title: Ð¡Ð¼ÐµÑÐ°Ð½Ð½ÑÐ¹ Ð¼ÐµÑÐ¾Ð´ ÐºÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð² Ð² ÑÑÐ°ÑÐ¸ÐºÐµ Ð¸ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐµ ÑÐ¾Ð½ÐºÐ¾ÑÑÐµÐ½Ð½ÑÑ ÑÑÐµÑÐ¶Ð½ÐµÐ¹
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Mixed finite element method in statics and dynamics of thin-walled beams
Creators: name: ÐÐ²Ð°Ð½Ð¾Ð², Ð¡ÐµÑÐ³ÐµÐ¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2019
Subjects: ÐÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð² Ð¼ÐµÑÐ¾Ð´
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ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð» Ð ÐµÐ¹ÑÑÐ½ÐµÑÐ°
ÑÐµÐ¾ÑÐ¸Ñ Ð¡Ð»Ð¸Ð²ÐºÐµÑÐ°

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description: In the given work finite-element model of thin-walled beam is constructed based on mixed variational approach. Using Reissner functional and polynomial shape functions stiffness and mass matrices of thin-walled beam are derived within Slivker semi-shear theory. Algorithm for automatic composing and solving the governing systems of equations for static and dynamic problems of thin-walled bars is presented. Comparison to the results by classical finite element method and the exact solutions of Euler equations is carried out. The analytical solution to the equations of motion by mixed and classical FEM for eigenfrequency problem of thin-walled bar is derived. The effect of âspuriousâ high-frequency modes in spectrum of thin-walled bar is revealed while using mixed finite element method.