the problem of stability of a hinged beam under pure bending in the exact formulation;Solution of the problem of stability of a hinged beam under pure bending in a strongly linearized formulation;Obtaining a criterion for finding the critical moment.    The fulfilled work came out with a solution to the stability problem, to solve the problem of stability, a spatial model of the rod is used, which considers all types of deformation (tension, shear, bending, and torsion) and, for a complete understanding, various types of stiffness are considered. In this paper, a variational statement of the stability problem was applied, which is formulated as a search for the minimum point of the Lagrange functional. The stability functional is equal to the Lagrange function's second variation; in turn, the stability equation is the Euler equation for the stability function.   In this paper, a solution to the stability problem was obtained. As a result, a criterion for finding the critical moment is received in the form of a simple trigonometric equation. This equation is easy to solve by numerical methods using any software package, for this case Mathcad has been used. The solutions obtained in the thesis work can be used in the design of new structures, as well as in the reconstruction of structures for various purposes.
- Subjects :
- critical load
поÑеÑÑ Ð¿Ð»Ð¾Ñкой ÑоÑÐ¼Ñ ÑавновеÑиÑ
following moment
loss of flat equilibrium
pure bending
ÑÑÑойÑивоÑÑÑ
stability
geometrically exact theory of rods
балка
геомеÑÑиÑеÑки ÑоÑÐ½Ð°Ñ ÑеоÑÐ¸Ñ ÑÑеÑжней
кÑиÑиÑеÑÐºÐ°Ñ Ð½Ð°Ð³ÑÑзка
beam
ÑиÑÑÑй изгиб
ÑледÑÑий моменÑ
Subjects
Details
- Language :
- Russian
- Database :
- OpenAIRE
- Accession number :
- edsair.doi...........2efae59c3562c2c663b8d48add376fcd
- Full Text :
- https://doi.org/10.18720/spbpu/3/2022/vr/vr22-1904